PYQ Vault

Day 129: CBSE Class 12 Maths

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

  1. Question 1

    Application of Derivatives. Asked once: 2023 (same type asked 2 times)

    21
    If the product of two positive numbers is 9, find the numbers so that the sum of their squares is minimum.

  2. Question 2

    Application of Derivatives. Asked once: 2023 (same type asked 2 times)

    32 (a)
    The median of an equilateral triangle is increasing at the rate of 232\sqrt{3} cm/s. Find the rate at which its side is increasing.

  3. Question 3

    Continuity and Differentiability. Asked once: 2024 (same type asked 2 times)

    24 (a)
    If y=cos⁡x+yy = \sqrt{\cos x + y}, prove that dydx=sin⁡x1−2y\frac{dy}{dx} = \frac{\sin x}{1 - 2y}.

  4. Question 4

    Continuity and Differentiability. Asked once: 2024 (same type asked 2 times)

    30 (b)
    Find dydx\dfrac{dy}{dx}, if 5x+5y=5x+y5^x + 5^y = 5^{x+y}.

  5. Question 5

    Determinants. Asked once: 2024 (same type asked 2 times)

    34 (b)
    If A=[1cot⁡x−cot⁡x1]A = \begin{bmatrix} 1 & \cot x \\ -\cot x & 1 \end{bmatrix}, show that A′A−1=[−cos⁡2x−sin⁡2xsin⁡2x−cos⁡2x]A'A^{-1} = \begin{bmatrix} -\cos 2x & -\sin 2x \\ \sin 2x & -\cos 2x \end{bmatrix}.