PYQ Vault

Day 64: CBSE Class 12 Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Probability. Asked once: 2026 (same type asked 5 times)

    18
    For two events A and B such that P(A)≠0P(A) \neq 0 and P(B)≠1P(B) \neq 1, P(A′/B′)=P(A'/B') =

    Tap an option to check your answer.

  2. Question 2

    Probability. Asked once: 2026 (same type asked 5 times)

    31 (a)
    The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that (i) target is hit (ii) atleast one shot misses the target.

  3. Question 3

    Three Dimensional Geometry. Asked once: 2025 (same type asked 5 times)

    31 (b)
    Find the shortest distance between the lines : r⃗=(2i^−j^+3k^)+λ(i^−2j^+3k^)\vec{r} = (2\hat{i} - \hat{j} + 3\hat{k}) + \lambda(\hat{i} - 2\hat{j} + 3\hat{k}) r⃗=(i^+4k^)+μ(3i^−6j^+9k^)\vec{r} = (\hat{i} + 4\hat{k}) + \mu(3\hat{i} - 6\hat{j} + 9\hat{k}).

  4. Question 4 (case study, 4 parts)

    Application of Derivatives. Asked once: 2025 (same type asked 4 times)

    A ladder of fixed length ‘h’ is to be placed along the wall such that it is free to move along the height of the wall. Based upon the above information, answer the following questions :
    37 (i)
    Express the distance (y) between the wall and foot of the ladder in terms of ‘h’ and height (x) on the wall at a certain instant. Also, write an expression in terms of h and x for the area (A) of the right triangle, as seen from the side by an observer.
    37 (ii)
    Find the derivative of the area (A) with respect to the height on the wall (x), and find its critical point.
    37 (iii) (a)
    Show that the area (A) of the right triangle is maximum at the critical point.
    37 (iii) (b)
    If the foot of the ladder whose length is 5 m, is being pulled towards the wall such that the rate of decrease of distance (y) is 2 m/s, then at what rate is the height on the wall (x) increasing, when the foot of the ladder is 3 m away from the wall ?

  5. Question 5

    Application of Derivatives. Asked once: 2025 (same type asked 4 times)

    26
    Find the interval/intervals in which the function f(x)=sin⁡3x−cos⁡3xf(x) = \sin 3x - \cos 3x, 0<x<π20 < x < \dfrac{\pi}{2} is strictly increasing.