Correct Answer: $\frac{\sqrt{3}}{2}$

Solution : Given:
$\cos^2 \theta=\frac{3}{4}$
⇒ $\cos \theta=\pm\frac{\sqrt3}{2}$
$\theta$ is an acute angle i.e. it will be less than 90°.
$\therefore \cos \theta=-\frac{\sqrt3}{2}$ will be rejected.
⇒ $\cos \theta=\frac{\sqrt3}{2}$
⇒ $\theta = 30°$
Now we have to find $\sin \left(\theta+30^{\circ}\right)$
$ = \sin(30° + 30°) = \sin

Correct Answer: I heard raucous laughter from the next room.

Solution : The correct choice is the fourth option.

Raucous is the correct spelling and it means loud and unpleasant.

Therefore, the correct sentence will be: I heard raucous laughter from the next room.

Correct Answer: $60^{\circ}$

Solution :
Given: AB is the chord of a circle such that AB = 10 cm.
The diameter of the circle is 20 cm.
The line segment connecting any two points on the circle's circumference is known as the chord of a circle.
In $\triangle AOC$,
AO

Correct Answer: (1)

Solution : The correct choice is the first option.

The word "too" should be replaced with "to" as "too" is an adverb that means in excess or also. Here, "to" is used to form the perfect infinitive with "have". So, "she seems to have subsisted" would

Correct Answer: $3abc$

Solution : Using the identity: $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$.
If $a + b + c = 0$, 
$a^3 + b^3 + c^3 - 3abc = 0$
⇒ $a^3

Correct Answer: 2

Solution : Given: $2 \sin \theta+2 \sin ^2 \theta=2$
⇒ $2\sin\theta + 2\sin^2\theta = 2(\sin^2\theta + \cos^2\theta)$
⇒ $2\sin\theta + 2\sin^2\theta = 2\sin^2\theta + 2\cos^2\theta$
⇒ $2\sin\theta = 2\cos^2\theta$
⇒ $\sin\theta = \cos^2\theta$
Putting the value in the given equation,
$2 \cos ^4 \theta+2 \cos ^2 \theta$

Correct Answer: 35

Solution : Given: The numbers are from 53 to 97.
Numbers with more than two factors are called composite numbers.
The composite number between 53 and 97 = 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77,

Correct Answer: 4

Solution : The correct option is 4

There are four main categories of microorganisms:

• Bacteria are single-celled microorganisms with no nucleus and no membrane-bound organelles.
• Algae are water-bound, photosynthetic, nucleus-bearing organisms that lack genuine roots, stems, and leaves.
• Fungi are eukaryotic microorganisms such as yeasts, moulds, and

Correct Answer: Neither I nor II

Solution : $33^{3}$ = $33^{3}$
$3^{33} =(3^{11})^3$
Since $3^{11}$ is clearly greater than $33$,
Thus, $3^{33} > 33^{3}$
So, statement I is false.
Now, $(3^3)^3 = 27^3 = (729×27)>333$
So, statement II is also false.
Hence, the correct answer is 'Neither I nor II'.

Correct Answer: Purify Islam

Solution : The correct answer is to Purify Islam.

By overthrowing non-Islamic rulers, the political goal was to impose an Islamic state. In India, the Wahabi movement focused mainly on achieving its religious, political, and social objectives. Purification, and dissemination of true Islamic principles were the