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MCQ

linear-equations-one-two-variables-l2 MCQ - Practice Questions with Answers

Solve 29 linear-equations-one-two-variables-l2 questions for RAS/RPSC preparation.

Practice questions

Q1Which statement is correct about a linear equation at upper-primary level?

A The variable has highest power 1.
B It has no equality sign.
C It must always have two variables.
D Its solution is never checked by substitution.
Explanation

NCERT's explanation ties linear equations to linear expressions and variable power 1. Asha should learn this as a recognition test before solving, because many distractors look algebraic but are not linear.

Q2Why does the equation x + y = 12 have more than one solution pair?

A Because a linear equation cannot contain an equality sign.
B Because both variables must always have the same value.
C Because many ordered pairs can have the same sum 12.
D Because the highest power of a variable is 2.
Explanation

In a two-variable linear equation, one relation can be satisfied by many ordered pairs. The sum condition x + y = 12 is met by several pairs, while the other choices misunderstand equality, variable values, or powers.

Q3Which set lists only common linear-equation MCQ traps?

A Photosynthesis, friction, shadow formation
B Rhyme, metre, alliteration
C Matrix rank, determinant zero, eigenvalue
D Sign error, one-side operation, missing answer check
Explanation

REET pedagogy items often ask the candidate to diagnose the error, not merely solve again. Sign errors, one-side operations and missing checks are exactly the traps a teacher should notice in Mary or Imran's work.

Q4A student says that 2x + 6 = 18 gives x = 12. Which teacher prompt best targets the missed step?

A After subtracting 6 from both sides, what does 2x equal, and what must be done to both sides next?
B Move 6 to the other side and write the answer quickly.
C Try changing 2x into x because x is the unknown.
D Check whether 12 plus 6 equals 18.
Explanation

The student subtracted 6 but treated 2x as x. A useful prompt makes the balance step explicit: 2x = 12, so both sides must be divided by 2; the other prompts either rush transposition or check the wrong expression.

Q5For the equation 2x - 3 = 11, which substitution check proves that x = 7 is a solution?

A 2(7) - 3 = 14 - 3 = 11
B 2(7) + 3 = 17
C 2(11) - 3 = 19
D 7 - 3 = 4
Explanation

Substitution checks an answer by putting the proposed value in place of the variable. With x = 7, the original left side becomes 11; the wrong options change the sign, substitute the wrong number, or ignore the coefficient.

You've seen 5 of 29 sample questions

Unlimited practice on linear-equations-one-two-variables-l2 comes with the RAS Test Series + Practice pack or Gate Pass.

More questions

6Which value of x satisfies the linear equation 5x + 3 = 28?

A5
B4
C6
D25

7In a class 6 to 8 lesson on simple linear equations, which teaching sequence best builds meaning before symbols?

AStart with transposition rules, then give a balance activity if time remains.
BUse a balance model, then a table or strip model, and then write equations with symbols.
CAvoid models and ask learners to memorize only solved examples.
DTeach two-variable graphs first and return to one-variable equations later.

8Which pair of steps correctly clears the denominator in (x + 3) / 2 = 7 and then solves the equation?

Ax + 3 = 7, so x = 4
Bx + 3 = 14, so x = 17
Cx + 3 = 9, so x = 6
Dx + 3 = 14, so x = 11

9Match the classroom situation with the most suitable equation. List I: (1) Devika's rectangle has width 5 cm and perimeter 34 cm. (2) Asha has 5 more marbles than Imran and together they have 31. List II: (a) 2l + 10 = 34 (b) x + x + 5 = 31.

A1-b, 2-a
B1-a, 2-b
C1-a, 2-a
D1-b, 2-b

10A student says that x + y = 12 has only one solution because the right side is 12. Which response is mathematically correct?

AThe equation has no solution because two variables are present.
BThe only solution is x = 12 and y = 12.
CThe only solution is x = 0 and y = 12.
DMany pairs can satisfy it, such as x = 5 and y = 7.

11A word problem says, "A number increased by 7 is 25." Before writing the equation, which variable statement is most suitable?

ALet 7 be the unknown number.
BLet x be the number.
CLet 25 be x plus 7.
DLet the answer be 25.

12Mary solves 3x - 4 = 11. Which option is the best checking line for her answer x = 5?

A3 + 5 - 4 = 4
B5 - 4 = 1
C3 times 5 - 4 = 11
D3 times 11 - 4 = 29

13Assertion: A teacher first uses a balance model for x + 4 = 16. Reason: Doing the same operation on both sides preserves equality.

ABoth assertion and reason are true, and the reason explains the assertion.
BBoth are true, but the reason does not explain the assertion.
CThe assertion is true, but the reason is false.
DThe assertion is false, but the reason is true.

14Which of the following is a linear equation in one variable?

Ax² + 3 = 7
Bx + y = 10
C3x - 5 = 10
D1/x + 2 = 4

15In a fraction equation, why should a teacher say "multiply the whole of both sides by the common denominator"?

ABecause only the first term needs to change.
BBecause denominators disappear without any operation.
CBecause it preserves equality while removing fractions from every term.
DBecause checking the final answer becomes unnecessary.

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