CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 56

Multiple Choice Questions (MCQs) for Class 8 Mathematics: 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.

Practice Chapter 02 Linear Equations in One Variable MCQs for Class 8 Mathematics

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: PQR is an equilateral triangle with \( PQ=(4x-7) \) cm and \( PR=(2x+5) \) cm. The length of QR is
(a) \( 15 \) cm
(b) \( 6 \) cm
(c) \( 17 \) cm
(d) \( 12 \) cm
Show Answer & Explanation

Answer: (c) \( 17 \) cm

Explanation:
1. \( 4x-7=2x+5 \) gives \( x=6 \).
2. Each side \( =2(6)+5=17 \) cm.

Teacher's Note:
1. All sides of an equilateral triangle are equal.

Question 2: The solution of \( (x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0 \) is
(a) \( -6 \)
(b) \( 6 \)
(c) \( 2 \)
(d) \( -1 \)
Show Answer & Explanation

Answer: (b) \( 6 \)

Explanation:
1. Expand: \( x^2+5x+6+x^2-5x+6-2x^2-2x=12-2x \).
2. \( 12-2x=0 \) gives \( x=6 \).

Teacher's Note:
1. The \( x^2 \) terms cancel, leaving a linear equation.

Question 3: The teacher says, "If you add \( 7 \) to \( 3 \) times the number I have thought of, you get \( 31 \)." The number is
(a) \( 9 \)
(b) \( 10 \)
(c) \( 7 \)
(d) \( 8 \)
Show Answer & Explanation

Answer: (d) \( 8 \)

Explanation:
1. \( 3x+7=31 \), so \( 3x=24 \) and \( x=8 \).

Teacher's Note:
1. Form the equation exactly as stated.

Question 4: The numerator of a fraction is \( 6 \) less than the denominator. If \( 3 \) is added to the numerator, the fraction becomes \( \frac23 \). The original fraction is
(a) \( \frac14 \)
(b) \( \frac12 \)
(c) \( \frac13 \)
(d) \( \frac29 \)
Show Answer & Explanation

Answer: (c) \( \frac13 \)

Explanation:
1. Fraction \( =\frac{d-6}{d} \): \( \frac{d-3}{d}=\frac23 \) gives \( 3d-9=2d \), so \( d=9 \).
2. Original fraction \( =\frac39=\frac13 \).

Teacher's Note:
1. Let the denominator be \( d \).

Question 5: If \( 27^k=\frac{9}{3^k} \), then \( \frac1{k^2} \) equals
(a) \( 9 \)
(b) \( 2 \)
(c) \( \frac14 \)
(d) \( 4 \)
Show Answer & Explanation

Answer: (d) \( 4 \)

Explanation:
1. \( 3^{3k}=3^{2-k} \), so \( 3k=2-k \) and \( k=\frac12 \).
2. \( \frac1{k^2}=4 \).

Teacher's Note:
1. Write everything as powers of \( 3 \).

Question 6: The solution of \( \frac23(x-5)-\frac14(x-2)=\frac92 \) is
(a) \( -\frac{25}{2} \)
(b) \( \frac{66}{5} \)
(c) \( \frac{88}{5} \)
(d) \( \frac{11}{2} \)
Show Answer & Explanation

Answer: (c) \( \frac{88}{5} \)

Explanation:
1. Multiply by \( 12 \): \( 8(x-5)-3(x-2)=54 \).
2. \( 5x-34=54 \), so \( x=\frac{88}{5} \).

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

Question 7: The solution of \( \frac{y-(7-8y)}{9y-(3+4y)}=\frac23 \) is
(a) \( \frac{16}{17} \)
(b) \( \frac{15}{17} \)
(c) \( \frac{13}{12} \)
(d) \( \frac{12}{11} \)
Show Answer & Explanation

Answer: (b) \( \frac{15}{17} \)

Explanation:
1. Numerator \( =9y-7 \) and denominator \( =5y-3 \).
2. \( 3(9y-7)=2(5y-3) \) gives \( 17y=15 \).

Teacher's Note:
1. Simplify numerator and denominator first.

Question 8: The value of \( x \) in \( 0.3x-(0.8-0.2x)=0.2-0.5x \) is
(a) \( 2 \)
(b) \( -1 \)
(c) \( 0.5 \)
(d) \( 1 \)
Show Answer & Explanation

Answer: (d) \( 1 \)

Explanation:
1. LHS \( =0.5x-0.8 \).
2. \( 0.5x-0.8=0.2-0.5x \) gives \( x=1 \).

Teacher's Note:
1. Open the bracket carefully.

