PYQ Vault

Day 48: CBSE Class 12 Maths

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

  1. Question 1

    Matrices. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    26
    Find the value of x, if [1x1][1322511532][12x]=O.\begin{bmatrix} 1 & x & 1 \end{bmatrix} \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 2 \\ x \end{bmatrix} = O.
  2. Question 2

    Matrices. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    1
    If A=[500050005]A = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}, then A3A^3 is :

    Tap an option to check your answer.

  3. Question 3

    Probability. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    7
    If E and F are two independent events such that P(E)=23P(E) = \frac{2}{3}, P(F)=37P(F) = \frac{3}{7}, then P(E/F‾)P(E/\overline{F}) is equal to :

    Tap an option to check your answer.

  4. Question 4

    Probability. This type asked 3 times: 2022, 2023, 2025. This one: 2025

    25 (a)
    10 identical blocks are marked with '0' on two of them, '1' on three of them, '2' on four of them and '3' on one of them and put in a box. If X denotes the number written on the block, then write the probability distribution of X and calculate its mean.
  5. Question 5

    Relations and Functions. This type asked 3 times: 2023, 2024, 2025. This one: 2025

    26 (a)
    Show that the function f:R→Rf : R \to R defined by f(x)=4x3−5f(x) = 4x^3 - 5, ∀ x∈R\forall\ x \in R is one-one and onto.