Algebra

Relations & Functions

Medium

core

Consider a function $f:\left[0,\frac{\pi}{2}\right] \to R$ , given by $f(x)=\sin x$ and $g:\left[0,\frac{\pi}{2}\right] \to R$ , given by $g(x)=\cos x$ , Where R is a set of real numbers, Which of the following statements are correct?

(A) f and g are one-one

(B) f and g are not one-one

(C) f+g is not one-one

(D) f+g is one-one

Choose the correct answer from the options given below:

(A) and (C) only

(B) and (C) only

(A) and (D) only

✅ Correct Option: 1

On $[0,\frac{\pi}{2}]$ , $\sin x$ is strictly increasing and $\cos x$ is strictly decreasing, so both are one-one and (A) holds.

$(f+g)(x)=\sqrt2\sin\left(x+\frac{\pi}{4}\right)$ peaks at $x=\frac{\pi}{4}$ ; for instance $(f+g)(0)=(f+g)\left(\frac{\pi}{2}\right)=1$ , so it is not one-one and (C) holds.

2026: 21 May Shift 2

The relation R on the set N of natural numbers defined as $R = \{(x,y): y = x+3 \text{ and } x \le 5\}$ is

2025: 30 May Shift 2

The relation R on the set of real numbers defined by $R = \{(a, b): a \leq b^2\}$ is

(A) Reflexive

(B) Not symmetric

(D) Transitive

Choose the correct answer from the options given below:

2022: 17 Aug Shift 2

Which of the following figures shows a bijective function from set $X_1$ to set $X_2$ :

Choose the correct answer from the options given below :

2022: 16 July Shift 2

If $f:\mathbb{R} \to [-5, \infty)$ is defined as $f(x) = x^2 - 5$ , then the function f is

A. one-one

B. many-one

C. onto

D. into

Which of the above statements are true?

Choose the correct answer from the options given below:

2025: 13 May Shift 2

Match List-I with List-II

Let $f: A \rightarrow B$ be a function given by $f(x) = x^2$

List-I	List-II
Domain and Co-domain	Kind
(A) $A = \mathbb{R}$ and $B = \mathbb{R}$	(I) $f$ is both one-one and onto
(B) $A = \mathbb{R}$ and $B = [0, \infty]$	(II) $f$ is one-one but not onto
(C) $A = B = [0, \infty]$	(III) $f$ is not one-one but onto
(D) $A = [0, \infty]$ and $B = \mathbb{R}$	(IV) $f$ is neither one-one nor onto

Choose the correct answer from the options given below:

2022: 30 Aug Shift 1

Which of the following is true on the basis of above diagram?

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)