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Match List-I with List-II | List-I | List-II | |---|---| | (A) The vectors λ i + j + 2 k and i + λ j + k are perpendicular if λ is equal to | (I) 1 |…

CUET UG 2025 — Mathematics Algebra

2025mcqmedium

Match List-I with List-II

List-I List-II
(A) The vectors λi^\lambda\hat{i}λi^ +j^+2k^+ \hat{j} + 2\hat{k}+j^​+2k^ and i⃗+λj^+k^\vec{i} + \lambda\hat{j} + \hat{k}i+λj^​+k^ are perpendicular if λ is equal to (I) 1
(B) The vectors 3i^+6j^−k^3\hat{i} + 6\hat{j} - \hat{k}3i^+6j^​−k^ and 2i^+4j^−λk^2\hat{i} + 4\hat{j} - \lambda\hat{k}2i^+4j^​−λk^ are collinear if λ is equal to (II) -1
(C) The number of vectors of unit-length which are perpendicular to both the vectors a⃗\vec{a}a = i^+j^+2k^\hat{i} + \hat{j} + 2\hat{k}i^+j^​+2k^ and b⃗\vec{b}b = 3i^−j^+5k^3\hat{i} - \hat{j} + 5\hat{k}3i^−j^​+5k^ is (III) 2/3
(D) If ∣a⃗∣=1\lvert \vec{a} \rvert = 1∣a∣=1 and a⃗+b⃗=0⃗\vec{a} + \vec{b} = \vec{0}a+b=0, then ∣b⃗∣\lvert \vec{b} \rvert∣b∣ is equal to (IV) 2

Choose the correct answer from the options given below:

Official previous-year question

Held on 21 May 2025 · Verified 13 Jul 2026.

Options

  1. A

    (A) - (II), (B) - (III), (C) - (IV), (D) - (I)

  2. B

    (A) - (I), (B) - (IV), (C) - (II), (D) - (III)

  3. C

    (A) - (III), (B) - (IV), (C) - (II), (D) - (I)

  4. D

    (A) - (IV), (B) - (III), (C) - (II), (D) - (I)

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