Consider the following hypothesis H_0: μ… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

Consider the following hypothesis

$H_0: \mu = 315$ and $H_a: \mu \neq 315$

A sample of 60 provided a sample mean of 324.6. The standard deviation ( $\sigma$ ) is 14 and level of significance $\alpha = 0.05$ . Then the confidence interval is:

[Given: $Z_{a/2}{\frac{14}{\sqrt60}} = 3.54$ ]

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
(321.06, 328.14)
B
(320.06, 327.14)
C
(322.06, 327.14)
D
(321.06, 327.14)

Did you get this right?

Solution

Given that the derivative of $ax^3 + ax^2 + ax + 1$ equals $9x^2 + 6x + 3$ .

Differentiating $ax^3 + ax^2 + ax + 1$ term by term:

$\frac{d}{dx}[ax^3] = 3ax^2$

$\frac{d}{dx}[ax^2] = 2ax$

$\frac{d}{dx}[ax] = a$

$\frac{d}{dx}[1] = 0$

The derivative is $3ax^2 + 2ax + a$

Setting the derivative equal to the given expression:

$3ax^2 + 2ax + a = 9x^2 + 6x + 3$

For two polynomials to be equal, coefficients of corresponding powers must be equal.

Comparing coefficients of $x^2$ :

$3a = 9$

$a = 3$

Comparing coefficients of $x$ :

$2a = 6$

$a = 3$

Comparing constant terms:

$a = 3$

Therefore, $a = 3$

Your note

CUET UG Statistics & Applications in other years

Statistics & Applications 2024

More CUET UG Statistics & Applications questions

The rise in prices before Diwali is an example of

2025easy

Mr. X purchased a house from a company for ₹ 7,00,000 and made a down payment of ₹ 1,50,000. He repays the balance in 25 years by equal monthly installments at 9 % per annum compounded monthly. The equated monthly installment (EMI) is: [Given that : (1.0075)⁻³⁰⁰ = 0.106]

2025medium

With reference to sampling, which of the following are correct? (A) Simple random sampling is probability sampling (B) Snow-ball sampling is non-probability sampling (C) Stratified sampling is probability sampling (D) Cluster sampling is non-probability sampling Choose the correct answer from the options given below:

2025medium

Let us suppose that two independent random samples of sizes $n_1$ and $n_2$ has been drawn from the same normal population then degree of freedom of statistic t-distribution is:

2025medium

The effective rate equivalent to a nominal rate of 12% compounded quarterly is: (Given $(1.03)^4=1.1256$)

2025medium

View all Statistics & Applications questions