If X is a random variable and $a$, $b$ are real numbers, then which of the following statements are true? (A) $Var(aX+b) = a^2 Var(X)$ (B) $E(aX+b)= a E(X) + b$ (C) $E(aX+b)= a E(X) - E(b)$ (D) $Var(aX+b)= a Var(X) + b$ Choose the correct answer from the options given below:

CUET UG 2025 — Mathematics Algebra

2025mcqmedium

If X is a random variable and $a$ , $b$ are real numbers, then which of the following statements are true?

(A) $Var(aX+b) = a^2 Var(X)$

(B) $E(aX+b)= a E(X) + b$

(D) $Var(aX+b)= a Var(X) + b$

Choose the correct answer from the options given below:

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
(A) and (B) only
B
(A) and (C) only
C
(B) and (D) only
D
(A), (C) and (D) only

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Solution

The equation $9x^2 + 4y^2 = 36$ has both $x^2$ and $y^2$ terms with different coefficients that are added together. This is an ellipse.

The standard form of an ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ .

Dividing the entire equation by 36:

$\frac{9x^2}{36} + \frac{4y^2}{36} = \frac{36}{36}$

$\frac{x^2}{4} + \frac{y^2}{9} = 1$

From $\frac{x^2}{4} + \frac{y^2}{9} = 1$ :

$a^2 = 4$ , so $a = 2$

$b^2 = 9$ , so $b = 3$

The area of an ellipse is given by $A = \pi ab$ .

$A = \pi \times 2 \times 3$

$A = 6\pi$

Therefore, the area of the region enclosed by the curve is $6\pi$ square units.

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Solution

The equation $9x^2 + 4y^2 = 36$ has both $x^2$ and $y^2$ terms with different coefficients that are added together. This is an ellipse.

The standard form of an ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ .

Dividing the entire equation by 36:

$\frac{9x^2}{36} + \frac{4y^2}{36} = \frac{36}{36}$

$\frac{x^2}{4} + \frac{y^2}{9} = 1$

From $\frac{x^2}{4} + \frac{y^2}{9} = 1$ :

$a^2 = 4$ , so $a = 2$

$b^2 = 9$ , so $b = 3$

The area of an ellipse is given by $A = \pi ab$ .

$A = \pi \times 2 \times 3$

$A = 6\pi$

Therefore, the area of the region enclosed by the curve is $6\pi$ square units.

CUET UG 2025 — Mathematics Algebra

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CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

Your note

CUET UG Algebra in other years

More CUET UG Algebra questions

Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Algebra