CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000?

Official previous-year question

Held on 21 May 2025 · Verified 13 Jul 2026.

Options

A
10%
B
5%
C
7%
D
12%

Did you get this right?

Solution

Given: $f(x) = \tan x - 4x$ where $x \in (0, \frac{\pi}{2})$

A function is strictly decreasing when its derivative is negative.

Taking the derivative:

$f'(x) = \sec^2 x - 4$

For the function to be strictly decreasing:

$f'(x) < 0$

$\sec^2 x - 4 < 0$

$\sec^2 x < 4$

Since $\sec^2 x = \frac{1}{\cos^2 x}$ :

$\frac{1}{\cos^2 x} < 4$

$1 < 4\cos^2 x$

$\cos^2 x > \frac{1}{4}$

Taking the square root (note that $\cos x$ is positive in $(0, \frac{\pi}{2})$ ):

$\cos x > \frac{1}{2}$

The value $\cos x = \frac{1}{2}$ at $x = \frac{\pi}{3}$

Since cosine decreases from 1 to 0 as $x$ goes from 0 to $\frac{\pi}{2}$ , the inequality $\cos x > \frac{1}{2}$ holds when $x < \frac{\pi}{3}$ .

Combined with the given domain:

$0 < x < \frac{\pi}{3}$

Therefore, the function is strictly decreasing in the interval $(0, \frac{\pi}{3})$ .

Your note

CUET UG Statistics & Applications in other years

Statistics & Applications 2024

More CUET UG Statistics & Applications questions

The behavior and pattern of the data in a time series is NOT based on which of the following component?

2025medium

Which of the following is not correct about the Compound Annual Growth Rate (CAGR)?

2025medium

An automobile dealer wishes to buy four luxury cars of different brands given in the table below with some down payment and balance in equal monthly installments (EMI) for 10 years. The bank charges 9% interest per annum compounded monthly. $\left( {Given } \frac{0.0075 \times(1.0075)^{120}}{(1.0075)^{120}-1} = 0.01266\right)$ | Luxury Car | Price of the Car (in Rs.) | Down payment (in Rs.) | |---|---|---| | P | 25,00,000 | 5,00,000 | | Q | 35,00,000 | 12,00,000 | | R | 45,00,000 | 15,00,000 | | S | 42,00,000 | 15,00,000 | Match List-I with List-II | List-I | List-II | |---|---| | Luxury Car | EMI (in Rs.) | | (A) P | (I) 34,182 | | (B) Q | (II) 37,980 | | (C) R | (III) 29,118 | | (D) S | (IV) 25,320 | Choose the correct answer from the options given below:

2025medium

What sum of money is needed to invest now, so as to get ₹5000 at the beginning of every month forever, if the money is worth 6% per annum compounded monthly?

2025medium

Mr. X wishes to purchase a flat for Rs. 44,65,000 with a down payment of Rs. 10,00,000 and balance in equated monthly installments (EMI) for 25 years. If the bank charges 6 % per annum compounded monthly, the EMI is: [Given: $(1.005)^{300} =4.4650$]

2025medium

View all Statistics & Applications questions

Keep practicing Statistics & Applications

Work through every CUET UG Statistics & Applications PYQ, year by year.

Browse all Mathematics topics

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

At what rate of interest will the present value of a perpetuity of Rs. 1000 payable at the end of every six months be Rs. 40000?

Official previous-year question

Held on 21 May 2025 · Verified 13 Jul 2026.

Options

A
10%
B
5%
C
7%
D
12%

Did you get this right?

Solution

Given: $f(x) = \tan x - 4x$ where $x \in (0, \frac{\pi}{2})$

A function is strictly decreasing when its derivative is negative.

Taking the derivative:

$f'(x) = \sec^2 x - 4$

For the function to be strictly decreasing:

$f'(x) < 0$

$\sec^2 x - 4 < 0$

$\sec^2 x < 4$

Since $\sec^2 x = \frac{1}{\cos^2 x}$ :

$\frac{1}{\cos^2 x} < 4$

$1 < 4\cos^2 x$

$\cos^2 x > \frac{1}{4}$

Taking the square root (note that $\cos x$ is positive in $(0, \frac{\pi}{2})$ ):

$\cos x > \frac{1}{2}$

The value $\cos x = \frac{1}{2}$ at $x = \frac{\pi}{3}$

Since cosine decreases from 1 to 0 as $x$ goes from 0 to $\frac{\pi}{2}$ , the inequality $\cos x > \frac{1}{2}$ holds when $x < \frac{\pi}{3}$ .

Combined with the given domain:

$0 < x < \frac{\pi}{3}$

Therefore, the function is strictly decreasing in the interval $(0, \frac{\pi}{3})$ .

Your note

CUET UG Statistics & Applications in other years

Statistics & Applications 2024

More CUET UG Statistics & Applications questions

The behavior and pattern of the data in a time series is NOT based on which of the following component?

2025medium

Which of the following is not correct about the Compound Annual Growth Rate (CAGR)?

2025medium

What sum of money is needed to invest now, so as to get ₹5000 at the beginning of every month forever, if the money is worth 6% per annum compounded monthly?

2025medium

View all Statistics & Applications questions

Keep practicing Statistics & Applications

Work through every CUET UG Statistics & Applications PYQ, year by year.

Browse all Mathematics topics

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

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