MathsCBSE Class 12 · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2025-26: question 2

From the official CBSE sample question paper for 2025-26, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQMatrices

If for three matrices $A = [a_{ij}]_{m \times 4}$ , $B = [b_{ij}]_{n \times 3}$ and $C = [c_{ij}]_{p \times q}$ products $A B$ and $A C$ both are defined and are square matrices of same order, then value of $m, n, p$ and $q$ are:

(A) $m = q = 3$ and $n = p = 4$
(B) $m = 2, q = 3$ and $n = p = 4$
(C) $m = q = 4$ and $n = p = 3$
(D) $m = 4, p = 2$ and $n = q = 3$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

Open one hint at a time and try again before the next.

Hint 1

A product $X Y$ is defined only when the columns of $X$ equal the rows of $Y$ .

Hint 2

$A B$ is of order $m \times 3$ . What must $m$ be for it to be square?

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$A B$ is defined, so the columns of $A$ equal the rows of $B$ : $n = 4$ . $A C$ is defined, so $p = 4$ .
$A B$ has order $m \times 3$ and $A C$ has order $m \times q$ . Both are square and of the same order, so $m = 3$ and $q = 3$ . Option (A).
1 mark

Answer: $m = q = 3$ , $n = p = 4$ , option (A)

Where the marks are

Uses the conditions for the products to be defined and square to get $n = p = 4$ , $m = q = 3$ (1 mark)

Revise the chapter

Chapter: Matrices (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Matrices, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26: every question, by section.

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CBSE Class 12 Mathematics sample paper 2025-26: question 2

Hints

Step-by-step solution

Revise the chapter

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