PYQ Vault

Day 137: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. Asked once: 2026 (same type asked 4 times)

    28 (b)
    Differentiate tan⁡−1(1+x2−1−x21+x2+1−x2)\tan^{-1}\left(\dfrac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}}\right) with respect to cos⁡−1x2\cos^{-1} x^2.

  2. Question 2

    Continuity and Differentiability. Asked once: 2024 (same type asked 4 times)

    26
    Given that y=(sin⁡x)x⋅xsin⁡x+axy = (\sin x)^{x} \cdot x^{\sin x} + a^{x}, find dydx\dfrac{dy}{dx}.

  3. Question 3

    Determinants. Asked once: 2023 (same type asked 4 times)

    3
    If [1212313a1]\begin{bmatrix} 1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & a & 1 \end{bmatrix} is non-singular matrix and a∈Aa \in A, then the set A is

    Tap an option to check your answer.

  4. Question 4

    Determinants. Asked once: 2025 (same type asked 4 times)

    4
    If ∣2x512x∣=∣6−543∣\begin{vmatrix} 2x & 5 \\ 12 & x \end{vmatrix} = \begin{vmatrix} 6 & -5 \\ 4 & 3 \end{vmatrix}, then the value of x is :

    Tap an option to check your answer.

  5. Question 5

    Differential Equations. Asked once: 2023 (same type asked 4 times)

    26 (a)
    Find the general solution of the differential equation : ddx(xy2)=2y(1+x2)\frac{d}{dx} (x y^2) = 2y (1 + x^2)