PYQ Vault

Day 111: CBSE Class 12 Maths

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

  1. Question 1

    Integrals. Asked once: 2025 (same type asked 4 times)

    27 (a)
    Find : ∫2x−1(x−1)(x+2)(x−3) dx\int \frac{2x - 1}{(x - 1)(x + 2)(x - 3)}\,dx

  2. Question 2

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

    24
    Find : ∫e4x−1e4x+1 dx\displaystyle\int \dfrac{e^{4x} - 1}{e^{4x} + 1}\, dx

  3. Question 3

    Probability. Asked once: 2025 (same type asked 4 times)

    29 (b)
    The probability distribution of a random variable X is given as :
    X1232λ2\lambda3λ3\lambda4λ4\lambda
    P(X)1130\frac{11}{30}115\frac{1}{15}110\frac{1}{10}310\frac{3}{10}115\frac{1}{15}110\frac{1}{10}
    (i) Calculate λ\lambda, if E(X)=3⋅2E(X) = 3{\cdot}2. (ii) Find P(X>1)P(X > 1).

  4. Question 4

    Probability. Asked once: 2025 (same type asked 4 times)

    30 (a)
    A die with number 1 to 6 is biased such that P(2)=310P(2) = \dfrac{3}{10} and probability of other numbers is equal. Find the mean of the number of times number 2 appears on the dice, if the dice is thrown twice.

  5. Question 5

    Three Dimensional Geometry. Asked once: 2024 (same type asked 4 times)

    17
    The Cartesian equation of the line passing through the point (1,−3,2)(1, -3, 2) and parallel to the line : r⃗=(2+λ)i^+λj^+(2λ−1)k^\vec{r} = (2 + \lambda)\hat{i} + \lambda\hat{j} + (2\lambda - 1)\hat{k} is

    Tap an option to check your answer.