PYQ Vault

Day 172: CBSE Class 12 Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2022 (same type asked 4 times)

    6
    Write the cartesian equation of the line PQ passing through points P(2,2,1)P(2, 2, 1) and Q(5,1,−2)Q(5, 1, -2). Hence, find the y-coordinate of the point on the line PQ whose z-coordinate is −2-2.

  2. Question 2

    Vector Algebra. Asked once: 2022 (same type asked 4 times)

    2
    In a parallelogram PQRS, PQ→=3i^−2j^+2k^\overrightarrow{PQ} = 3\hat{i} - 2\hat{j} + 2\hat{k} and PS→=−i^−2k^\overrightarrow{PS} = -\hat{i} - 2\hat{k}. Find ∣PR→∣|\overrightarrow{PR}| and ∣QS→∣|\overrightarrow{QS}|.

  3. Question 3

    Vector Algebra. Asked once: 2023 (same type asked 4 times)

    14
    A unit vector a^\hat{a} makes equal but acute angles on the co-ordinate axes. The projection of the vector a^\hat{a} on the vector b⃗=5i^+7j^−k^\vec{b} = 5\hat{i} + 7\hat{j} - \hat{k} is

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  4. Question 4

    Vector Algebra. Asked once: 2024 (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) : Projection of a⃗\vec{a} on b⃗\vec{b} is same as projection of b⃗\vec{b} on a⃗\vec{a}. Reason (R) : Angle between a⃗\vec{a} and b⃗\vec{b} is same as angle between b⃗\vec{b} and a⃗\vec{a} numerically.

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  5. Question 5

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

    35
    If A1A_1 denotes the area of region bounded by y2=4xy^2 = 4x, x=1x = 1 and x-axis in the first quadrant and A2A_2 denotes the area of region bounded by y2=4xy^2 = 4x, x=4x = 4, find A1:A2A_1 : A_2.