CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

Mr. X invested Rs. 4,00,000 in shares for 5 years. The value of this investment was Rs. 4,50,000 at the end of the second year, Rs. 490000 at the end of the third year and on maturity, the final value stood at Rs. 6,00,000. The compound annual growth rate of this investment is:

[Given that: $(1.5)^{1/5} = 1.084]$

Official previous-year question

Held on 15 May 2025 · Verified 13 Jul 2026.

Options

A
8.4 %
B
10.8 %
C
9.084 %
D
11 %

Did you get this right?

Solution

Given: $\displaystyle \int e^x\left(\frac{x-1}{(x+1)^3}\right)dx = \frac{Ae^x}{(x+1)^B} + C$

For integrals involving $e^x$ , the formula is:

$\int e^x[f(x) + f'(x)]dx = e^x \cdot f(x) + C$

From the answer form $\frac{Ae^x}{(x+1)^B}$ , let:

$f(x) = \frac{A}{(x+1)^B}$

Finding $f'(x)$ :

$f'(x) = A \cdot (-B) \cdot (x+1)^{-B-1}$

$f'(x) = \frac{-AB}{(x+1)^{B+1}}$

Calculate $f(x) + f'(x)$ :

$f(x) + f'(x) = \frac{A}{(x+1)^B} + \frac{-AB}{(x+1)^{B+1}}$

$= \frac{A(x+1) - AB}{(x+1)^{B+1}}$

$= \frac{A(x+1-B)}{(x+1)^{B+1}}$

Matching with the given expression:

$\frac{A(x+1-B)}{(x+1)^{B+1}} = \frac{x-1}{(x+1)^3}$

Comparing denominators:

$B + 1 = 3$

$B = 2$

Comparing numerators:

$A(x+1-B) = x-1$

Substituting $B = 2$ :

$A(x-1) = x-1$

$A = 1$

Therefore:

(B) $A = 1$ is correct

(D) $B = 2$ is correct

The correct answer is: (B) and (D) only

Your note

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Solution

Given: $\displaystyle \int e^x\left(\frac{x-1}{(x+1)^3}\right)dx = \frac{Ae^x}{(x+1)^B} + C$

For integrals involving $e^x$ , the formula is:

$\int e^x[f(x) + f'(x)]dx = e^x \cdot f(x) + C$

From the answer form $\frac{Ae^x}{(x+1)^B}$ , let:

$f(x) = \frac{A}{(x+1)^B}$

Finding $f'(x)$ :

$f'(x) = A \cdot (-B) \cdot (x+1)^{-B-1}$

$f'(x) = \frac{-AB}{(x+1)^{B+1}}$

Calculate $f(x) + f'(x)$ :

$f(x) + f'(x) = \frac{A}{(x+1)^B} + \frac{-AB}{(x+1)^{B+1}}$

$= \frac{A(x+1) - AB}{(x+1)^{B+1}}$

$= \frac{A(x+1-B)}{(x+1)^{B+1}}$

Matching with the given expression:

$\frac{A(x+1-B)}{(x+1)^{B+1}} = \frac{x-1}{(x+1)^3}$

Comparing denominators:

$B + 1 = 3$

$B = 2$

Comparing numerators:

$A(x+1-B) = x-1$

Substituting $B = 2$ :

$A(x-1) = x-1$

$A = 1$

Therefore:

(B) $A = 1$ is correct

(D) $B = 2$ is correct

The correct answer is: (B) and (D) only

CUET UG 2025 — Mathematics Statistics & Applications

Options

Did you get this right?

Solution

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CUET UG Statistics & Applications in other years

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Other Mathematics topics for CUET UG

Algebra

Calculus

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Geometry

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CUET UG 2025 — Mathematics Statistics & Applications

Options

Did you get this right?

Solution

Your note

CUET UG Statistics & Applications in other years

More CUET UG Statistics & Applications questions

Other Mathematics topics for CUET UG

Algebra

Calculus

Applied-Mathematics

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Statistics & Applications