1) Assertion: An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b  are not both zero, is called a linear equation in two variables.

Reason:  A linear equation in two variables has infinitely many solutions.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

2) Assertion: The graph of every linear equation in two variables is a straight line.

Reason:  x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

3) Assertion:  the graph of y = a is a straight line parallel to the y-axis.

Reason:The graph of x= a is a straight line parallel to the x-axis.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

4) Assertion: . An equation of the type y = mx represents a line passing through the origin.

Reason: Every point on the graph of a linear equation in two variables is a solution of the quadratic equation.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

5) Assertion: There are infinite number of lines which passes through (3, 2).

Reason: A linear equation in two variables has infinitely many solutions.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

6) Assertion: If x = 2, y = 1 is a solution of the equation 2x + 3y = k, then the value of k is 7.

Reason: The solution of the line will satisfy the equation of the line.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

7) Assertion: If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, then the value of k is 10.

Reason: A linear equation in two variables has infinitely many solutions

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

8) Assertion:  Assertion: x + y = 3 is not  the equation of a line passing through the origin.

Reason: y = 2x is the equation of a line passing through the origin.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

9) Assertion: Assertion: X = 3 and y = 2 is a solution of the linear equation 2x + 3y = 12.

Reason: X = 4 and y = 2 is a solution of the linear equation x + 3y = 10.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

10) The point (3, 0) lies on the graph of the linear equation 4x + 3y = 12.

Reason: (3, 0) satisfies the equation 4x + 3y = 12.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is  the correct explanation for Assertion

11) Assertion: A linear equation in two variables has infinitely many solutions.

 Reason:  A linear equation 3x + 5y = 2 has a unique solution.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: assertion is true but reason is false

12) Assertion : The graph of the linear equation 2x – y = 1 passes through the point (2, 3).

Reason: Every point lying on graph is not a solution of 2x – y = 1.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false.

13) Assertion: Assertion: y = 3x represents a line passing through the origin.

Reason: Any line parallel to the x-axis is y = a.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

14) Assertion: The point (2, 2) is the solution of x + y = 4.

Reason: Every point which satisfy the linear equation is a solution of the equation

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both assertion and reason are true and reason is the correct explanation for assertion.

15) Assertion: The graph of the linear equations 3x+2y=12 and 5x-2y=4 gives a pair of intersecting lines.

Reason: The graph of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 gives a pair of intersecting lines if a1/a2 ≠ b1/b2

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

16) Assertion: If the pair of lines are coincident, then we say that pair of lines is consistent and it has a unique solution.

Reason: If the pair of lines are parallel, then the pairs has solution and is called inconsistent pair of equations.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both Assertion and reason are false

17) Assertion: The linear equations x-2y-3=0 and 3x+4y-20=0 have exactly one solution

Reason: The linear equation 2x+3y-9=0 and 4x+6y-18=0 have a unique solution.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false

18) Assertion: The graph of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 gives a pair of intersecting lines if a1/a2 ≠ b1/b2

Reason: the graphical representation of the equations x+2y=3 and 2x+4y+7=0 gives a pair of coincident lines.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is correct and reason is false.

19) Assertion: The value of k for which the system of equations 3x+ky=0 and 2x-y=0 has a unique solution is k ≠ -3/2

Reason: The graph of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 gives a pair of intersecting lines if a1/a2 ≠ b1/b2

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion

20) Assertion: The number of common solutions for the system of linear equations 5x+4y+6=0 and 10x+8y=12 is zero.

Reason: The graph of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 gives a pair of intersecting lines if a1/a2 ≠ b1/b2

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

21) . Assertion: The value of k for which the system of linear equations 3x-4y=7 and 6x-8y=k have infinite number of solution is 14.

Reason: The graph of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 gives a pair of intersecting lines if a1/a2 ≠ b1/b

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false

22) Assertion:  If the pair of lines are intersecting, then the pair has unique solution and is called consistent pair of equations.

Reason: A pair of linear equations has no solution (s) if it is represented by intersecting lines graphically.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason. Is false

23) Assertion: The value of q=±2, if x=3, y=1 is the solution of the line 2x+y-q2-3=0.

Reason: The solution of the line will satisfy the equation of the line.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are true and reason is the correct explanation for Assertion

24) Assertion: getting a solution is to take x = 0 and get thecorresponding value of y. Similarly, we can put y = 0 and obtain the corresponding value of x.

Reason: 4x+3y=12 Taking x = 0, we get 3y = 12, i.e., y = 4. So, (0, 4) is a solution of the given equation. Similarly, by taking y = 0, we get x = 3. Thus, (3, 0) is also a solution.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a)both  Assertionand reason are correct  and  reason is the correct explanation for Assertion

25) Assertion: the linear equation in two variblec3x-11y=10 has infinitely many solution.

Reason: 3x-11y=10

y=(3x-10)/11 for infinite values of x, y will also have infinite solutions.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion.

26) Assertion: 3x+10 =0 will has only one solution

Reason: 3x+10 = 0,   x = -10/3.

Hence, only one solution is possible.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion

27) Assertion: The solution of equation x-2y = 4 is (0,2)

Reason: The graph of linear equation x+2y = 2, cuts the y-axis at (2,0)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

28) Assertion: Any point on line x = y is of the form (k, k)

Reason: The graph of x = 3 is a line parallel to the y-axis at a distance of 2units from the origin

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false

29) Assertion: in equation y= mx+ c is a slope

Reason: linear equation in two variables is of the form ax + by + c = 0, where a ≠ 0, b ≠ 0

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

30) Assertion: Any point on the x-axis is of the form (x,0)

Reason: Any point on the x-axis is of the form (x, 0). On the x-axis,  x can take any values, whereas y should be equal to 0.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion

31) Assertion:Any point on the y-axis is of the form (0,y)

Reason:  Any point on the y-axis is of the form (0, y). On the y-axis, y can take any values and x should be equal to 0.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

32) Assertion: The linear equation 2x – 5y = 7 has no solution.

