PYQ Vault

Day 281: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Relations and Functions. Asked once: 2025

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : Let A={x∈R:−1≤x≤1}A = \{x \in R : -1 \le x \le 1\}. If f:A→Af : A \to A be defined as f(x)=x2f(x) = x^2, then f is not an onto function. Reason (R) : If y=−1∈Ay = -1 \in A, then x=±−1∉Ax = \pm\sqrt{-1} \notin A.

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  2. Question 2

    Vector Algebra. Asked once: 2025

    2
    If vector a⃗=3i^+2j^−k^\vec{a} = 3\hat{i} + 2\hat{j} - \hat{k} and vector b⃗=i^−j^+k^\vec{b} = \hat{i} - \hat{j} + \hat{k}, then which of the following is correct ?

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  3. Question 3

    Application of Derivatives. Asked once: 2023

    22
    A particle moves along the curve 3y=ax3+13y = ax^3 + 1 such that at a point with xx-coordinate 1, y-coordinate is changing twice as fast at xx-coordinate. Find the value of a.

  4. Question 4

    Relations and Functions. Asked once: 2025

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : Let f(x)=exf(x) = e^x and g(x)=log⁡xg(x) = \log x. Then (f+g) x=ex+log⁡x(f + g)\,x = e^x + \log x where domain of (f+g)(f + g) is R. Reason (R) : Dom(f+g)=Dom(f)∩Dom(g)\text{Dom}(f + g) = \text{Dom}(f) \cap \text{Dom}(g).

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  5. Question 5

    Vector Algebra. Asked once: 2025

    17
    Let a⃗\vec{a} be a position vector whose tip is the point (2,−3)(2, -3). If AB→=a⃗\overrightarrow{AB} = \vec{a}, where coordinates of A are (−4,5)(-4, 5), then the coordinates of B are :

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