For the given 5 values, 15, 18, 21,… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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For the given 5 values, 15, 18, 21, 27,39; the three year moving averages are:

Official previous-year question

Held on 14 May 2025 · Verified 13 Jul 2026.

Options

A
18,21,29
B
18,22,29
C
18, 23, 37
D
18, 20,28

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Solution

To determine the properties of $f(x) = 10x$ , we need to check if the function is one-one (injective) and onto (surjective).

A function is one-one if $f(x_1) = f(x_2)$ implies $x_1 = x_2$ .

Suppose $f(x_1) = f(x_2)$

$10x_1 = 10x_2$

$x_1 = x_2$

Therefore, $f$ is one-one.

A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is onto if for every real number $y$ , there exists an $x$ such that $f(x) = y$ .

Let $y$ be any real number. Solve for $x$ :

$f(x) = y$

$10x = y$

$x = \frac{y}{10}$

Since $y$ is a real number, $\frac{y}{10}$ is also a real number. Every real number can be achieved as an output.

Therefore, $f$ is onto.

Since $f(x) = 10x$ is both one-one and onto, the function is bijective.

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