Reason: The linear equation 3x – y = x – 1 has unique solution.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

33) Assertion: The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point(0,2)

Reason: The equation 2x + 5y = 7 has a unique solution, if x, y are natural number.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

34) Assertion: The point of the form (a, a) always lies on y=x

Reason: If we multiply or divide both sides of a linear equation with the same non-zero number, then the solution of the linear equation remains the same.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

35) Assertion: the graph  of y=4x is line passing through the origin.

Reason: the pair of equations x=0 and x=5 has two solutions.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertio

36) Assertion: One equation of a pair of dependent linear equations is 2x + 5y = 3. The second equation will be. -10x-25y+15=0

Reason: If a pair of linear equations is consistent, then the lines will be intersecting or coincident

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:  b) both Assertion and reason are correct but reason is not correct explanation for Assertion

37) Assertion: The pair of equations 3x – 5y = 7 and – 6x + 10y = 7 have no solution

Reason: Two equations in two variables taken together are called linear equation

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c)Assertion is true but reason is false

38) Assertion:  the system of equations ax + by = c, lx + my = n, has a unique solution.

Reason: Graphically, the pair of equations 7x – y = 5; 21x – 3y = 10 represents two lines which are parallel.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

39) Assertion: If x = a, y = b is the solution of the equations x + y = 5 and 2x – 3y = 4, then the values of a and b are (19/5,6/5)

Reason: The graph of the equation 2x + 3y = 5 is a straight line

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

40) Assertion: x = 3 and y = -2 is a solution of the equation 4px – 3y = 12, then the value of p is 1/2

Reason: Graph of linear equation ax + by + c = 0, a * 0, 6*0 cuts x-axis and y-axis respectively at the points (x,0) ,(y,0)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: C) Assertion is true but reason is false

41) Assertion: Solution of linear equation 2x + 0.y + 9 = 0 is(-9/2,0)

Reason: Cost of book (x) exceeds twice the cost of pen (y) by Rs 10. This statement can be expressed as linear equation x-2y-10=0

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b)both Assertion and reason are correct but reason is not correct explanation for Assertion

42) Assertion: If x represents the age of father and y represents the present age of the son, then the statement for ‘present age of father is 5 more than 6 times the age of the son’ in terms of mathematical equation is x= 6y+5

Reason:Equation of a line passing through origin is x- y=0

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) assertion is true but reason is false.

43) Assertion: Straight line passing through the points (-1, 1), (0, 0) and (1, -1) has equationx=2y

Reason: If a linear equation has solutions (–3, 3), (0, 0) and (3, –3), then it is of the form y-x=0

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

44) Assertion: The equation y = 5, in two variables, can be written 0.x+1.y=5

Reason: The solution of a linear equation is not affected when the same number is added to or subtracted from both the sides of the equation

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion

45) Assertion: 2x+3y=4.37 is a linear equation in two variable

Reason ax+b is also written as ax+0y +b

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

46) Assertion: 2x+3y=7 is linear equation  and the value of a=2,b=3,c=7

Reason: ax+by+c =0 is the form of linear equation where a,b,c are the real number.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is not correct explanation for Assertion

47) Assertion: 1/x+1/y=1/6 is the not  linear equation in two variable.

Reason: 6x+6y=xy  is not form of the y=mx+c ,hence it is not linear equation.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

48) Assertion: the graph of linear equation in two variables need not be a line .

Reason:  one number is 5  more than seven times the other number it can be represented by x+7y=5

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

49) Assertion: linear equation in one variable has only one variable  with power one

Reason:  4x+6=0 is a linear equation in one variable

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

50) Assertion: if (1/5)-x=-4/5 then xis 1

Reason: p/4+p/3=55-(p+40)/50 then the value of p is 89.834

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion

51) Assertion: If 4a−3=13, then the value of 10a²−5a+6.is 149

Reason: Every horizontal line has an undefined slope.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

52) Assertion: The graph of every linear equation in two variables need not   be a line.

Reason : The x-intercept of 6x-5y=30 is (5, 0)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

53) Assertion: A linear system with fewer equations than unknowns must have infinitely many solutions.

Reason: If the system Ax=b has a no solution, then A must be a square matrix.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false.

54) Assertion: This  system is a linear system:x+y=2 ,2x-3y=0

Reason: Some equations may not even be linear to begin with, but they can be brought to a linear form by multiplying both sides of the equation by a suitable expression.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

55) Assertion: Just as numbers, variables can, also, be transposed from one side of the equation to the other

Reason: 3(t-3)=5(2t+1) is +1

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) both Assertion and reason are false

56) Assertion: The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. Then the breadth of the pool is 25

Reason: Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. then the age of Baichungs grandfather is 22

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false

57) Assertion: 5x−2(2x−7)=2(3x−1)+ 7/2 is -2

Reason: x+3 is an example of two variable expression

​a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

58) Assertion: In equations, we have positive sign which is missing in expressions.

Reason: In an equation the values of the expressions on the LHS and RHS are different

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d)  both assertionis and  reason are false

59) Assertion: If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation remains the same

Reason:

The graph represents the linear equation x = 3.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct abut reason is not correct explanation for Assertion.

60) Assertion: If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation y = 9/5(x-273)+32. If the temperature is 158° F, then the temperature in Kelvin is 343°k

Reason: The Autorikshaw fare in a city is charged Rs 10 for the first kilometer and Rs 4 per kilometer for subsequent distance covered. Then  the linear equation to express the above statement is Y=4x+6

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both are correct but reason is not correct explanation for Assertion.

1) Assertion: The horizontal line is called x-axis

Reason :The vertical line is called x-axis

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:b) both Assertion and reason are correct but reason is not correct explanation for assertion.

