CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 54

Download CBSE MCQs for Class 8 Mathematics: Chapter 02 Linear Equations in One Variable

Review structured MCQ sets for Class 8 Mathematics Chapter 02 Linear Equations in One Variable. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Chapter-wise Objective Questions: Chapter 02 Linear Equations in One Variable

Navigate directly to the 50 objective questions for Chapter 02 Linear Equations in One Variable using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: Eight less than three times a number is equal to one. The number is
(a) \( 3 \)
(b) \( 2 \)
(c) \( 9 \)
(d) \( \frac13 \)
Show Answer & Explanation

Answer: (a) \( 3 \)

Explanation:
1. \( 3x-8=1 \), so \( 3x=9 \) and \( x=3 \).

Teacher's Note:
1. Translate the words to an equation first.

Question 2: The solution of \( \frac{5(x+6)-15(2-x)}{3x-1}=10 \) is
(a) \( 5 \)
(b) \( 1 \)
(c) \( 6 \)
(d) \( 2 \)
Show Answer & Explanation

Answer: (b) \( 1 \)

Explanation:
1. Numerator \( =5x+30-30+15x=20x \).
2. \( 20x=10(3x-1) \) gives \( 10x=10 \), \( x=1 \).

Teacher's Note:
1. Simplify the numerator first.

Question 3: Solve \( 2x-7=\frac{x+3}{3} \).
(a) \( x=5 \)
(b) \( x=\frac{18}{5} \)
(c) \( x=\frac{12}{5} \)
(d) \( x=\frac{24}{5} \)
Show Answer & Explanation

Answer: (d) \( x=\frac{24}{5} \)

Explanation:
1. Multiply both sides by \( 3 \): \( 6x-21=x+3 \).
2. \( 5x=24 \), so \( x=\frac{24}{5} \).

Teacher's Note:
1. Clear the fraction first, then collect the \( x \) terms on one side.

Question 4: The solution of \( \frac{3x}{4}-\frac{x-1}{2}=\frac{x-2}{3} \) is
(a) \( -14 \)
(b) \( 14 \)
(c) \( 22 \)
(d) \( 15 \)
Show Answer & Explanation

Answer: (b) \( 14 \)

Explanation:
1. Multiply by \( 12 \): \( 9x-6(x-1)=4(x-2) \).
2. \( 3x+6=4x-8 \), so \( x=14 \).

Teacher's Note:
1. LCM of \( 4,2,3 \) is \( 12 \).

Question 5: \( 9 \) subtracted from a number gives \( \frac{21}{5} \). The number is
(a) \( 13 \)
(b) \( \frac{21}{5} \)
(c) \( \frac{66}{5} \)
(d) \( \frac{24}{5} \)
Show Answer & Explanation

Answer: (c) \( \frac{66}{5} \)

Explanation:
1. \( x-9=\frac{21}5 \), so \( x=9+\frac{21}{5}=\frac{66}5 \).

Teacher's Note:
1. Add \( 9 \) to both sides.

Question 6: In a rational number, twice the numerator is \( 2 \) more than the denominator. If \( 3 \) is added to both numerator and denominator, the new fraction is \( \frac23 \). The original number is
(a) \( \frac{7}{12} \)
(b) \( \frac32 \)
(c) \( \frac9{12} \)
(d) \( \frac92 \)
Show Answer & Explanation

Answer: (a) \( \frac{7}{12} \)

Explanation:
1. Numerator \( n \), denominator \( 2n-2 \): \( \frac{n+3}{2n+1}=\frac23 \).
2. \( 3n+9=4n+2 \), so \( n=7 \) and the number is \( \frac7{12} \).

Teacher's Note:
1. Express the denominator in terms of the numerator.

Question 7: The solution of \( \left(\frac{x+1}{x+2}\right)^2=\frac{x+2}{x+4} \) is
(a) \( -\frac43 \)
(b) \( -\frac53 \)
(c) \( \frac{11}{3} \)
(d) \( \frac13 \)
Show Answer & Explanation

Answer: (a) \( -\frac43 \)

Explanation:
1. \( (x+1)^2(x+4)=(x+2)^3 \).
2. \( x^3+6x^2+9x+4=x^3+6x^2+12x+8 \), so \( -3x=4 \) and \( x=-\frac43 \).

Teacher's Note:
1. The cubic terms cancel.

Question 8: A square paper is folded in half breadthwise. If the perimeter of the rectangle formed is \( 12 \) cm, the area of the square paper is
(a) \( 12 \) cm\( ^2 \)
(b) \( 9 \) cm\( ^2 \)
(c) \( 36 \) cm\( ^2 \)
(d) \( 16 \) cm\( ^2 \)
Show Answer & Explanation

Answer: (d) \( 16 \) cm\( ^2 \)

Explanation:
1. Let the side be \( s \); the rectangle is \( s \) by \( \frac s2 \).
2. \( 2\left(s+\frac s2\right)=3s=12 \), so \( s=4 \) cm and area \( =16 \) cm\( ^2 \).

