PYQ Vault

Day 42: CBSE Class 12 Maths

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

  1. Question 1

    Matrices. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    3
    Which of the following properties is/are true for two matrices of suitable orders ? (i) (A+B)′=A′+B′(A + B)' = A' + B' (ii) (A−B)′=B′−A′(A - B)' = B' - A' (iii) (AB)′=A′B′(AB)' = A'B' (iv) (kAB)′=kB′A′(kAB)' = kB'A' (k is a scalar)

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  2. Question 2

    Matrices. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    2
    If A and B are square matrices of same order, then which of the following statements is/are always true ? (i) (A+B)(A−B)=A2−B2(A + B) (A - B) = A^2 - B^2 (ii) AB=BAAB = BA (iii) (A+B)2=A2+AB+BA+B2(A + B)^2 = A^2 + AB + BA + B^2 (iv) AB=0⇒A=0AB = 0 \Rightarrow A = 0 or B=0B = 0

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  3. Question 3

    Matrices. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    34 (b)
    Given that P=[2−134]P = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}, Q=[5274]Q = \begin{bmatrix} 5 & 2 \\ 7 & 4 \end{bmatrix} and R=[2538]R = \begin{bmatrix} 2 & 5 \\ 3 & 8 \end{bmatrix}, find a matrix S such that PQ−RSPQ - RS is a null matrix.

  4. Question 4

    Probability. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    31 (b)
    The probability of simultaneous occurrence of atleast one of the two events X and Y is a. If the probability that exactly one of the events X, Y occurs is b, prove that P(X′)+P(Y′)=2−2a+bP(X') + P(Y') = 2 - 2a + b.

  5. Question 5

    Relations and Functions. This type asked 3 times: 2023, 2024, 2026. This one: 2026

    32
    Show that f:R→Rf : R \to R defined as f(x)=x1+x2f(x) = \dfrac{x}{\sqrt{1 + x^2}} is one-one but not onto.