2) Assertion: Point A(-7, -9) lies on III quadrant

Reason: A point both of whose coordinates are negative lies in III quadrant

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

3) Assertion: : A point whose abscissa is 2 and ordinate is -3 lies in fourth quadrant

Reason: Points of the type (-; +) lie in the second quadrant

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

4) Assertion: The perpendicular distance of a point from y-axis is called its x-coordinate.

Reason: The x co-ordinate of the point on y-axis is zero.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion.

5) Assertion: Point (4, -2) lies in IV quadrant.

Reason:Point (-1,2) lies in Il-quadrant and (2,- 1) lies in IV quadrant

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

6) Assertion: The points (-7, 2) and (2,- 7) are at different positions in the coordinate plane.

Reason:The perpendicular distance of the point A(5, 6) from the y-axis is 6

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:c) Assertion is true but reason is false.

7) Assertion: The abscissa of a point (4, 8) is 4.

Reason:The point (0,4) lies on y-axis.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:b) both Assertion and reason are correct but reason is not correct explanation for Assertion

8) Assertion : A point both of whose coordinates are negative will lie in third quadrants

Reason: If the ordinate of a point is equal to its abscissa, then the point lies either in the first quadrant or in the second quadrant.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) b assertion is true but reason is false.

9) Assertion:  the section formed by horizontal and vertical  lines determining the poisition of a point in a Cartesian plane is called quadrant.

Reason: the point of intersection of horizontal and vertical  line determining the position of point in a Cartesian plane is called origin.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion

10) Assertion: Abscissa of a point is positive in I andIV quadrant

Reason: If (x + 2, 4) = (5, y – 2), then coordinates (x, y) are(3,6)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:b) both assertion and reason are Corry and reason but reason is not correct explanation for assertion.

11) Assertion: mirror image of the point on the (9,-8) in x-axis is (-9,-8)

Reason: The coordinates of the point which lies on y-axis at a distance of 4 units in negative direction of y-axis is (6,5)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false.

12) Assertion: The point M lies in the IV quadrant. The coordinates of point M are(a,-b)

Reason: The number of parts the coordinates axes divide the plane is four quadrant

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

13) Assertion: abscissa of all points on y-axis is 0

Reason: ordinate of all points on y-axis is any number.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

14) Assertion: If the perpendicular distance of a point P from the x-axis is 7 units and the foot of the perpendicular lies on the negative direction of x-axis, then the point P has y coordinate is 7 or -7 only

Reason: The coordinates of any point on the y-axis are of the form (0, k), where |k| is the distance of the point from the x-axis

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true bu the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

15) Assertion:The point P on x -axis equidistant from the points A( -1,0)and B(5,0)is (2,0)

Reason: distance of the point P(3,4) from x-axis is 6 units

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:c) both Assertion is true but reason is false

16) Assertion: If the points (a,0),(0 ,b )and (1, 1) are collinear, then 1/a+1/b=1

Reason : condition of collinierity x₁y₂+x₂y₃+x₃y₁=x₂y₁+x₃y₂+x₁y₃

ab+0+0=0+b+a

                                                  1/a+1/b=1

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both asst and reason are true and reason is the correct explanation for Assertion.

17) Assertion: the coordinate of origin are (0,0)

Reason : the distance from the y-axis is called y co-ordinate

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c)assertion is correct but reason is false.

18) Assertion:  if x ≠ y,then the position of (x, y) in the Cartesian plane is different from the position of (y, x).

Reason:  a point is in the 1st quadrant, then the point will be in the form (+, +)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

19) Assertion: x-co-ordinate is also called as abscissa

Reason : y-cordinate is also called as ordinate.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

20) Assertion: the coordinates describe  the points in the plane uniquely.

Reason: in second quadrant (x,y) is (+,+)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false

21) Assertion: the equation of line parallel to y-axis is x=k

Reason: the coordinate pair (x,y) is called as ordered pair

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

22) Assertion: (x,y) shows three dimensional co-ordinate system

Reason: ordinate of all points in the x-axis is -1

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

23) Assertion: the points(-1,-5) lies in III quadrant.

Reason: In III quadrant (x,y) is (-,-).

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion.

24) Assertion:  The point (+4,+5) is lies in 2nd quadrant.

Reason: The point (0,-5) lies in x-axis.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

25) Assertion: The distance of the point P(2,3) from the x-axis is 3.

Reason: the distance from the x-axis is equal to its ordinate .

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

26) Assertion:The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is 53

Reason:  Area of ΔABC = 12 [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

27) Assertion: The distance of the point (α, β) from the origin is√(α²+β²)

Reason:The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is 11

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

28) Assertion: The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio 3:4

Reason: If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is -6

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false.

29) Assertion: The points (1,1), (-2, 7) and (3, -3) are collinear.

Reason: The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12) and (8, 0) is (16/3, 6)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

30) Assertion: The area of the triangle formed by the points A(-1.5, 3), B(6, -2) and C(-3, 4) is 0

Reason: Area of ΔABC = 12 [-1.5(-2 – 4) + 6(4 – 3) + (-3) (3 + 2)] = 12 [9 + 6 – 15] = 0. It is a straight line.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.

31) Assertion: If the points P(1, 2), B(0, 0) and C(a, b) are collinear, then2a=b

Reason:  If the distance between the points (x, -1) and (3, 2) is 5, then the value of x ib 7

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

32) Assertion: . The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a Rectangle.

Reason: AB = CD and BC = AD hence given points A,B,C and D are the vertices of a rectangle.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

33) Assertion: The distance between the points A (0, 6) and B (0, –2) is 8

Reason: . AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is√32

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false.

34) Assertion: The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the IV quadrant.

