CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 52

Mathematics Objective Questions and Answers: Chapter 02 Linear Equations in One Variable

Access targeted multiple-choice questions for Chapter 02 Linear Equations in One Variable designed to align with the latest CBSE academic syllabus for Class 8 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Download Chapter 02 Linear Equations in One Variable MCQs with Answers

Access the complete set of multiple-choice questions for Chapter 02 Linear Equations in One Variable below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official CBSE textbooks.

Multiple Choice Questions

Question 1: The solution of \( (3x-8)(3x+2)-(4x-11)(2x+1)=(x-3)(x+7) \) is
(a) \( 1 \)
(b) \( 4 \)
(c) \( -4 \)
(d) \( 8 \)
Show Answer & Explanation

Answer: (b) \( 4 \)

Explanation:
1. LHS \( =9x^2-18x-16-(8x^2-18x-11)=x^2-5 \).
2. RHS \( =x^2+4x-21 \), so \( -5=4x-21 \) and \( x=4 \).

Teacher's Note:
1. The \( x^2 \) terms cancel.

Question 2: Five times a number minus \( 5 \) equals \( 4 \) more than twice the number. The number is
(a) \( 6 \)
(b) \( 4 \)
(c) \( 3 \)
(d) \( 5 \)
Show Answer & Explanation

Answer: (c) \( 3 \)

Explanation:
1. \( 5x-5=2x+4 \), so \( 3x=9 \) and \( x=3 \).

Teacher's Note:
1. Translate carefully.

Question 3: Multiply \( x \) by \( 3 \) and then subtract \( 3 \) from it. If the result is \( 9 \), the value of \( x \) is
(a) \( 3 \)
(b) \( 6 \)
(c) \( 5 \)
(d) \( 4 \)
Show Answer & Explanation

Answer: (d) \( 4 \)

Explanation:
1. \( 3x-3=9 \), so \( x=4 \).

Teacher's Note:
1. Add \( 3 \) then divide by \( 3 \).

Question 4: The sum of four consecutive integers is \( 178 \). The integers are
(a) \( 43, 44, 45, 46 \)
(b) \( 40, 44, 46, 48 \)
(c) \( 44, 45, 46, 47 \)
(d) \( 42, 43, 44, 45 \)
Show Answer & Explanation

Answer: (a) \( 43, 44, 45, 46 \)

Explanation:
1. Let them be \( x, x+1, x+2, x+3 \): \( 4x+6=178 \).
2. \( x=43 \); integers \( 43,44,45,46 \).

Teacher's Note:
1. Four consecutive integers differ by \( 1 \).

Question 5: Divide \( x \) by \( 4 \) and then add \( 13 \). If the result is \( 33 \), the value of \( x \) is
(a) \( 46 \)
(b) \( 80 \)
(c) \( 113 \)
(d) \( 20 \)
Show Answer & Explanation

Answer: (b) \( 80 \)

Explanation:
1. \( \frac x4+13=33 \), so \( \frac x4=20 \) and \( x=80 \).

Teacher's Note:
1. Undo operations in reverse order.

Question 6: A boy's age is one-fourth that of his father. After \( 24 \) years the boy will be half as old as his father. Their present ages are
(a) \( 8 \) years and \( 32 \) years
(b) \( 15 \) years and \( 60 \) years
(c) \( 12 \) years and \( 48 \) years
(d) \( 10 \) years and \( 40 \) years
Show Answer & Explanation

Answer: (c) \( 12 \) years and \( 48 \) years

Explanation:
1. Let the boy be \( b \) and father \( 4b \): \( b+24=\frac{4b+24}{2} \).
2. \( 2b+48=4b+24 \), so \( b=12 \) and father \( =48 \).

Teacher's Note:
1. Add \( 24 \) to both ages.

Question 7: In an isosceles triangle PQR with \( PQ=PR \), it is given that \( PQ=\frac34x \) cm and \( PR=12 \) cm. The value of \( x \) is
(a) \( 16 \)
(b) \( 12 \)
(c) \( 24 \)
(d) \( 8 \)
Show Answer & Explanation

Answer: (a) \( 16 \)

Explanation:
1. \( \frac34x=12 \), so \( x=16 \).

Teacher's Note:
1. Equal sides give an equation.

Question 8: Which of the following statements are true?
(i) If \( \frac{3x-1}{4}-\frac{2x+5}{3}=\frac52 \), then \( x=53 \).
(ii) If \( \frac{x+0.25}{3}-0.5=x \), then \( x=-0.625 \).
(iii) The sum of three consecutive odd numbers is \( 63 \), so the numbers are \( 19, 21, 23 \).
(iv) Two complementary angles differ by \( 16^\circ \), so the angles are \( 62^\circ \) and \( 28^\circ \).
(a) (ii), (iii) and (iv)
(b) (i), (ii) and (iv)
(c) (i) and (iv)
(d) (i), (ii) and (iii)
Show Answer & Explanation

Answer: (d) (i), (ii) and (iii)

Explanation:
1. (i) \( 9x-3-8x-20=30 \) gives \( x=53 \): true.
2. (ii) \( x+0.25-1.5=3x \) gives \( x=-0.625 \): true.
3. (iii) \( 19+21+23=63 \): true.
4. (iv) The angles are \( 53^\circ \) and \( 37^\circ \); \( 62^\circ \) and \( 28^\circ \) differ by \( 34^\circ \): false.

