The maximum value of ( x)( x) is : Option 1: 1 Option 2: 1/2 Option 3: 1/4 Option 4: √2

Answer: 1/2. Solution: x x = 1/2 2x. Maximum value of 2x is 1, so max of x x is 1/2.

Geometry

Trigonometry

Easy

core

The maximum value of $(\sin x)(\cos x)$ is :

$\frac{1}{2}$

$\frac{1}{4}$

$\sqrt{2}$

✅ Correct Option: 2

$\sin x \cos x = \frac{1}{2}\sin 2x$ . Maximum value of $\sin 2x$ is 1, so max of $\sin x \cos x$ is $\frac{1}{2}$ .

2025: 3 June Shift 2

The value of $\tan^{-1}(2) + \tan^{-1}(3)$ is equal to

2023: 30 May Shift 3

Let $a \leq \tan^{-1} x + \cot^{-1} x + \sin^{-1} x \leq b$ . If $\alpha$ and $\beta$ denote the minimum and maximum possible values of a and b respectively, then :

2022: 6 Aug Shift 2

The value of $\cos^{-1} \left( \sin \left( \cos^{-1} \frac{1}{2} \right) \right) + \tan^{-1}(1)$

2025: 26 May Shift 2

Arrange the principal values of the following functions in ascending order

(A) $\cosec^{-1}(2)$

(B) $\tan^{-1}(-\sqrt{3})$

(D) $\tan^{-1}\left(\cos\frac{3\pi}{7}\right)$

Choose the correct answer from the options given below:

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) $\tan^{-1}\frac{2}{11} + \tan^{-1}\frac{7}{24}$	(I) $\frac{3\pi}{4}$
(B) $\tan^{-1}2 + \tan^{-1}3$	(II) $\pi$
(C) $\tan^{-1}1 + \tan^{-1}2 + \tan^{-1}3$	(III) $\tan^{-1}\frac{1}{2}$
(D) $\tan^{-1}\frac{1}{7} + \tan^{-1}\frac{1}{13}$	(IV) $\tan^{-1}\frac{2}{9}$

Choose the correct answer from the options given below:

2025: 22 May Shift 1

The value of $\tan^2(\sec^{-1} 2) + \cot^2(\cosec^{-1} 3)$ is equal to

The maximum value of (sin⁡x)(cos⁡x)(\sin x)(\cos x)(sinx)(cosx) is :

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CUET Mathematics Past Year Questions (Topic-Wise)

The maximum value of $(\sin x)(\cos x)$ is :