PYQ Vault

Day 135: CBSE Class 12 Maths

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

  1. Question 1

    Probability. Asked once: 2025 (same type asked 5 times)

    17
    If P(A)=17P(A) = \dfrac{1}{7}, P(B)=57P(B) = \dfrac{5}{7} and P(A∩B)=47P(A \cap B) = \dfrac{4}{7}, then P(A‾∣B)P(\overline{A} \mid B) is :

    Tap an option to check your answer.

  2. Question 2

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

    31
    A survey was conducted on the patients who have undergone knee replacement surgeries. It was found that, Robotic Knee replacement surgeries have 90% success rate. On a particular day, robotic surgery was performed on three patients, A, B and C, one after the other. Assuming that the success and failure of each surgery is independent of each other, find the probability that : (i) exactly one surgery is successful, (ii) at most two surgeries are successful.

  3. Question 3

    Three Dimensional Geometry. Asked once: 2024 (same type asked 5 times)

    35 (a)
    Find the distance between the line x2=2y−64=1−z−1\dfrac{x}{2} = \dfrac{2y-6}{4} = \dfrac{1-z}{-1} and another line parallel to it passing through the point (4,0,−5)(4, 0, -5).

  4. Question 4

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

    33
    The relation between the height of the plant (y cm) with respect to exposure to sunlight is governed by the equation y=4x−12x2y = 4x - \frac{1}{2}x^2, where x is the number of days exposed to sunlight. (i) Find the rate of growth of the plant with respect to sunlight. (ii) In how many days will the plant attain its maximum height ? What is the maximum height ?

  5. Question 5

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

    21
    Determine whether the function f(x)=x2−6x+3f(x) = x^2 - 6x + 3 is increasing or decreasing in [4, 6].