Correct Answer: 343

Solution : In each figure, the number on the left side is the square of the number given at the bottom of the figure and on the right side is the cube of the number given at the bottom of the figure.

Figure 1: 9² =

Correct Answer: Arun Goel

Solution : Correct answer is Arun Goel

Arun Goyal assumed the role of Election Commissioner of India on November 21, 2022. He is an Indian Administrative Service officer from the 1985 batch. His appointment was initially challenged in the Supreme Court due to procedural concerns,

Correct Answer: pay attention to

Solution : The correct choice is the second option.

The phrase lend an ear means to listen attentively or carefully while discussing a problem. Hence, the option, pay attention to is the correct meaning of the given idiom.

Correct Answer: behind

Solution : The most appropriate option is the third option.

Explanation:
The sentence structure indicates that the footprints being left are connected to the steps taken. Therefore, the most fitting word to follow leave and complete the sentence is behind, indicating the location where footprints are left

Correct Answer: sympathetic

Solution : The correct answer is the third option.

Sympathetic means feeling, showing, or expressing sympathy whereas callous means showing or having an insensitive and cruel disregard for others.

The meanings of the other options are as follows:

• Rationalistic: This term relates to a philosophical or religious

Correct Answer: Alimony

Solution : The correct option is the second option.

Explanation:
Alimony refers to the financial support or allowance that a husband provides to his wife after a legal separation or divorce. It is specifically related to the financial assistance or support given by one spouse to another,

Correct Answer: $-1$

Solution : $\sin 600^\circ \cos 750^\circ+\sin 150^\circ \cos 240^\circ$
$=\sin (540^\circ+60^\circ) \cos (720^\circ+30^\circ)+\sin (180^\circ-30^\circ) \cos (180^\circ+60^\circ)$
$= -\sin 60^\circ\cos 30^\circ + \sin 30^\circ ×(-\cos 60^\circ)$
$= (-\frac{\sqrt3}{2}$ ×$\frac{\sqrt3}{2})$ + $(\frac{1}{2} × \frac{-1}{2})$
$= \frac{-3}{4} -\frac{1}{4} = –1$
Hence, the correct answer is $-1$.

Correct Answer: 24

Solution : Given: Mean = 60 Median = 48
We know, Mode = (3 Median – 2 Mean)
⇒ Mode = (3 × 48) – (2 × 60)
⇒ Mode = 144 – 120
$\therefore$ Mode = 24
Hence, the correct answer is 24.

Correct Answer: $r^{2}(\pi -2)$

Solution :

Let the radius of the circle be $r$ units.
Area of circle = $\pi r^2$
Diagonal of ABCD = BD = $2r$ units
Area of square = $\frac{1}{2}\times \text{(BD)}^2$
= $\frac{1}{2}\times 4r^2$
= $2r^2$
Required difference = Area of the circle – Area of

Correct Answer: 2

Solution : Given: $a^{3}+\frac{1}{a^{3}}=2$
⇒ $a^{3}+\frac{1}{a^{3}}=2$
⇒ $a^{6}+1 =2a^3$
⇒ $a^{6}-2a^3+1=0$
⇒ $(a^3-1)^2=0$
$a = 1$, the above equation is satisfied.
Now putting $a = 1$, in the equation, we get
$\frac{a^{2}+1}{a} = \frac{1^{2}+1}{1} = 2$
Hence, the correct answer is 2.