PYQ Vault

Day 98: 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 2 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=6i^+2j^−8k^\vec{a} = 6\hat{i} + 2\hat{j} - 8\hat{k} b⃗=10i^−2j^−6k^\vec{b} = 10\hat{i} - 2\hat{j} - 6\hat{k} c⃗=4i^−4j^+2k^\vec{c} = 4\hat{i} - 4\hat{j} + 2\hat{k} represent the sides of a right angled triangle. Reason (R) : Three non-zero vectors of which none of two are collinear forms a triangle if their resultant is zero vector or sum of any two vectors is equal to the third.

    Tap an option to check your answer.

  2. Question 2

    Application of Integrals. Asked once: 2022 (same type asked 2 times)

    7
    If the area of the region bounded by the line y=mxy = mx and the curve x2=yx^2 = y is 323\dfrac{32}{3} sq. units, then find the positive value of m, using integration.

  3. Question 3

    Application of Integrals. Asked once: 2022 (same type asked 2 times)

    11
    Find the area of the region bounded by curve 4x2=y4x^2 = y and the line y=8x+12y = 8x + 12, using integration.

  4. Question 4

    Integrals. Asked once: 2023 (same type asked 2 times)

    26
    Evaluate : ∫0π2[log⁡(sin⁡x)−log⁡(2cos⁡x)] dx\int\limits_{0}^{\frac{\pi}{2}} [\log (\sin x) - \log (2 \cos x)] \, dx.

  5. Question 5

    Probability. Asked once: 2022 (same type asked 2 times)

    1
    A bag contains 3 red and 4 white balls. Three balls are drawn at random, one-by-one without replacement from the bag. If the first ball drawn is red in colour, then find the probability that the remaining two balls drawn are also red in colour.