Reason: The ratio in which the point P (3/4, 5/12)divides the line segment joining the Points A (1/2, 3/2) and B (2, –5) is 1:5

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:b) both Assertion and reason are correct but reason is not correct explanation for Assertion

35) Assertion: The ratio in which the point P (3/4, 5/12)divides the line segment joining the Points A (1/2, 3/2) and B (2, –5) is scalene triangle

Reason: all 3 sides have different lengths, so it is a scalene triangle.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion

36) Assertion: the coordinate of the point ( 5/2, 0) where the line2x-3y-5 =0 cut the x-axis.

Reason:  line 2x-3y-5=0 will cut the x-axis at x=0,also it satisfy the equation of line 2x–5=0

x=5/2 hence, (5/2,0)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.

37) Assertion: If the vertices of triangle ABC are A(5,-1),B(-3,-2) C(-1,8) the length of median A through will be √65

Reason: A line intersects the y-axis and x-axis at the points P and Q . If (2, -5) is the mid-point of PQ, then the coordinates of P and Q will be1/3

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ansb) both Assertion and reason are correct but reason is not correct explanation for Assertion.

39) Assertion:  If the distance of P(x,y)  from A(6, 2) and B(-2 ,6)are equal, then y=3x

Reason:  (5/3,3) are the co-ordinates of the points of trisection of the line segment joining the points A(1,-2) and B(-3,4)

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans : d) both Assertion and reason are false.

40) Assertion: The ordinate of a point A on y-axis is 5 and B has coordinates (–3, 1). Then the length of AB is 5 units.

Reason: the points o(0,0) lies in quadrant I

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: Assertion is true but reason is false

41) Assertion: the mirror image of the pointA(4,5) in the y-axis is A'(-4,5)

Reason:the point (0,-6) lies in III quadrant

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:c) Assertion is true but reason is false.

42) Assertion: the points (-6,-7) lies in III qudrant

Reason: the signs of point inthe I,II, III,IV quadrants are (+,+),(-,+),(-,-),(+,-).

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion

43) Assertion: ordinate 3 and absicca 6 the this point lie in I quadrant

Reason: absicca 7 and ordinate -4 the the point lie in IV quadrant

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion.

44) Assertion: the perpendicular distance  of the point (5,6) from x-axis is 6

Reason:the perpendicular distance of the point(2,3) from y-axis is 2

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) Assertion and reason are correct but reason is not correct explanation for Assertion

45) assertion:

Reason:

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

46) Assertion: A Cartesian plane consists of two mutually perpendicular lines intersecting at their zeros. 

Reason: The Cartesian plane consists of two perpendicular and directed lines whose intersection point is the zero point for both the lines.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is the correct explanation for assertion

47) Assertion: the point (x,y) lies in the I quadrant where x<0,y<0

Reason: In  11:10 ratio is the line segment joining (−2,4) and (−3,2) divided by the line x−y=5

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

48) Assertion: the point(x,0) ,x<0 lies on ox’

Reason: (0,14),(0,-28/3) are the points on the y−axis whose distance from the line  3x + 4y =1 is 8 unit

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion

49) Assertion:  (0,0) the co-ordinates of the point which divides the line segment joining P(-3,-4) and Q(6,8) in the ratio 1:2.

Reason:the distance between points M (4,5) and N (-3,8)is √58

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:b) both Assertion and reason are correct but reason is not correct explanation for Assertion

50) Assertion: Reflection of a point P(x,y) across the X−axis is Q(x,−y), which is found by changing the sign of the y-coordinate of P(x,y).

Reason:Reflection of a point P(x, y) across the Y-axis is Q(-x,y), which is found by changing the sign of the x-coordinate of P(x,y).

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

51) Assertion: 3x+4y=7 is the equation of a line parallel to 3x+4y = 5 and passing through points (1,1).

Reason::Mid-point divides the given line in the ratio of 1:1.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans:b) both Assertion and reason are correct but reason is not correct explanation for Assertion

52) Assertion: (-7,0) the point on the x-axis which is equidistant from (2, – 5) and (- 2, 9).

Reason: 5 or -6 are the values of y for which the distance between the points P (2, – 3) and Q (10, y) is 10 units.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: c) Assertion is true but reason is false

53) Assertion: -6 is the slope of the line perpendicular to the line passing through the points (-5, 1) and (-2, 0)

Reason: x+3y=-18  is the equation of a line having slope -1/3 and y-intercept equal to 6

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false.

54) Assertion: 1 is the slope of the line passing through the points J (-2, 3) and (2, 7)

Reason: [(y₂-y₁)/(x₂-x₁)]

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: a) both Assertion and reason are correct and reason is  the correct explanation of assertion

55) Assertion: (3,4) is the coordinates of the circum-centre of the triangle whose vertices are (0, 0), (8,0) and (0,6).

Reason: The distance of the point P(-6, 8) from the origin is 10

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

56) Assertion: The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is 11

Reason: The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is 6

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason is false .

57) Assertion: the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then AP= 1/4

Reason: The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is 7

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

58) Assertion: 10x+29=4y is the relation between x and y such that the point P(x, y) is equidistant from the points A (2, 5) and B (-3, 7)

Reason: 1:7 is the ratio in which the point P(3/4,5/12) divides the line segment joining the points A(1/2,3/2) and B(2, -5).

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d) both Assertion and reason are false

59) Assertion: If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b), then bx = ay.

Reason: If the points A(x, y), B(3, 6) and C(-3, 4) are collinear, then x – 3y + 15 = 0.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b)both are Assertion and reason are correct but reason is not correct explanation for Assertion.

1) Assertion: The constant  polynomial 0 is called zero polynomial.

Reason:√x+3 is a polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true the reason is false.

2) Assertion: degree of non zero constant polynomial is zero

Reason: polynomial having two terms are called binomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion.

3) Assertion: y²-5 is a quadratic polynomial.

Reason: degree of polynomial 2 is called quadratic polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is the correct explanation for Assertion.

