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 aQuestion 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 aQuestion 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 aQuestion 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 aQuestion 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 aQuestion 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 CQuestion 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 dQuestion 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 dQuestion 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 aQuestion 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 aQuestion 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 bQuestion 13:

Assertion: The two lines intersect each other in a
single pointReason: The two lines are not intersecting that
means these lines are parallel to each other
Ans bQuestion 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 pointsReason: 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 inconsistentReason: 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 cQuestion 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 is11Reason: 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 aQuestion 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 withunknowns 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 cQuestion 21:

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

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ASSERTION & REASON QUESTIONS CLASS 10

CHAPTER 1 REAL NUMBERS

Assertion and Reason Questions

Chapter 3 Class 10

Pair of Linear Equations in Two Variables

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