PYQ Vault

Day 114: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. Asked once: 2025 (same type asked 3 times)

    34 (a)
    For a positive constant 'a', differentiate at+1ta^{t + \frac{1}{t}} with respect to (t+1t)a\left(t + \dfrac{1}{t}\right)^a, where t is a non-zero real number.

  2. Question 2

    Continuity and Differentiability. Asked once: 2024 (same type asked 3 times)

    21 (b)
    If y=tan⁡xy = \sqrt{\tan \sqrt{x}}, prove that x  dydx=1+y44y\sqrt{x} \; \frac{dy}{dx} = \frac{1 + y^4}{4y}.

  3. Question 3

    Continuity and Differentiability. Asked once: 2026 (same type asked 3 times)

    25
    If x=sin⁡t−cos⁡tx = \sin t - \cos t, y=sin⁡tcos⁡ty = \sin t \cos t, find dydx\dfrac{dy}{dx} at t=π4t = \dfrac{\pi}{4}.

  4. Question 4

    Continuity and Differentiability. Asked once: 2026 (same type asked 3 times)

    32
    If x=3sin⁡t−sin⁡3tx = 3 \sin t - \sin 3t, y=3cos⁡t−cos⁡3ty = 3 \cos t - \cos 3t find dydx\frac{dy}{dx} and prove that d2ydx2=−cosec⁡32t⋅cosec⁡t3\frac{d^2y}{dx^2} = \frac{-\operatorname{cosec}^3 2t \cdot \operatorname{cosec} t}{3}

  5. Question 5

    Continuity and Differentiability. Asked once: 2024 (same type asked 3 times)

    26 (a)
    Find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}, if (cos⁡x)y=(cos⁡y)x(\cos x)^{\mathrm{y}} = (\cos \mathrm{y})^{x}.