If the matrix A=bmatrix0&r&-2\\3&p&t\&-4&0bmatrix is skew-symmetric, then value of (q+t)/(p+r) is.... (A) -2 (B) 0 (C) 1 (D) 2

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

CBSE Class 12 Mathematics sample paper 2025-26: question 3

From the official CBSE sample question paper for 2025-26, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQMatrices

If the matrix $A = 03 q r p - 4 - 2 t 0$ is skew-symmetric, then value of $\frac{q + t}{p + r}$ is....

(A) $- 2$
(B)0
(C)1
(D)2

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

In a skew-symmetric matrix, what are the diagonal entries?

Hint 2

Compare $a_{12}$ with $a_{21}$ , and so on.

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.

For a skew-symmetric matrix, $a_{ij} = - a_{j i}$ and every diagonal entry is 0. So $p = 0$ , $r = - 3$ , $q = 2$ and $t = 4$ .
$\frac{q + t}{p + r} = \frac{2 + 4}{0 - 3} = - 2$ . Option (A).
1 mark

Answer: $- 2$ , option (A)

Where the marks are

Finds $p, q, r, t$ from $a_{ij} = - a_{j i}$ and evaluates the ratio as $- 2$ (1 mark)

Revise the chapter

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

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 3

Hints

Step-by-step solution

Revise the chapter

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