For the following data: | | Size | Mean | Standard deviation | |---|---|---|---| | Sample 1 | 4 | 40 | 8 | | Sample 2 | 5 | 50 | 10 | The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to

For the following data: | | Size | Mean… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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For the following data:

	Size	Mean	Standard deviation
Sample 1	4	40	8
Sample 2	5	50	10

The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
11
B
10
C
7
D
9

Did you get this right?

Solution

For a 2×2 matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ , the determinant equals $(a × d) - (b × c)$ .

Calculate the left side determinant:

$\begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix}$

$= (2x)(x) - (5)(8)$

$= 2x^2 - 40$

Calculate the right side determinant:

$\begin{vmatrix} 3 & 0 \\ 4 & -8 \end{vmatrix}$

$= (3)(-8) - (0)(4)$

$= -24$

Set the determinants equal:

$2x^2 - 40 = -24$

$2x^2 = 16$

$x^2 = 8$

$x = \pm\sqrt{8}$

$x = \pm 2\sqrt{2}$

Therefore, the values of $x$ are $\pm 2\sqrt{2}$ .

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