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CUET · MATHS · PYQ PAPER 2025

Let X be a random variable. Let E(X) and Var(X) denote the mean and the variance of X respectively.
Match List - I with List - II
List - IList - II
(A) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(2 X +3)\) is(I) \(11 \alpha\)
(B) If \(E ( X )=\alpha\), then \(E (2 X )\) is(II) \(6 \alpha\)
(C) If \(\operatorname{Var}( X )=\alpha\), then \(\operatorname{Var}(3 X -\alpha)+\operatorname{Var}(\sqrt{2} X +\beta)\) is(III) \(4 \alpha\)
(D) If \(E(X) = 3\) \(\frac{5\alpha}{12}, \text{ then E(12X + } \alpha)\) is(IV) \(2 \alpha\)
Choose the correct answer from the options given below:

  1. A (A) - (IV), (B) - (III), (С) - (I), (D) - (II)
  2. B (А) - (III), (B) - (IV), (C) - (II), (D) - (I)
  3. C (А)- (III), (В) - (IV), (C) - (I), (D) - (II)
  4. D (А) - (III), (В) - (I), (C) - (IV), (D) - (II)
Verified Solution

Answer & Solution

Correct Answer

(A) (A) - (IV), (B) - (III), (С) - (I), (D) - (II)

Step-by-step Solution

Detailed explanation

(A) \( \operatorname{Var}(2 X +3) = 2^2 \operatorname{Var}(X) \) \( = 4\alpha \) (B) \( E (2 X ) = 2 E (X) \) \( = 2\alpha \) (C) \( \operatorname{Var}(3 X -\alpha)+\operatorname{Var}(\sqrt{2} X +\beta) = 3^2 \operatorname{Var}(X) + (\sqrt{2})^2 \operatorname{Var}(X) \)…
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