PYQ Vault

Day 227: CBSE Class 12 Maths

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

  1. Question 1

    Three Dimensional Geometry. Asked once: 2023 (same type asked 4 times)

    25 (b)
    The equations of a line are 5x−3=15y+7=3−10z5x - 3 = 15y + 7 = 3 - 10z. Write the direction cosines of the line and find the coordinates of a point through which it passes.

  2. Question 2

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

    9 (a)
    The two adjacent sides of a parallelogram are represented by vectors 2i^−4j^+5k^2\hat{i} - 4\hat{j} + 5\hat{k} and i^−2j^−3k^\hat{i} - 2\hat{j} - 3\hat{k}. Find the unit vector parallel to one of its diagonals. Also, find the area of the parallelogram.

  3. Question 3

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

    8
    If a⃗=2i^−j^+k^\vec{a} = 2\hat{i} - \hat{j} + \hat{k}, b⃗=i^+j^−2k^\vec{b} = \hat{i} + \hat{j} - 2\hat{k} and c⃗=i^+3j^−k^\vec{c} = \hat{i} + 3\hat{j} - \hat{k} and the projection of vector c⃗+λb⃗\vec{c} + \lambda \vec{b} on vector a⃗\vec{a} is 262\sqrt{6}, then find the value of λ\lambda.

  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) : For two non-zero vectors a⃗\vec{a} and b⃗\vec{b}, a⃗⋅b⃗=b⃗⋅a⃗\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{a}. Reason (R) : For two non-zero vectors a⃗\vec{a} and b⃗\vec{b}, a⃗×b⃗=b⃗×a⃗\vec{a} \times \vec{b} = \vec{b} \times \vec{a}.

    Tap an option to check your answer.

  5. Question 5

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

    22
    Evaluate : ∫0a3x2x6+a6 dx\displaystyle\int_0^{a^3} \dfrac{x^2}{x^6 + a^6}\, dx