The average cost function for a… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

2025mcqmedium

The average cost function for a commodity is given by $AC = 0.05x^2 - 5x + 1000 + \frac{3000}{x}$ in terms of output x. The fixed cost is

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
1000
B
3000
C
5
D
0.05

Did you get this right?

Solution

For an $n \times n$ matrix $A$ , the determinant of a scalar multiple is given by $|kA| = k^n \times |A|$ .

For an $n \times n$ matrix $A$ , the determinant of the adjoint matrix is given by $|adj\ A| = |A|^{n-1}$ .

Given: Order of matrix $A$ is $3$ and $|A| = 2$

To find $|adj\ 2A|$ , first find $|2A|$ .

$|2A| = 2^3 \times |A|$

$|2A| = 8 \times 2$

$|2A| = 16$

Now treat $2A$ as a single matrix. Since $2A$ is also a $3 \times 3$ matrix:

$|adj\ 2A| = |2A|^{3-1}$

$|adj\ 2A| = |2A|^2$

$|adj\ 2A| = (16)^2$

$|adj\ 2A| = 256$

Therefore, $|adj\ 2A| = 256$ .

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

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

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

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