PYQ Vault

Day 58: CBSE Class 12 Maths

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

  1. Question 1

    Linear Programming. This type asked 2 times: 2024, 2025. This one: 2025

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : The shaded portion of the graph represents the feasible region for the given Linear Programming Problem (LPP). Min Z=50x+70yZ = 50x + 70y subject to constraints 2x+y≥82x + y \ge 8, x+2y≥10x + 2y \ge 10, x, y≥0x,\ y \ge 0 Z=50x+70yZ = 50x + 70y has a minimum value =380= 380 at B(2,4)B(2, 4). Reason (R) : The region representing 50x+70y<38050x + 70y < 380 does not have any point common with the feasible region.

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  2. Question 2

    Matrices. This type asked 2 times: 2024, 2025. This one: 2025

    13
    If A=[70x07000y]A = \begin{bmatrix} 7 & 0 & x \\ 0 & 7 & 0 \\ 0 & 0 & y \end{bmatrix} is a scalar matrix, then yxy^x is equal to

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  3. Question 3

    Relations and Functions. This type asked 2 times: 2024, 2025. This one: 2025

    3
    For real x, let f(x)=x3+5x+1f(x) = x^3 + 5x + 1. Then :

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  4. Question 4

    Vector Algebra. This type asked 2 times: 2022, 2025. This one: 2025

    23
    The diagonals of a parallelogram are given by a⃗=2i^−j^+k^\vec{a} = 2\hat{i} - \hat{j} + \hat{k} and b⃗=i^+3j^−k^\vec{b} = \hat{i} + 3\hat{j} - \hat{k}. Find the area of the parallelogram.
  5. Question 5

    Vector Algebra. This type asked 2 times: 2024, 2025. This one: 2025

    11
    If a⃗+b⃗+c⃗=0⃗\vec{a} + \vec{b} + \vec{c} = \vec{0}, ∣a⃗∣=37|\vec{a}| = \sqrt{37}, ∣b⃗∣=3|\vec{b}| = 3 and ∣c⃗∣=4|\vec{c}| = 4, then angle between b⃗\vec{b} and c⃗\vec{c} is

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