4) Assertion: 2x-1 is the linear polynomial.

Reason: A polynomial of degree 1 is called linear polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for Assertion.

5) Assertion:  the degree of zero polynomial is not defined.

Reason : Each term of polynomial has coefficient.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason is correct but reason is not correct explanation for Assertion.

6) Assertion:  5t-√7  it’s degree is 1

Reason: the highest power of the varible is 1 so the degree of polynomial is 1.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is the correct explanation for Assertion.

7) Assertion:  a polynomial can have more than one zero.

Reason: every real number is zero of zero polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion.

8) Assertion : 2a²+5 value of polynomial at a= 2 is 136

Reason:  p(x) x+2  is not a zero polynomial at x=-2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are false.

9) Assertion: 3x²+ x-1 = (x+1)(3x-2)+1

Reason : dividend = divisor *quotient + remainder.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

10) Assertion : x³+x  has only one real zero.

Reason: A quadratic polynomial  can have at most two zero.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are true but reason is not correct explanation for Assertion.

11) Assertion: Assertion : If one zero of poly-nominal p(x) = (k² + 4)x² + 13x + 4k is reciprocal of other, then k = 2.

Reason : If (x – a) is a factor of p(x), then p(a) = 0 i.e. a is a zero of p(x)

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:  b) both assertion and reason are correct but reason is not correct explanation for Assertion.

12) Assertion: a quadratic polynomial can have at most two zero.

Reason: x²+7x +9 has two zero.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:c) Assertion is true but the reason is false.

13) Assertion : If the product of the zeroes of the quadratic polynomial x² + 3x + 5k

is -10 then value of k is -2.

Reason : Sum of zeroes of a quadratic polynomial ax² + bx + c is –b/a

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion  and reason are true but reason is not correct explanation for Assertion .

14) Assertion: The polynomial 3x⁴-4x^-3/2+x² is not a polynomial

Reason: because the power in the term 4x^3/2which is not a whole number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is the correct explanation for Assertion.

15) Assertion: a polynomial of degree 3 is called cubic polynomial.

Reason: 3z³-2z²+7z+9 is a cubic polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is the correct explanation for Assertion.

16) Assertion: A quadratic polynomial can have at the most two zeroes.

Reason: Sum of zeroes of a quadratic polynomial ax²+bx+c is -b/a

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:b) both assertion and reason are correct but reason is not correct explanation for Assertion.

17) Assertion: The highest power of x in the polynomial P(x) is the degree of the polynomial.

Reason: 7x⁹-5x³+4x⁵+3The degree of polynomial is 3.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true but reason is false.

18) Assertion:  If one zero of polynomial p(x) = (k²+4)x²+13x+4k is reciprocal of the other, then k=2.

Reason: Irrational zeros  always occurs in pairs.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion .

19) Assertion: x³+x has only one real zero.

Reason: A polynomial of nth degree must have n real zeroes

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) assertion true but reason is false.

20) Assertion: If one zero of polynomial p(x) = (k2+4)x2+13x+4k is reciprocal of the other, then k=2.

Reason: If (x-a) is a factor of p(x), then p(a) = 0 i.e., a is a zero of p(x).

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b ) both assertion and reason are correct but reason is not correct explanation for Assertion.

21) Assertion: Zeroes of polynomial  p(x)=x²-3x+2 is 1

Reason:7x is the zero polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true but reason is false

22) Assertion: In a homogeneous expression, all the terms will have same degree.

Reason :The degree of the equation, given  (x+2)(x-1)=(x+1)(x+3), is 1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and reason  are correct but reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion.

23) Assertion: p(x) = x⁵   degree=5

Reason: 4√t+t⁶degree is 6

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:c) assertion is true but reason is false.

24) Assertion: degree of p(x)= -2/7 is 0

Reason: degree of p(x)= x³y²z⁵ is 10

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion.

25) Assertion: The degree of the sum of two polynomials each of degree 5 is always 5.

Reason: 3x-2 is a quadratic polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d)both Assertion and reason are false.

26) Assertion: a linear polynomial has one and only one zero always.

Reason: zero of polynomial  x²-4x+3 are 1,3

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:b) both assertion and reason are true but reason is not correct explanation for Assertion.

27) Assertion: The polynomials in which the highest power of the variable in any term is one are known as linear polynomials.

Reason: if (2x²-3x+1)(2x²+5x+1) =9x² then equation has four equal roots.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both assertion and reason are true but reason is not correct explanation for Assertion.

28) Assertion: a real number α is said to be a zero of the polynomial p(x) if  p(α)=0

Reason: The zero polynomial is the additive identity of the additive group of polynomials.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion.

29) Assertion: A polynomial whose coefficients are all equal to 0 is called zero polynomial.

Reason: a degree of p(x)=7xyz is 3

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:b) both assertion and reason are correct but reason is correct but reason is not correct explanation for Assertion.

30) Assertion: 2x²-5x+9 is a quadratic polynomial.

Reason: 5x+8 is  not a linear polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true but reason is false.

31) Assertion: if a,b,c be the zero of polynomial f(x)=ax³+bx²+cx+d then sum of zeros =

 -cofficent of x²/-cofficent ofx³

Reason:(2-√3) is one zero of quadratic polynomial then other zero will be (2+√3)

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion.

32) Assertion: Polynomial is the algebraic equation in the form of single variable.

Reason : polynomial which has three term are called trinomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason is true but reason is not correct explanation for Assertion.

33) Assertion:x²+7y is not polynomial.

Reason: the sum of several terms that contain different powers of the same variablesis known as polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion vand reason are correct and reason is the correct explanation for Assertion.

34) Assertion: p(x)=1,p(x)=5 are the zero of zero  ploynomial

Reason : all real number is the zero of zero polynomial.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct but reason is the correct explanation for Assertion.

