Correct Answer: $1$

Solution : Given, $\frac{a+b}{a-b} \div \frac{(a+b)^2}{\left(a^2-b^2\right)}$
$=\frac{(a+b)(a^2-b^2)}{(a-b)(a+b)^2}$
$=\frac{(a+b)(a+b)(a-b)}{(a-b)(a+b)^2}$
$=1$
Hence, the correct answer is $1$.

Correct Answer: 6.5 km

Solution : Firstly, we will draw the diagram as per the given instructions –

The distance between the initial point (A) and the final point (F) = 2.5 + 4 = 6.5 km

So, Raju is 6.5 km away from the starting point. Hence, the first

Correct Answer: 56.25%

Solution : The cost price of 1 kg potato = INR 20
Selling price of 800gm potato = INR 25
The cost price of 800 gm potato = $\frac{20\times 800}{1000}$ = INR 16
Profit percentage = $\frac{\text{Selling price – Cost price}}{\text{Cost price}}×100$
= $\frac{25-16}{16}\times100$
= $56.25$%
Hence,

Correct Answer: INR 822

Solution : Given: Selling price = INR 402
Loss = 33%
Selling price = 67%
Let the cost price be $x$.
So, $\frac{67x}{100}=402$
$\therefore x = 600$
To get 37% profit, selling price = $\frac{137}{100}\times$cost price $=\frac{137}{100}\times600=822$
Hence, the correct answer is INR 822.

Correct Answer: reserved

Solution : The correct choice is the third option.

"Discreet" means to be careful in actions to keep something confidential, and "reserved" suggests being careful and restrained in one's behaviour. 

The meanings of the other options are as follows:

• "Loud" means capable of producing much noise.
• "Noisy"

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

Solution : Given, $\cos 5 \alpha=\sin \alpha$
We know, $\cos(90°-\theta)=\sin\theta$
⇒ $\cos5\alpha=\cos(90°-\alpha)$
⇒ $5\alpha=90°-\alpha$
⇒ $6\alpha=90°$
⇒ $\alpha=15°$
Now, $\tan 2 \alpha=\tan(2\times 15°)=\tan30°=\frac{1}{\sqrt3}$
Hence, the correct answer is $\frac{1}{\sqrt3}$.

Correct Answer: 1001 A.D.

Solution : The correct option is 1001 A.D.

The Battle of Peshawar between Raja Jayapala and Mahmud of Ghazni took place in 1001. Mahmud, the ruler of the Ghaznavid Empire, sought to expand his empire into the Indian subcontinent. The battle was a significant conflict in

Correct Answer: 266

Solution : Given:
(536, 428, 365)

The sum of the digits of the given numbers is constant.
536 = 5 + 3 + 6 = 14
428 = 4 + 2 + 8 = 14
365 = 3 + 6 + 5 = 14

Let's check the

Correct Answer: Profit, 3.5%

Solution : Suppose, the number of goods is 100.
Here cost price is denoted by CP, selling price is denoted by SP.
CP of each item = Rs.1
Total CP = Rs. 100
Then the number of items remaining after theft = 90
SP of 1

Correct Answer: Rs. 2,376

Solution : Given: Length, $h$ = 120 cm
Diameter = 84 cm
Radius, $r$ = 42 cm
The curved surface area of the cylinder = $2\pi rh$ where $r$ is the radius and $h$ is the height of the cylinder. 
Area covered by roller in 1