PYQ Vault

Day 158: CBSE Class 12 Maths

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

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 2024 (same type asked 2 times)

    21
    Evaluate : sec⁡2(tan⁡−112)+cosec⁡2(cot⁡−113)\sec^2\left(\tan^{-1}\dfrac{1}{2}\right) + \operatorname{cosec}^2\left(\cot^{-1}\dfrac{1}{3}\right)

  2. Question 2

    Matrices. Asked once: 2024 (same type asked 2 times)

    5
    If for the matrix A=[tan⁡x1−1tan⁡x]A = \begin{bmatrix} \tan x & 1 \\ -1 & \tan x \end{bmatrix}, A+A′=23 IA + A' = 2\sqrt{3}\, I, then the value of x∈[0,π2]x \in \left[0, \dfrac{\pi}{2}\right] is :

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  3. Question 3

    Matrices. Asked once: 2025 (same type asked 2 times)

    2
    If A=[0−38305−8−50]A = \begin{bmatrix} 0 & -3 & 8 \\ 3 & 0 & 5 \\ -8 & -5 & 0 \end{bmatrix}, then A is a :

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  4. Question 4

    Relations and Functions. Asked once: 2024 (same type asked 2 times)

    32
    A relation R on set A={−4,−3,−2,−1,0,1,2,3,4}A = \{-4, -3, -2, -1, 0, 1, 2, 3, 4\} be defined as R={(x,y):x+yR = \{(x, y) : x + y is an integer divisible by 2}2\}. Show that R is an equivalence relation. Also, write the equivalence class [2][2].

  5. Question 5

    Three Dimensional Geometry. Asked once: 2023 (same type asked 2 times)

    2
    The direction ratios of a line parallel to z-axis are :

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