35) Assertion: If (x-1) is the factor of 4x³+3x²-4x+k then k=-3

Reason: (x+y)² =x²+y²+2xy

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason correct but reason is not correct explanation for assertion.

36) Assertion: (3x+4y)³ =27x³+64y³+36xy(3x+4y)

Reason: (x+y)³= x³+y³+3xy(x+y)

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is the correct explanation for Assertion.

37) Assertion: degree of cubic polynomial is 3

Reason: degree of quadratic polynomial is 2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for Assertion.

38) Assertion: (x+1)is the linear factor of 3x²+8x+5

Reason: 3x²+8x+5 = (3x+5)(x+1)

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is correct explanation for Assertion.

39) Assertion: the value of 10²-9²=19

Reason: 10²-9²=100-81=19

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is the correct explanation for Assertion.

40) Assertion: if (x+2) is a factor of x³ -2ax²+16  the value of a is 7

Reason: if one of the factor of x²+x-20 is (x+5)and other is ( x+4)

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both assertion and reason are false.

41) Assertion: . If one of the zeroes of the cubic polynomial x3 + px² + qx + r is -1, then the product of the other two zeroes is p-q-1.

Reason: If one zero of the quadratic polynomial x² + 3x + b is 2, then the value of b is 9.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:d) both Assertion and reason are false

42) Assertion: The maximum number of zeroes that a polynomial of degree 4 can have is 4.

Reason: The graph of the polynomial p(x) = 5x – 7 is a straight line which intersects the x-axis at exactly one point  is (7/5, 0)

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both Assertion and reason are correct but reason isnotcorrect explanation for Assertion.

43) Assertion: The graph of the polynomial ax² + bx + c is a downward parabola if a=0

Reason: if a polynomial of degree 4 is divided by quadratic polynomial, the degree of the remainder is ≤ 1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b)both assertion and reason are correct but reason is not correct explanation for assertion.

44) Assertion: x³+0x²+0x-64 by x-4 quotient is x²+4x+16

Reason: dividend = divisor *quotient+ remainder

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans : a) both assertion and reason is the correct explanation for assertion

45) Assertion: if α, β are the zeroes of the polynomial x² – 16, then αβ(α + β) is 0

Reason: x² – 16=0

X²=16 ,x=+4,-4

4(-4)(4-4)=-16(0)=0

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

And: a) both  assertion and reason are correct but reason is not correct explanation for assertion.

46) Assertion: the graph of qudratic  polynomial is parabola

Reason : if x+y=3 , x²+y^2.=5 then xy is 2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

47) Assertion: If one of the zeroes of a quadratic polynomial of the form x² + ax + b is the negative of the other, then it has no linear term and the constant term is positive.

Reason:. The zeroes of the quadratic polynomial x2 + 99x + 127 are both positive.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

And. d) both assertion and reason are false.

48) Assertion:. The zeroes of the quadratic polynomial x² + 99x + 127 are more than 4.

Reason : The number of polynomials having zeroes as -2 and 5 is 1

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

And: c) assertion is true but reason is false.

49) Assertion:  if the graph of polynomial intersect the x-axis  at exactly two point then it can be cubic or qudratic polynomial.

Reason:  if y⁹⁷+97 is divided by (y+1) the remainder is 96

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:b) both assertion and reason are correct but reason is not correct explanation for Assertion

50) Assertion: The LCM of (x²+x -6) and 4(4-x )² is 4(x+3)(x+2)(x-2)

Reason: x¹⁰⁰+2x⁹⁹+k is divisible by (x+1) then the value of k is 2

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true but reason is false.

51) Assertion: the factor of x⁴+4 are (x²+2x+2)(x²-2x+2)

Reason : the sum of zeroes of ax²+bx+c is -b/a

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion

52) Assertion:  the product of (4+2x)(4-2x) is 4²-(2x)²

Reason: (a+b)(a-b) = a²-b²

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is the correct explanation for assertion

53) Assertion: the difference between the polynomial is7x-3x²+7 at x=1andx=2 is -2

Reason: if one of the zero of p(x) = 5×2+13x-m is the reciprocal of the other then the value of m is 2

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:c) Assertion is true but reason is false.

 54) Assertion:  a cubic polynomial x=f(y) cut Y axis at most 3points

Reason: graph of ax2+bx+c intersect x-axis at two distinct point if b²-4ac>=0

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

55) Assertion: if p(x)= 7x+7= 56 at x=7

Reason: The zeroes of a polynomial f (x) are the coordinates of the points where the graph of y f (x) intersects x-axis

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion .

56) Assertion: the value of polynomial x⁸-x⁵+x²-x+1 is positive for all real numbers

Reason : f(x) is positive f(x)>0 ,f(x) is positive for all real value x

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans : a) both Assertion and reason are correct and reason is the correct explanation for Assertion.

57) Assertion: if a³-3a²b +3ab² is divided by a-b then the remainder is 0

Reason : a linear polynomial is always represented by straigth line.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not the correct explanation for Assertion.

58) Assertion: if a,b,c are the zeroes of x³-2x²+qx-r and a+b =0then 2q=r

Reason: if a, b, c are the zeroes of tx³+ux²+vx+w then

a+b+c=-u/t, ab+bc+ca=v/a, abc= -w/a

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

a) both Assertion and reason are correct and reason is the correct explanation for Assertion.

59) Assertion:every polynomial equation has at least one real root

Reason: graph of quadratic polynomial is an ellipse.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d)  both Assertion and reason are false.

60) Assertion: remainder is not equal to zero when the divisor is not the factor of dividend.

Reason : identity equation is valid for all the value of its variable .

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and  reason are correct but reason is not correct explanation for assertion.

61) Assertion: degree of the remainder is always smaller or less than the divisor.

Reason: if x= 0.6 then x+9x= 6

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

62) Assertion: (x+y+z)²= x²+ y² +z²

Reason : 25+36+64= (5+6+8)²

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: d)both Assertion and reason are false.

