PYQ Vault

Day 136: 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)

    4
    If f(x)={1−sin⁡3x3cos⁡2x,for x≠π2k,for x=π2f(x) = \begin{cases} \frac{1 - \sin^3 x}{3\cos^2 x}, & \text{for } x \ne \frac{\pi}{2} \\ k, & \text{for } x = \frac{\pi}{2} \end{cases} is continuous at x=π2x = \frac{\pi}{2}, then the value of k is :

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  2. Question 2

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

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : f(x)={3x−8,x≤52k,x>5f(x) = \begin{cases} 3x - 8, & x \leq 5 \\ 2k, & x > 5 \end{cases} is continuous at x=5x = 5 for k=52k = \frac{5}{2}. Reason (R) : For a function f to be continuous at x=ax = a, lim⁡x→a−f(x)=lim⁡x→a+f(x)=f(a)\lim_{x \to a^{-}} f(x) = \lim_{x \to a^{+}} f(x) = f(a).

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  3. Question 3

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

    25 (b)
    If f(x)={2x−3,−3≤x≤−2x+1,−2<x≤0f(x) = \begin{cases} 2x - 3, & -3 \le x \le -2 \\ x + 1, & -2 < x \le 0 \end{cases} Check the differentiability of f(x)f(x) at x=−2x = -2.

  4. Question 4

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

    9
    If f(x)=−2x8f(x) = -2x^8, then the correct statement is :

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  5. Question 5

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

    18
    If ex+y=3xe^{x + y} = 3x, then dydx\dfrac{dy}{dx} is

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