PYQ Vault

Day 82: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked once: 2024 (same type asked 3 times)

    24
    If a⃗\vec{a} and b⃗\vec{b} are two non-zero vectors such that (a⃗+b⃗)⊥a⃗(\vec{a} + \vec{b}) \perp \vec{a} and (2a⃗+b⃗)⊥b⃗(2\vec{a} + \vec{b}) \perp \vec{b}, then prove that ∣b⃗∣=2  ∣a⃗∣|\vec{b}| = \sqrt{2} \; |\vec{a}|.

  2. Question 2

    Application of Derivatives. Asked once: 2025 (same type asked 3 times)

    9
    f(x)=xxf(x) = x^x has a critical point at :

    Tap an option to check your answer.

  3. Question 3

    Application of Derivatives. Asked once: 2025 (same type asked 3 times)

    5
    The values of λ\lambda so that f(x)=sin⁡x−cos⁡x−λx+Cf(x) = \sin x - \cos x - \lambda x + C decreases for all real values of x are :

    Tap an option to check your answer.

  4. Question 4

    Application of Derivatives. Asked once: 2025 (same type asked 3 times)

    26
    Find the value of 'a' for which f(x)=3sin⁡x−cos⁡x−2ax+6f(x) = \sqrt{3}\sin x - \cos x - 2ax + 6 is decreasing in R.

  5. Question 5

    Application of Integrals. Asked once: 2023 (same type asked 3 times)

    32
    Using integration, find the area of the region bounded by the circle x2+y2=16x^2 + y^2 = 16, line y=xy = x and y-axis, but lying in the 1st quadrant.