PYQ Vault

Day 22: CBSE Class 12 Maths

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

  1. Question 1

    Vector Algebra. Asked 2 times: 2022*, 2024 (* = numbers or wording changed that year)

    30
    Find the projection of vector (b⃗+c⃗)(\vec{b} + \vec{c}) on vector a⃗\vec{a}, where a⃗=2i^+2j^+k^\vec{a} = 2\hat{i} + 2\hat{j} + \hat{k}, b⃗=i^+3j^+k^\vec{b} = \hat{i} + 3\hat{j} + \hat{k} and c⃗=i^+k^\vec{c} = \hat{i} + \hat{k}.

  2. Question 2

    Vector Algebra. Asked 2 times: 2022*, 2024 (* = numbers or wording changed that year)

    21
    a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} are three mutually perpendicular unit vectors. If θ\theta is the angle between a⃗\vec{a} and (2a⃗+3b⃗+6c⃗)(2\vec{a} + 3\vec{b} + 6\vec{c}), find the value of cos⁡θ\cos \theta.

  3. Question 3

    Three Dimensional Geometry. Asked 2 times: 2023*, 2024 (* = numbers or wording changed that year)

    16
    If a line makes an angle of π4\dfrac{\pi}{4} with the positive directions of both x-axis and z-axis, then the angle which it makes with the positive direction of y-axis is :

    Tap an option to check your answer.

  4. Question 4

    Application of Integrals. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    34
    Using integration, find the area of region bounded by line y=3xy = \sqrt{3}x, the curve y=4−x2y = \sqrt{4 - x^2} and y-axis in first quadrant.

  5. Question 5

    Application of Integrals. Asked 2 times: 2022*, 2023 (* = numbers or wording changed that year)

    35
    Find the area of the region bounded by the curves x2=yx^2 = y, y=x+2y = x + 2 and x-axis, using integration.