63) Assertion: (100+4)³=1124864

Reason: (x+y)³=x³+y³+3x²y+3xy²

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

^{Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion.}

64) Assertion: 4x²+7x+8 cofficent of the polynomial are 4,7,8

Reason : 8 is the constant term in above polynomial.

a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false

Ans: b) both are correct but reason is not correct explanation for Assertion.

1) Assertion: 15 is the composite number.

Reason: 15 is odd number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:  b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

2) Assertion: every integer is a rational number

Reason: every integer is expressed in the form of m/1 so it is rational number

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

3)  Assertion: √5 is an irrational number.

Reason: A number is called irrational, if it cannot be written in the form p/q, where p and q are integers and q≠0

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

4) Assertion: 0.468 is a terminating decimal.

Reason: A decimal in which a digit or a set of digits is repeated periodically, is called a repeating, or a recurring decimal.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans: b) Both Assertion and Reason are correct and Reason is not correct explanation for Assertion.

5) Assertion: -25 is  not a rational number.

Reason : -25 can not be written in in the form of p/q.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans:d.) if both assertion and reason are false.

6) Assertion :every  whole number is  not a natural number.

Reason: zero is whole number but not natural number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

7)  Assertion: Every rational number is an integer.

Reason: 3/5 is not an integer.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) Both Assertion and reason are correct and reason is the correct explanation for Assertion.

8) Assertion: √2 is a irrational number.

Reason: it can not be written inthe  form of p/q.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:a)  both Assertion and reason are correct and reason is the correct explanation for Assertion.

9)  Assertion: 3/5 is terminating decimal expansion

Reason: the remainder become zero.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans:a) both Assertion and reason are correct and reason is the correct explanation for Assertion.

10) Assertion: 7 is rational number

Reason: square root of all rational number is irrational.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true but reason is false.

11) Assertion: Decimal expansion of every rational number is only terminating.

 Reason : Decimal expansion of every irrational number is terminating  recurring

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both Assertion and reason are false.

12) Assertion: 1/7 and 2/7 in between only five irrational number are present.

Reason: Every rational number between limited irrational number are present.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both Assertion and reason are false.

13) Assertion :7√5, √2+21 are the irrational number.

Reason: every integer is an rational number

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both Assertion and reason are correct and reason is not correct explanation for Assertion.

14) assertion: 31 is rational number.

Reason: square root of all rational number is always rational

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans: c) Assertion is true reason is false.

15) Assertion: 6√2+7√2 is a rational number.

Reason: the sum of every rational and irrational number is irrational

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a)both  Assertion and reason are true and reason is the correct explanation of Assertion.

16) Assertion :the rationalizing factor of  2+√5 is 2-√5

Reason: the product or quotient of non zero rational number with  irrational number is rational.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans:c) Assertion is true but the reason is false.

17) Assertion :8√15÷2√3=4√5

Reason : quotient of non zero rational number with an irrational number is irrational.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans: a)both assertion and reason are correct and reason is correct explanation for assertion.

18) Assertion: every rational number is written in the form if p/q where p and q are integers, q=0

reason : 7√3 is a rational number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.)  both assertion and reason are false.

Ans: d) both Assertion and reason are false.

19) 10/3 is non terminating Decimal expansion .

 Reason: the remainder of non terminating Decimal expansion is never be zero.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:a) both Assertion and reason are correct and reason is the correct explanation for Assertion

20)  Assertion: 1/2=3/6=4/8are the equivalent rational numbers.

Reason: Every rational number is an integer.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true but the reason is false.

21) Assertion: the real number is either rational or irrational.

Reason :√7 is a rational number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c)  Assertion is true but the reason is false.

22) Assertion : Sum of two irrational numbers 2 + √3 is an irrational number.

Reason : Sum of a rational number and an irrational numbers is always an irrational number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a)both  assertion and reason is correct and reason is the correct explanation for assertion.

23) Assertion: sum of two irrational numbers 5+√3 and 7+√3 is a irrational number.

Reason: if the product of two irraational numbers is rational the each one is  called the rationalizing factor of other.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

And: b) both Assertion and reason are correct but reason is not the correct explanation for assertion.

24) Assertion :19⁹÷19⁸=19

Reason: if a>0  be a real number and  p and q be rational number then a^p÷a^q=a^p-q

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: a) both Assertion and reason are correct and reason is the correct explanation for assertion.}

^{25) Assertion : all the rational and irrational number makes up the collection of real number.}

^{Reason:if r is rational and s is irrational then r+s and r-s are irraational number.}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: both Assertion and reason are correct but reason is the correct explanation for reason}

^{26) Assertion: 1,2,3,4 are the natural numbers.}

^{Reason:  1/4 ,2/7  9/5 are the rational numbers.}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: d) both assertion and reason are false.}

^{27) Assertion: Natural numbers are a subset of integers.}

^{Reason: Natural numbers without zero are called positive integers, and when written with a negative sign are called as negative integers.}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: both Assertion and reason are correct and reason is the correct explanation for reason .}

^{28) Assertion :Sum of two natural numbers is a natural number.}

^{Reason : All whole numbers are natural numbers.}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: c) Assertion is true but the reason is false.}

^{29) Assertion: 2,3,5,7 are the prime numbers.}

^{Reason: A number, other than 1, which is not a prime number is called a composite number}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: both Assertion and reason are correct  but reason is not correct explanation for Assertion.}

^{30) Assertion: (2,3), (3,4), (5,7) are the coprime numbers pair}

^{Reason : Two numbers are co-prime of their HCF is 1.}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: a) both Assertion and reason correct and reason is the correct explanation for Assertion.}

^{31) Assertion: 3√2 is a irrational number.}

^{Reason:  If m is a positive integer which is not a perfect cube, then  3√m is irrational}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion.}

^{32) Assertion: The difference of rational and irrational number is irrational.}

^{Reason: Product of rational and irrational is irrational.}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.}

^{32) Assertion: 1/6 is the reciprocal of 6}

^{Reason: Improper fraction is the fraction in which numerator is less than denominator.}

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

^{Ans: b) both Assertion and reason are correct but reason is not correct explanation for}

^{33) Assertion: All whole numbers are rational number except 0}

Reason:a^ma ⁿ=a^m+n

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both assertion and reason are correct but reason is not correct explanation for assertion.

