PYQ Vault

Day 65: CBSE Class 12 Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

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

    7
    If f(x)={sin⁡xx+cos⁡x,x≠0k,x=0f(x) = \begin{cases} \dfrac{\sin x}{x} + \cos x, & x \neq 0 \\ k, & x = 0 \end{cases} is continuous at x=0x = 0, then the value of k is :

    Tap an option to check your answer.

  2. Question 2

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

    8
    If f(x)={1,if x≤3ax+b,if 3<x<57,if 5≤xf(x) = \begin{cases} 1, & \text{if } x \le 3 \\ ax + b, & \text{if } 3 < x < 5 \\ 7, & \text{if } 5 \le x \end{cases} is continuous in R, then the values of a and b are :

    Tap an option to check your answer.

  3. Question 3 (case study, 4 parts)

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

    Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as follows : f(x)={x4−4x2+4,0≤x<3x2+40,x≥3f(x) = \begin{cases} x^4 - 4x^2 + 4, & 0 \leq x < 3 \\ x^2 + 40, & x \geq 3 \end{cases} Based on given information, answer the following questions :
    38 (i)
    Find f′(x)f'(x) for 0<x<30 < x < 3.
    38 (ii)
    Find f′(4)f'(4)
    38 (iii) (a)
    Test for continuity of f(x)f(x) at x=3x = 3.
    38 (iii) (b)
    Test for differentiability of f(x)f(x) at x=3x = 3.

  4. Question 4

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

    28
    Differentiate y=log⁡{sin⁡(x33−1)}y = \sqrt{\log\left\{\sin\left(\dfrac{x^3}{3} - 1\right)\right\}} with respect to x.

  5. Question 5

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

    21 (b)
    If 3(x2+y2)=4xy\sqrt{3}(x^2 + y^2) = 4xy, then find dydx\frac{dy}{dx} at (12,32)\left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right).