MathsCBSE Class 12 · Sample paper, session 2024-25 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2024-25: question 2

From the official CBSE sample question paper for 2024-25, section A, question 2, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q2 · 1 mark · MCQMatrices

Assume $X, Y, Z, W$ and $P$ are matrices of order $2 \times n$ , $3 \times k$ , $2 \times p$ , $n \times 3$ and $p \times k$ , respectively. Then the restriction on $n$ , $k$ and $p$ so that $P Y + W Y$ will be defined are:

(A) $k = 3, p = n$
(B) $k$ is arbitrary, $p = 2$
(C) $p$ is arbitrary, $k = 3$
(D) $k = 2, p = 3$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

A product $A B$ needs columns of A = rows of B.

Hint 2

Two matrices can be added only if they have the same order.

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.

$P Y$ : $(p \times k) (3 \times k)$ is defined only if $k = 3$ ; then $P Y$ is $p \times k$ .
$W Y$ : $(n \times 3) (3 \times k)$ is $n \times k$ . For the sum, orders must match, so $p = n$ . Option (A).
1 mark

Answer: $k = 3, p = n$ , option (A)

Where the marks are

Gets $k = 3$ from $P Y$ and $p = n$ from equal orders (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 2024-25: every question, by section.

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CBSE Class 12 Mathematics sample paper 2024-25: question 2

Hints

Step-by-step solution

Revise the chapter

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