A 95% confidence interval for a population mean was reported to be 152 to 160. If standard deviation σ = 15… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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A 95% confidence interval for a population mean was reported to be 152 to 160. If standard deviation $\sigma = 15$ . Then the sample size is : ( $Z_{0.025}$ =1.96)

Official previous-year question

Held on 29 May 2025 · Verified 13 Jul 2026.

Options

A
40
B
60
C
54
D
50

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Solution

For a differential equation:

Order = The highest derivative in the equation

Degree = The power of the highest order derivative (after removing fractions/radicals)

In this problem:

Order = 4 (contains fourth derivative $\frac{d^4y}{dx^4}$ )
Degree = 1 (fourth derivative appears to power 1)

The number of arbitrary constants in the general solution of a differential equation equals the order of the differential equation.

The degree does not affect the number of constants.

For this differential equation:

Order = 4

Therefore, number of arbitrary constants = 4

When solving a differential equation of order 4, integration is performed 4 times:

First integration introduces constant $C_1$
Second integration introduces constant $C_2$
Third integration introduces constant $C_3$
Fourth integration introduces constant $C_4$

The general solution contains 4 arbitrary constants: $C_1, C_2, C_3, C_4$

Number of arbitrary constants = 4

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