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.
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