Teacher's Note:
1. Folding halves one dimension.

Question 9: The number to be added to each of \( 2, 7, 10, 25 \) so that they are in proportion is
(a) \( 5 \)
(b) \( 2 \)
(c) \( 3 \)
(d) \( 4 \)
Show Answer & Explanation

Answer: (b) \( 2 \)

Explanation:
1. \( (2+x):(7+x)=(10+x):(25+x) \) gives \( (2+x)(25+x)=(7+x)(10+x) \).
2. \( 50+27x=70+17x \), so \( x=2 \). Check: \( 4:9=12:27 \).

Teacher's Note:
1. Product of extremes equals product of means.

Question 10: The solution of \( \frac7x+35=\frac1{10} \) is
(a) \( \frac{23}{349} \)
(b) \( -\frac{23}{349} \)
(c) \( \frac{70}{349} \)
(d) \( -\frac{70}{349} \)
Show Answer & Explanation

Answer: (d) \( -\frac{70}{349} \)

Explanation:
1. \( \frac7x=\frac1{10}-35=-\frac{349}{10} \).
2. \( x=-\frac{70}{349} \).

Teacher's Note:
1. Isolate \( \frac7x \) first.

Question 11: Solve \( 7p-13=3(5p-4) \).
(a) \( p=\frac14 \)
(b) \( p=\frac18 \)
(c) \( p=-\frac18 \)
(d) \( p=-8 \)
Show Answer & Explanation

Answer: (c) \( p=-\frac18 \)

Explanation:
1. \( 7p-13=15p-12 \).
2. \( -1=8p \), so \( p=-\frac18 \).

Teacher's Note:
1. Bring variable terms to one side and constants to the other.

Question 12: One number is \( 5 \) more than another, and \( 6 \) times the smaller number equals \( 5 \) times the larger. The numbers are
(a) \( 30 \) and \( 35 \)
(b) \( 25 \) and \( 30 \)
(c) \( 20 \) and \( 25 \)
(d) \( 15 \) and \( 20 \)
Show Answer & Explanation

Answer: (b) \( 25 \) and \( 30 \)

Explanation:
1. Smaller \( =x \): \( 6x=5(x+5) \), so \( x=25 \).

Teacher's Note:
1. Form the equation from the second condition.

Question 13: The solution of \( \frac{45-2x}{15}-\frac{4x+10}{5}=\frac{15-14x}{9} \) is
(a) \( -6 \)
(b) \( \frac{11}{14} \)
(c) \( \frac{15}{14} \)
(d) \( -\frac1{14} \)
Show Answer & Explanation

Answer: (c) \( \frac{15}{14} \)

Explanation:
1. Multiply by \( 45 \): \( 3(45-2x)-9(4x+10)=5(15-14x) \).
2. \( 45-42x=75-70x \), so \( 28x=30 \) and \( x=\frac{15}{14} \).

Teacher's Note:
1. LCM of \( 15,5,9 \) is \( 45 \).

Question 14: If \( \frac35 \) is added to twice the reciprocal of a number, the sum is \( 1 \). The number is
(a) \( 1 \)
(b) \( 6 \)
(c) \( 5 \)
(d) \( 2 \)
Show Answer & Explanation

Answer: (c) \( 5 \)

Explanation:
1. \( \frac35+\frac2x=1 \), so \( \frac2x=\frac25 \).
2. \( x=5 \).

Teacher's Note:
1. Reciprocal of \( x \) is \( \frac1x \).

Question 15: The sum of two numbers is \( 40 \) and one number is \( 10 \) more than the other. The numbers are
(a) \( 30 \) and \( 10 \)
(b) \( 20 \) and \( 20 \)
(c) \( 35 \) and \( 5 \)
(d) \( 25 \) and \( 15 \)
Show Answer & Explanation

Answer: (d) \( 25 \) and \( 15 \)

Explanation:
1. Let the smaller be \( x \): \( x+(x+10)=40 \).
2. \( 2x=30 \), \( x=15 \); the numbers are \( 15 \) and \( 25 \).

Teacher's Note:
1. Let one number be \( x \) and express the other in terms of \( x \).

Question 16: One-third of which number must be subtracted from \( \frac7{11} \) to give \( \frac{24}{55} \)?
(a) \( \frac35 \)
(b) \( \frac{5}{3} \)
(c) \( \frac15 \)
(d) \( \frac{3}{11} \)
Show Answer & Explanation

Answer: (a) \( \frac35 \)

Explanation:
1. \( \frac7{11}-\frac x3=\frac{24}{55} \), so \( \frac x3=\frac{35}{55}-\frac{24}{55}=\frac{11}{55}=\frac15 \).
2. \( x=\frac35 \).

Teacher's Note:
1. Isolate \( \frac x3 \) first.

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Chapter 02 Linear Equations in One Variable Objective Questions & Solutions for Class 8 Mathematics

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FAQs

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