PYQ Vault

Day 97: CBSE Class 12 Maths

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

  1. Question 1

    Matrices. Asked once: 2023 (same type asked 2 times)

    32 (b)
    If f(α)=[cos⁡α−sin⁡α0sin⁡αcos⁡α0001]f(\alpha) = \begin{bmatrix} \cos \alpha & -\sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix}, prove that f(α)⋅f(−β)=f(α−β)f(\alpha) \cdot f(-\beta) = f(\alpha - \beta)

  2. Question 2

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

    33 (b)
    A relation R is defined on N×NN \times N (where N is the set of natural numbers) as (a,b) R (c,d)⇔ac=bd(a, b)\ R\ (c, d) \Leftrightarrow \dfrac{a}{c} = \dfrac{b}{d}. Show that R is an equivalence relation.

  3. Question 3

    Three Dimensional Geometry. Asked once: 2024 (same type asked 2 times)

    14
    The vector equation of a line passing through the point (1,−1,0)(1, -1, 0) and parallel to Y-axis is :

    Tap an option to check your answer.

  4. Question 4

    Three Dimensional Geometry. Asked once: 2024 (same type asked 2 times)

    34
    Equations of sides of a parallelogram ABCD are as follows : AB : x+11=y−2−2=z−12\frac{x + 1}{1} = \frac{y - 2}{-2} = \frac{z - 1}{2} BC : x−13=y+2−5=z−53\frac{x - 1}{3} = \frac{y + 2}{-5} = \frac{z - 5}{3} CD : x−41=y+7−2=z−82\frac{x - 4}{1} = \frac{y + 7}{-2} = \frac{z - 8}{2} DA : x−23=y+3−5=z−43\frac{x - 2}{3} = \frac{y + 3}{-5} = \frac{z - 4}{3} Find the equation of diagonal BD.

  5. Question 5

    Vector Algebra. Asked once: 2023 (same type asked 2 times)

    9
    The value of (i^×j^)⋅j^+(j^×i^)⋅k^(\hat{i} \times \hat{j}) \cdot \hat{j} + (\hat{j} \times \hat{i}) \cdot \hat{k} is :

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