PYQ Vault

Day 66: 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)

    8
    If sin⁡−1x=y\sin^{-1} x = y, then dydx\dfrac{dy}{dx} is :

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  2. Question 2

    Continuity and Differentiability. Asked once: 2025 (same type asked 4 times)

    32 (b)
    Find dydx\frac{dy}{dx}, if y=xtan⁡x+x2+12y = x^{\tan x} + \frac{\sqrt{x^2 + 1}}{2}.

  3. Question 3

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

    8
    If [4+xx−1−23]\begin{bmatrix} 4+x & x-1 \\ -2 & 3 \end{bmatrix} is a singular matrix, then the value of x is :

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  4. Question 4

    Determinants. Asked once: 2026 (same type asked 4 times)

    4
    If Δ1=∣100020003∣\Delta_1 = \begin{vmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{vmatrix} and Δ2=∣020100006∣\Delta_2 = \begin{vmatrix} 0 & 2 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 6 \end{vmatrix}, then

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  5. Question 5

    Differential Equations. Asked once: 2026 (same type asked 4 times)

    34 (a)
    Solve the differential equation yey dx=(y3+2xey)dyy e^y\, dx = \left(y^3 + 2x e^y\right) dy, when y(0)=1y(0) = 1.