PYQ Vault

Day 123: CBSE Class 12 Maths

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

  1. Question 1

    Matrices. Asked once: 2024 (same type asked 3 times)

    5
    Let A=[1−1202−33−24]A = \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} and B=13[−20192−361λ]B = \dfrac{1}{3}\begin{bmatrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & \lambda \end{bmatrix}. If AB=IAB = I, then the value of λ\lambda is :

    Tap an option to check your answer.

  2. Question 2

    Probability. Asked once: 2024 (same type asked 3 times)

    31
    E and F are two independent events such that P(E‾)=0⋅6P(\overline{E}) = 0{\cdot}6 and P(E∪F)=0⋅6P(E \cup F) = 0{\cdot}6. Find P(F) and P(E‾∪F‾)P(\overline{E} \cup \overline{F}).

  3. Question 3

    Probability. Asked once: 2023 (same type asked 3 times)

    31 (a)
    Two numbers are selected from first six even natural numbers at random without replacement. If X denotes the greater of two numbers selected, find the probability distribution of X.

  4. Question 4

    Relations and Functions. Asked once: 2024 (same type asked 3 times)

    26 (b)
    A function f is defined from R→RR \to R as f(x)=ax+bf(x) = ax + b, such that f(1)=1f(1) = 1 and f(2)=3f(2) = 3. Find function f(x). Hence, check whether function f(x) is one-one and onto or not.

  5. Question 5

    Relations and Functions. Asked once: 2025 (same type asked 3 times)

    28 (a)
    A student wants to pair up natural numbers in such a way that they satisfy the equation 2x+y=412x + y = 41, x, y∈Nx,\ y \in N. Find the domain and range of the relation. Check if the relation thus formed is reflexive, symmetric and transitive. Hence, state whether it is an equivalence relation or not.