PYQ Vault

Day 110: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked once: 2025 (same type asked 4 times)

    12
    If projection of a⃗=αi^+j^+4k^\vec{a} = \alpha\hat{i} + \hat{j} + 4\hat{k} on b⃗=2i^+6j^+3k^\vec{b} = 2\hat{i} + 6\hat{j} + 3\hat{k} is 4 units, then α\alpha is

    Tap an option to check your answer.

  2. Question 2

    Vector Algebra. Asked once: 2026 (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) : The vectors a⃗\vec{a} and (−2a⃗)(-2\vec{a}), where a⃗≠0⃗\vec{a} \ne \vec{0} are collinear vectors. Reason (R) : a⃗⋅(−2a⃗)=0\vec{a} \cdot (-2\vec{a}) = 0.

    Tap an option to check your answer.

  3. Question 3

    Application of Integrals. Asked once: 2024 (same type asked 4 times)

    13
    Area of the region bounded by curve y2=4xy^2 = 4x and the X-axis between x=0x = 0 and x=1x = 1 is :

    Tap an option to check your answer.

  4. Question 4

    Differential Equations. Asked once: 2024 (same type asked 4 times)

    29
    Find the particular solution of the differential equation given by x2dydx−xy=x2cos⁡2(y2x)x^2 \frac{dy}{dx} - xy = x^2 \cos^2 \left( \frac{y}{2x} \right), given that when x=1x = 1, y=π2y = \frac{\pi}{2}.

  5. Question 5

    Integrals. Asked once: 2025 (same type asked 4 times)

    34 (a)
    Evaluate : ∫0π/4sin⁡xcos⁡xcos⁡4x+sin⁡4x dx\int\limits_0^{\pi/4} \frac{\sin x \cos x}{\cos^4 x + \sin^4 x}\, dx