PYQ Vault

Day 165: 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 4 times)

    8
    If f(x)={3x−2,0<x≤12x2+ax,1<x<2f(x) = \begin{cases} 3x - 2, & 0 < x \le 1 \\ 2x^2 + ax, & 1 < x < 2 \end{cases} is continuous for x∈(0,2)x \in (0, 2), then a is equal to :

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  2. Question 2

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

    14
    If A denotes the set of continuous functions and B denotes set of differentiable functions, then which of the following depicts the correct relation between set A and B ?

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  3. Question 3

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

    13
    The derivative of sin⁡(x2)\sin (x^2) w.r.t. x, at x=πx = \sqrt{\pi} is :

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  4. Question 4

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

    21 (b)
    If tan⁡−1(x2+y2)=a2\tan^{-1}(x^2 + y^2) = a^2, then find dydx\frac{dy}{dx}.

  5. Question 5

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

    8
    Derivative of cos⁡−1(sin⁡x+cos⁡x2)\cos^{-1}\left(\dfrac{\sin x + \cos x}{\sqrt{2}}\right), −π4<x<π4-\dfrac{\pi}{4} < x < \dfrac{\pi}{4} with respect to x is :

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