Question 9: The value of \( x \) in \( 2(x+3)-3x=8-2(2x-5) \) is
(a) \( 4 \)
(b) \( 3 \)
(c) \( 5 \)
(d) \( 2 \)
Show Answer & Explanation

Answer: (a) \( 4 \)

Explanation:
1. \( 6-x=18-4x \), so \( 3x=12 \) and \( x=4 \).

Teacher's Note:
1. Expand both sides.

Question 10: The largest of four consecutive integers whose sum is \( 178 \) is
(a) \( 46 \)
(b) \( 44 \)
(c) \( 45 \)
(d) \( 43 \)
Show Answer & Explanation

Answer: (a) \( 46 \)

Explanation:
1. \( 4x+6=178 \) gives \( x=43 \).
2. The integers are \( 43,44,45,46 \).

Teacher's Note:
1. The largest is \( x+3 \).

Question 11: The sum of one-fourth, one-ninth and one-third of a number is \( 25 \). The number is
(a) \( 30 \)
(b) \( 36 \)
(c) \( 24 \)
(d) \( 45 \)
Show Answer & Explanation

Answer: (b) \( 36 \)

Explanation:
1. \( \frac x4+\frac x9+\frac x3=\frac{9x+4x+12x}{36}=\frac{25x}{36} \).
2. \( \frac{25x}{36}=25 \), so \( x=36 \).

Teacher's Note:
1. Use LCM \( 36 \).

Question 12: The sum of the digits of a two-digit number is \( 8 \). If the number formed by reversing the digits is \( 18 \) less than the original number, the original number is
(a) \( 53 \)
(b) \( 55 \)
(c) \( 54 \)
(d) \( 56 \)
Show Answer & Explanation

Answer: (a) \( 53 \)

Explanation:
1. Let digits be \( a \) (tens) and \( b \) (units): \( a+b=8 \) and \( (10a+b)-(10b+a)=18 \), so \( a-b=2 \).
2. \( a=5,\ b=3 \); the number is \( 53 \).

Teacher's Note:
1. Reversing swaps the tens and units digits.

Question 13: Ravish has three boxes of total weight \( 60\frac12 \) kg. Box B weighs \( 3\frac12 \) kg more than box A and box C weighs \( 5\frac12 \) kg more than box B. The weights of boxes A, B and C respectively are
(a) \( 18 \) kg, \( 23 \) kg, \( 19\frac12 \) kg
(b) \( 16 \) kg, \( 19\frac12 \) kg, \( 25 \) kg
(c) \( 8 \) kg, \( 33 \) kg, \( 19\frac12 \) kg
(d) \( 16 \) kg, \( 25 \) kg, \( 19\frac12 \) kg
Show Answer & Explanation

Answer: (b) \( 16 \) kg, \( 19\frac12 \) kg, \( 25 \) kg

Explanation:
1. Let A \( =a \): B \( =a+3.5 \), C \( =a+9 \).
2. \( 3a+12.5=60.5 \), so \( a=16 \); B \( =19.5 \) and C \( =25 \).

Teacher's Note:
1. Express every weight in terms of box A.

Question 14: The solution of \( 6.5x+\frac{19.5x-32.5}{2}=6.5x+13+\frac{13x-26}{2} \) is
(a) \( 5 \)
(b) \( -5 \)
(c) \( 4 \)
(d) \( 3 \)
Show Answer & Explanation

Answer: (a) \( 5 \)

Explanation:
1. Cancel \( 6.5x \): \( \frac{19.5x-32.5}{2}=13+\frac{13x-26}{2} \).
2. \( 19.5x-32.5=26+13x-26 \), so \( 6.5x=32.5 \) and \( x=5 \).

Teacher's Note:
1. Cancel equal terms on both sides.

Question 15: A mother is \( 25 \) years older than her daughter. Five years hence the mother will be twice as old as the daughter. Their present ages are
(a) \( 35 \) years and \( 10 \) years
(b) \( 40 \) years and \( 15 \) years
(c) \( 45 \) years and \( 20 \) years
(d) \( 50 \) years and \( 25 \) years
Show Answer & Explanation

Answer: (c) \( 45 \) years and \( 20 \) years

Explanation:
1. Daughter \( =d \), mother \( =d+25 \): \( d+30=2(d+5) \).
2. \( d=20 \) and mother \( =45 \).

Teacher's Note:
1. Add \( 5 \) to both ages.

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Multiple Choice Questions (MCQs) for Class 8 Mathematics Chapter 02 Linear Equations in One Variable

Chapter MCQs with Answers for Class 8 Mathematics

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FAQs

Where can I access latest CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 56?

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Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 8 material?

Yes, our CBSE Class 8 Mathematics Linear Equations in One Variable MCQs Set 56 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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