Assertion & Reason Questions For Math Class 10 | Linear Equations in Two Variables

ASSERTION & REASON QUESTIONS CLASS 10

CHAPTER 1 REAL NUMBERS

Competency based questions on PAIR OF LINEAR EQUATIONS IN TWO VARIABLES class 10 chapter 3 , Assertion and Reason based questions for class 10 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES chapter 3

Assertion and Reason Questions

Directions

Each of these questions contain two statements Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of which is correct answer.

You have to select one of the codes (a ), (b ), (c ), (d ) given below

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.

Chapter 3 Class 10

Pair of Linear Equations in Two Variables

Question 1:

Assertion: The pairs of equations x + 2y - 5 = 0 and - 4x - 8y + 20 = 0 have infinitely many solution.
Reason: if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ then the pair of equations has infinitely many solutions.

Ans a

Question 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.
Ans a

Question 3:

Assertion: The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have no solution.
Reason: $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$ So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.

Ans a

Question 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 $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$
Ans a

Question 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 $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$
Ans a

Question 6:

Assertion: The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has infinitely many solution.
Reason: $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$ it satisfy the condition of infinitely many solution .
Ans C

Question 7:

Assertion: The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have unique solution
Reason: an equations $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ Hence, the given pair of equations have no solution
Ans d

Question 8:

Assertion: 3x + 4y + 5 = 0 and 6x + ky + 9 = 0 represent parallel line if K = 5
Reason: a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂= 0 represent parallel line if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$

Ans d

Question 9:

Assertion: The given pair of linear equations are −3x − 4y − 12 = 0 and 3x + 4y − 12 = 0 inconsistent .

Reason: if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$ the the pair of linear equation is inconsistant

Ans a

Question 10:

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.

Ans a

Question 11:

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 $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$

Ans a

Question 12:

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
Ans b

Question 13:

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
Ans b

Question 14:

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
Ans a
Question 15:

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.
Ans a
Question 16:

Assertion: If the lines given by 3x + 2ky = 2, 2x + 5y + 1 = 0 are parallel, then the value of k is 15/4
Reason: For parallel lines $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$ ⇒ 3/2 = 2k/5 ⇒ K =15/4

Ans a

Question 17:

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: The pair of linear equation is given by a₁x + b₁y + c₁= 0 and a₂x + b₂y + c₂= 0 is inconsistent if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq\frac{c_{1}}{c_{2}}$
Ans c

Question 18:

Assertion: x and y are 2 different digits. If the sum of the two digit numbers formed by using both the digits is a perfect square, then value of x + y is11

Reason: numbers that can be formed are xy and yx . Hence, (10x + y) + (10y + x) = 11(x + y) if this is a perfect square that x + y = 11
Ans a

Question 19:

Assertion: Homogeneous system of linear equations is always consistent.

Reason: x = 0, y = 0 is always a solution of the homogeneous system of equations with

unknowns x and y.
Ans a

Question 20:

Assertion: The linear equations x − 2y − 3 = 0 and 3x + 4y − 20 = 0 have exactly one solution.

Reason: The linear equations 2x + 3y − 9 = 0 and 4x + 6y − 18 = 0 have a unique solution.
Ans c

Question 21:

Assertion: The point (0, 4) lies on the graph of the linear equation 4x + 4y = 16

Reason: (0, 4) satisfies the equation 4x + 4y = 16.
Ans a

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