Correct Answer: 92.25 kg

Solution : Total number of staff members initially = 120
Their average weight = 62.5 kg
We know, Average = $\frac{\text{Sum of weights}}{\text{Number of people}}$
So, $62.5 = \frac{\text{Sum of weights}}{120}$
or, Sum of weights = 7500 kg
After a staff member left, the number of

Correct Answer: $\frac{1-\alpha^2}{2 \alpha}$

Solution : $\tan 40^{\circ}=\alpha$
$\frac{\tan 320^{\circ}-\tan 310^{\circ}}{1+\tan 320^{\circ} \cdot \tan 310^{\circ}}$
$= \frac{\tan(360°-40°) - \tan(270°+40°)}{1+\tan(360°-40°)\cdot\tan(270°+40°)}$
$= \frac{-\tan 40° + \cot 40°}{1-\tan40° \cdot\cot 40°}$
$= \frac{-\alpha + \frac{1}{\alpha}}{1+\alpha×\frac{1}{\alpha}}$
$= \frac{-\alpha^2 + 1}{2\alpha}$
$=\frac{1-\alpha^2}{2\alpha}$
Hence, the correct answer is $\frac{1-\alpha^2}{2\alpha}$.

Correct Answer: Three

Solution : The correct answer is Three.

On March 30, 2022, the Lok Sabha approved a measure that aims to combine Delhi's three municipal corporations into one. The purpose of the law is to guarantee a strong framework for coordinated planning, efficient resource use, and enhanced

Correct Answer: His community recognised his services.

Solution : The correct choice is the first option.

Active voice is the voice where the subject performs the action. When transforming a passive voice sentence into an active voice sentence the object of the passive voice becomes the subject of the active

Correct Answer: make a right choice

Solution : The second option is the correct choice.

Explanation: We use "make a choice" to express the act of selecting or deciding. "Take a choice" is not a standard phrase, making "make a right choice" the correct and appropriate phrase for expressing

Correct Answer: $\frac{1}{\sqrt{3}}$

Solution : $\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$
$= \tan (45^{\circ}-15^{\circ})$
$=\tan 30^{\circ}$
$= \frac{1}{\sqrt3}$
Hence, the correct answer is $\frac{1}{\sqrt3}$.

Correct Answer: Thoughtful

Solution : The correct choice is the third option.

Judicious refers to having or showing good judgement, discretion, or wisdom in making decisions or taking action. Thoughtful shares a similar connotation of being considerate, careful, and showing good judgement, which aligns well with the meaning of

Correct Answer: 2

Solution : Given: $x=8(\sin \theta+\cos \theta)$ and $y=9(\sin \theta-\cos \theta)$
Now, $\frac{x^2}{8^2}+\frac{y^2}{9^2}$
= $\frac{[8(\sin \theta+\cos \theta)]^2}{8^2}+\frac{[9(\sin \theta-\cos \theta)]^2}{9^2}$
= $\frac{64(\sin^2 \theta+\cos^2 \theta+2\sin \theta\cos \theta)}{64}+\frac{81(\sin^2 \theta+\cos^2 \theta-2\sin \theta\cos \theta)}{81}$
= $1+2\sin \theta\cos \theta +1-2\sin \theta\cos \theta$
= $2$
Hence, the correct answer is 2.

Correct Answer: Genuine

Solution : The sentence begins by talking about Rahul's reaction, which is "surprised." To complete the sentence correctly, we need a word that describes the kind of smile on Tarun's face. The word "genuine" fits perfectly in the context, indicating that the smile on Tarun's face was

Correct Answer: Renounce

Solution : The correct choice is the fourth option.

The appropriate antonym of renounce is endorse because it means to support or approve, while "renounce" means to formally reject or disapprove, providing a clear contrast in terms of approval or endorsement.

The meanings of the other options