Chapter 3 Pair of Linear Equations in Two Variables Assertation & Reasoning Questions Class 10th

Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true

1). Assertion:The pairs of equations x+2y-5 = 0 and -4x-8y+20=0 have infinitely many solution.

Reason: if a1/a2 = b1/b2 = c1/c2 then  the pair of equations has infinitely many solutions.

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

2) Assertion: If a pair of linear equations is consistent, then the lines are intersecting or coincident

Reason: Because the two lines definitely have a solution.

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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: The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have no solution.

Reason: a1/a2 = b1/b2 ≠ c1/c2 So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

4) Assertion: If the lines 3x+2ky – 2 = 0 and 2x+5y+1 = 0 are parallel, then  the value of k is 15/4

Reason: The condition for parallel lines is a1/a2 = b1/b2 ≠ c1/c2

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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: If one equation of a pair of dependent linear equations is -3x+5y-2=0. The second equation will be -6x+10y-4=0

Reason: The condition for dependent linear equations is a1/a2 = b1/b2 = c1/c2

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

6) Assertion: The angles of cyclic quadrilaterals ABCD are: A = (6x+10), B=(5x)°, C = (x+y)° and D=(3y-10)°. The value of x and y is 20° and 30°

Reason: in cyclic quadrilaterals, the sum of the opposite angles are 180°.

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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: The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has infinitely many solution.

Reason: a1/a2 = b1/b2 ≠ c1/c2 it satisfy the condition of infinitely many solution .

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but reason is false

d) both assertion and reason are false

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

8)Assertion: The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have unique solution

Reason: an equations a1/a2= b1 /b2 = c1/c2 Hence, the given pair of equations have no solution

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but reason is false

d) both assertion and reason are false

Ans: d) both Assertion and reason are false

9) Assertion: The graphical representation of a pair of equations 4x + 3y – 1 = 5 and 12x + 9y = 15 will be parallel lines.

Reason: if the the given pair of equations has no solution.That means, the lines representing the given pair of equations are parallel to each other.

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

10)Assertion: a1x+b1y+c1=0; a2x+b2y+c2=0 represent parallel line if  a1/a2 = b1/b2 ≠ c1/c2

Reason: 3x+4y+5=0 and 6x+ky+9=0 represent parallel line if K= 5

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but reason is false

d) both assertion and reason are false

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

11) Assertion: The given pair of linear  equations are inconsistent

−3x−4y−12=0 and 3x+4y−12=0

Reason:  if a1/a2 = b1/b2 ≠ c1/c2  the the pair of linear equation is inconsistant

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

12) Assertion: A straight line is just a line with no curves.

Reason: a line that extends to both sides till infinity and has no curves is called a straight line.

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

13) Assertion: a pair of line given by ax^2+2hxy+by^2+2gx+2fy+c=0 are perpendicular if a-b=0

Reason: the equation 2x^2+3xy-2y^2+5x-5y+3=0 is not represent a pair of perpendicular straight line

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but reason is false

d) both assertion and reason are false

Ans: d) both Assertion and reason are false.

13) Assertion:  lines are x+2y−4=0 and 2x+4y−12=0 the graphical representation of line is parallel line.

Reason: if pair of given lines are parallel then a1/a2=b1/b2≠ c1/c2

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

14) Assertion: The two linear equations in the same two variables X and Y are called pair of linear equation in two variable

Reason: The equation of the form ax + by + c= 0 where a and b both are not zero is called linear equation in two variable

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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 two lines intersect each other in a single point

Reason: The two lines are not intersecting that means these lines are parallel to each other

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

16) Assertion: The slope of the line 2x-y= 0 is 2

Reason: The slope of the line which lies in first and third quadrant is positive

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

17) Assertion: The slope of the line which lies in the second and fourth quadrant is negative.

Reason: The slope of the line y= -x +6 is-1

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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: only one line passes through two points

Reason: the line will connect the two points as one as the initial and another point as the ending point.

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

19) Assertion: If the lines given by3x + 2ky = 22x + 5y + 1 = 0 are parallel, then the value of k is 15/4

Reason: For parallel lines a1/a2=b1/b2≠ c1/c2

3/2= 2k/5

K=15/4

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but 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

20)Assertion: If the lines intersect at a point, then that point gives the unique solution of the two equations. In this case, the pair of equations is inconsistent

Reason:  pair of linear equation is given by a₁x+ b₁y+ c₁=0 and a₂x +b₂y +c₂=0 a1/a2=b1/b2≠ c1/c2  In this case,the pair of linear equations is consistent

a) both assertion and reason are correct and reason is correct explanation for assertion

b) both assertion and reason are correct but reason is correct explanation for assertion

c) assertion is correct but reason is false

d) both assertion and reason are false

Ans: c) Assertion is correct but reason is false