The simple random sample consists of six… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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The simple random sample consists of six observations: 5, 8, 10, 7, 10, 14. The point estimate of the population mean is:

Official previous-year question

Held on 14 May 2025 · Verified 13 Jul 2026.

Options

A
1
B
4
C
9
D
25

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Solution

The region is bounded by:

$y^2 = 4x$ : A parabola opening to the right
$y$ -axis: The line $x = 0$
$y = 3$ : A horizontal line at height 3

The region is a slice between the $y$ -axis (left edge) and the parabola (right edge), from $y = 0$ to $y = 3$ .

From the parabola equation $y^2 = 4x$ , we express $x$ in terms of $y$ :

$x = \frac{y^2}{4}$

The region extends from $x = 0$ (the $y$ -axis) to $x = \frac{y^2}{4}$ (the parabola) for each value of $y$ from $0$ to $3$ .

The area is given by:

$\text{Area} = \int_{0}^{3} \left(\frac{y^2}{4} - 0\right) dy$

$= \int_{0}^{3} \frac{y^2}{4} dy$

$= \frac{1}{4} \int_{0}^{3} y^2 \, dy$

$= \frac{1}{4} \left[\frac{y^3}{3}\right]_{0}^{3}$

$= \frac{1}{4} \left[\frac{27}{3} - 0\right]$

$= \frac{1}{4} \times 9$

$= \frac{9}{4}$

Therefore, the area of the region is $\frac{9}{4}$ square units.

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