Correct Answer: $3a$

Solution : Given:
$a^3-7a-6$
= $a^3-a-6a-6$
= $a(a^2-1)-6(a+1)$
= $a(a-1)(a+1)-6(a+1)$
= $(a+1)(a^2-a-6)$
= $(a+1)(a-3)(a+2)$
So, three factors x, y, z are $(a+1)(a-3)(a+2)$.
$\therefore x+y+z= (a+1)+(a-3)+(a+2)=3a$
Hence, the correct answer is $3a$.

Correct Answer: 15 years

Solution : The total age difference of the group = number of members × change in average age = 5 × 3 = 15
As the average remains the same, the required difference is 15 years.
Hence, the correct answer is 15 years.

Correct Answer: Potassium

Solution : The correct option is potassium.

Malleability refers to the quality of metals that permits them to be hammered or moulded into thin sheets. Because of its softness and limited mechanical strength, potassium cannot be beaten into sheets. It reacts quickly with oxygen and moisture,

Correct Answer: Defamation

Solution : The third option is the correct choice.

Defamation specifically refers to the action of damaging the good reputation of someone through false statements or actions.

The meanings of the other options are as follows:

• A delegate refers to a person designated to represent others or

Correct Answer: $\frac{5}{4}$

Solution : Let the fraction be $x$.
According to the question,
$x-\frac{1}{x}=\frac{9}{20}$
$\Rightarrow 20x^2-9x-20=0$
$\Rightarrow 20x^2-25x + 16x-20=0$
$\Rightarrow 5x (4x-5) + 4x (4x-5)=0$
$\Rightarrow (4x-5) (5x+4)=0$
$\Rightarrow (4x-5) =0$ or $ (5x+4)=0$
$\therefore x=\frac{-4}{5},\frac{5}{4}$
Hence, the correct answer is $\frac{5}{4}$.

Correct Answer: 75° and 60°

Solution : Let the two angles be x and y.
So, x + y = 135°------------------------------(1)
The difference of the two angles is $\frac{\pi}{12}$.
So, x – y = $\frac{\pi}{12}=\frac{180}{12}$ = 15° ---------------------------(2)
Solving equations (1) and (2), we get,
x = 75°
So, y

Correct Answer:

Solution : Since the rotation is restricted. So, the embedded figure will have the same orientation as the main figure. By comparison of the question figure with all the option figures, the given question figure is embedded only in the first option figure.

Hence, the first option is

Correct Answer: (a)   (b)   (c)   (d)

3       4     1    2

Solution : The correct answer is 

(a)   (b)   (c)   (d)

3       4     1    2

Mark Spitz is a former American swimmer and won 9 gold medals in the 1972 Summer Olympics, the most ever won by a single athlete at

Correct Answer: Exhilarated

Solution : The correct option is the fourth option.

Explanation:
Exhilarated means feeling very happy, animated, or excited about something. In the context of the sentence, the speaker couldn't sleep due to being too eager, indicating a high level of excitement or enthusiasm, which aligns well

Correct Answer: Leave has been applied for by Harsh.

Solution : The correct choice is the third option.

Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in the