Teacher's Note:
1. Solve each statement independently.

Question 9: The value of \( x \) in \( 5\left(\frac{7x+5}{3}\right)-\frac{23}{3}=13-\frac{4x-2}{3} \) is
(a) \( 3 \)
(b) \( 5 \)
(c) \( 2 \)
(d) \( 1 \)
Show Answer & Explanation

Answer: (d) \( 1 \)

Explanation:
1. Multiply by \( 3 \): \( 5(7x+5)-23=39-(4x-2) \).
2. \( 35x+2=41-4x \), so \( 39x=39 \) and \( x=1 \).

Teacher's Note:
1. Multiply every term by \( 3 \).

Question 10: If \( 5 \) is added to \( x \), the result is \( 20 \). The value of \( x \) is
(a) \( 20 \)
(b) \( 5 \)
(c) \( 10 \)
(d) \( 15 \)
Show Answer & Explanation

Answer: (d) \( 15 \)

Explanation:
1. \( x+5=20 \), so \( x=15 \).

Teacher's Note:
1. Subtract \( 5 \) from both sides.

Question 11: Sunita is twice as old as Ashima. If \( 6 \) years are subtracted from Ashima's age and \( 4 \) years are added to Sunita's age, Sunita will be four times as old as Ashima. The present ages of Sunita and Ashima are
(a) \( 28 \) years and \( 14 \) years
(b) \( 16 \) years and \( 10 \) years
(c) \( 18 \) years and \( 12 \) years
(d) \( 24 \) years and \( 12 \) years
Show Answer & Explanation

Answer: (a) \( 28 \) years and \( 14 \) years

Explanation:
1. Ashima \( =a \), Sunita \( =2a \): \( 2a+4=4(a-6) \).
2. \( 2a=28 \), \( a=14 \); Sunita \( =28 \).

Teacher's Note:
1. Form the equation from the changed ages.

Question 12: Solve \( 2(x-3)+3(x+1)=5(2x-1) \).
(a) \( x=\frac52 \)
(b) \( x=2 \)
(c) \( x=\frac25 \)
(d) \( x=-\frac25 \)
Show Answer & Explanation

Answer: (c) \( x=\frac25 \)

Explanation:
1. LHS \( =5x-3 \) and RHS \( =10x-5 \).
2. \( -3+5=10x-5x \), so \( 5x=2 \) and \( x=\frac25 \).

Teacher's Note:
1. Expand brackets before moving terms.

Question 13: The sum of \( x \) and \( x+3 \) is \( 15 \). The value of \( x \) is
(a) \( 6 \)
(b) \( 12 \)
(c) \( 10 \)
(d) \( 8 \)
Show Answer & Explanation

Answer: (a) \( 6 \)

Explanation:
1. \( 2x+3=15 \), so \( 2x=12 \) and \( x=6 \).

Teacher's Note:
1. Combine like terms.

Question 14: If \( \frac13 \) is added to a number and the sum is multiplied by \( 2 \), the answer is \( \frac83 \). The number is
(a) \( \frac43 \)
(b) \( 1 \)
(c) \( \frac13 \)
(d) \( 2 \)
Show Answer & Explanation

Answer: (b) \( 1 \)

Explanation:
1. \( 2\left(x+\frac13\right)=\frac83 \), so \( x+\frac13=\frac43 \).
2. \( x=1 \).

Teacher's Note:
1. Divide both sides by \( 2 \) first.

Question 15: Assertion (A): The solution of the linear equation \( 3x+5=0 \) is \( -\frac53 \).
Reason (R): The solution of \( ax+b=0 \) (\( a\neq0 \)) is always \( -\frac ba \).
(a) Both A and R are false
(b) A is true but R is false
(c) Both A and R are true and R is the correct explanation of A
(d) Both A and R are true but R is not the correct explanation of A
Show Answer & Explanation

Answer: (c) Both A and R are true and R is the correct explanation of A

Explanation:
1. \( 3x=-5 \), so \( x=-\frac53 \).
2. With \( a=3 \), \( b=5 \) the general formula \( -\frac ba=-\frac53 \) gives the same result, so R explains A.

Teacher's Note:
1. The general solution \( -\frac ba \) applies when \( a\neq0 \).

Question 16: Solve \( q-\frac{q+1}{3}=\frac{q-1}{5}+q \).
(a) \( q=\frac14 \)
(b) \( q=-\frac14 \)
(c) \( q=-4 \)
(d) \( q=-\frac12 \)
Show Answer & Explanation

Answer: (b) \( q=-\frac14 \)

Explanation:
1. Multiply by \( 15 \): \( 15q-5(q+1)=3(q-1)+15q \).
2. \( 10q-5=18q-3 \), so \( -2=8q \) and \( q=-\frac14 \).

Teacher's Note:
1. Multiply by the LCM of the denominators.

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FAQs

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