34) assertion: 4is the first smallest composite number.

Reason:1 is a prime number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c)Assertion is true but reason is false.

35) Assertion:3√7+4√7=7√7

Reason:(3+4)√7= 7√7

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

And: a) both assertion and reason are true but reason is correct explanation for reason.

36) Assertion:0/9 is rational number.

Reason: 0/9 is a rational number that is equal to 0.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason is correct and reason is the correct explanation for assertion.

37) Assertion:the rational number equivalent to 7/9 is 49/63

Reason: (16)^4.   =2 ⁶

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:c) assertion is true but the reason is false.

38) assertion:  x^4. =X⁵/x ¹

Reason: a^b/a^c= a^b-c

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both assertion and reason are correct and reason is the correct explanation for assertion.

39) Assertion:3*8*9+6 is a composite number.

Reason:  A composite number has factors one,any natural  number and itself.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is the correct and reason is the correct explanation for Assertion

40) Assertion: the square root of any primenumber is irrational .

Reason: the rationlizong factor of 2+√7 is 5+ √ 3

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true but reason is false.

41) Assertion: the conjugate of 4+√6 is 4-√6

Reason: √27 is not a rational number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both Assertion and reason is correct but reason is correct explanation for Assertion

42) Assertion: The terminating decimal has a number of finite terms after the decimal point.

Reason : the decimal expansion of π is terminating.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:c) Assertion is true but the reason is false.

43) Assertion: The product of two consecutive positive integers is divisible by 2

Reason:the decimal expansion of 15/169999= 0.0065789

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:c) Assertion is true but reason is false.

44) Assertion: 5⁰=1

Reason: a⁰=1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c)both  Assertion and reason is true and reason is the correct explanation for Assertion.

45) Assertion: 7¹=7

Reason: a¹=a

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is correct and reason is the correct explanation for Assertion.

46) Assertion: (5⁷)³=5²¹

Reason: 9 is a irrational number

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is correct but reason is false.

47) Assertion: √n is rational if n is not a perfect square.

Reason : 1/aⁿ=a⁺ⁿ

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: d) both Assertion and reason are false.

48)Assertion : the sum of first five prime number is 28

Reason: the sum of three consugative integer is 54

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

49) Assertion : the rationalize factor of 6+√7 is 6-√7.

Reason: 7,8,10,are the negative integers.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is correct and reason is false.

50) Assertion: 1 is the multiplicative identity of set of natural number.

Reason: √ab = √a√b

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Reason : b) both Assertion and reason are true but reason is not correct explanation for reason.

51) Assertion: 7/8+9/8=16/8

Reason: p/q+r/q= p+r/q

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion.

52) Assertion: 3/5-2/12=13/30

Reason: p /q-r/s=ps-qr/qs

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is the correct explanation for Assertion.

53) Assertion:  (18,25) is a pair of coprime numbers.

Reason:  pair of coprime number has common factor2.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: c) Assertion is true but reason is false.

54) Assertion: Every point on the number line corresponds to a real number which may be either rational or irrational.

Reason: the Decimal representaion of the rational number 8/27 is 0.296.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is correct but reason is not correct explanation for Assertion.

55) Assertion: If two irrational number whose quotient is a rational number.

Reason: If two irrational number whose product is irrational number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is not the correct explanation for Assertion.

56) Assertion : the Decimal fraction of12/125 is 0.096

Reason: the Decimal fraction of 1/9 is o.111.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both Assertion and reason is not correct explanation for Assertion.

57) Assertion: √(7*8)= √7*√8

Reason: √ab= √a*√b

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is the correct explanation for Assertion.

58 ) Assertion:( 2+√2)²=6+4√2

Reason: (a+b)²=a²+b²+2ab

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason are correct and reason is the correct explanation for Assertion.

59) Assertion: {-1,-5,-6}  are the rational number.

Reason: All negative integers are rational number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is the correct explanation for Assertion.

60) Assertion: coprime number are the number which are the having GCF as1.

Reason: any two prime numbers does not form the pairs of coprime numbers.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:c) Assertion is correct but reason is false.

61) Assertion: In 56.49 the whole part is 56.00

Reason: in the number 3456 the place value of 4 is 400

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both Assertion and reason is not correct explanation for Assertion.

62) Assertion: The smallest perfect number is 6, which is the sum of 1, 2, and 3.

Reason: The numbers which are the positive integers and which can be expressed as the sum of their proper divisors are called as perfect number.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is the correct and reason is the correct explanation for Assertion.

63) Assertion: HCF of (23,53) is 1.

Reason : If p anand are primes,then HCF (p,q)=1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a) both Assertion and reason is the correct and reason is the explanation for Assertion.

64) Assertion : if p and  q are prime ,then HCF (p,q)=1

Reason: 123/6250 is a terminating Decimal.

Ans: b) both Assertion and reason is not  correct explanation for Assertion.

65)If a and b are two positive integers then HCF*LCM= a*b

Reason : A number N Is divided by 15 gives the remainder 2 then  the remainder  is same  when is divided by 5

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion.

66) Assertion: 32^2/5=4

Reason 🙁 32)^2/5=(2⁵)^2/5

             =2²=4

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.)  assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans:a) both Assertion and reason are correct and reason is the correct explanation for Assertion.