Correct Answer:

Solution : Based on the general information, the lens is used in the spectacles. So, the circle that represents the lens will lie inside the circle that represents spectacles. But, the mirror is not related to spectacles and lenses. So, the circle that represents the mirror will be drawn separately from the other two circles.
Therefore, the Venn diagram is as follows –

Hence, the fourth option is correct.

Correct Answer: 570

Solution : Total number of people = 2500
People who have saving habit is 60% = $\frac{60}{100}$ × 2500 = 1500
People who saves with bank is 30% = $\frac{30}{100}$ × 1500 = 450
People who saves with post office is 32% = $\frac{32}{100}$ × 1500 = 480
Remaining people who save with share = 1500 –  450 – 480 = 570
Hence, the correct answer is 570.

Correct Answer: 1,00,000

Solution : Let the present value of the motorcycle be $x$.
Value after 2 years $= x × (1-\frac{R}{100})^2$, where $R$ is the rate.
So, $84640 = x × (1-\frac{8}{100})^2$
⇒ $84640 = x × (\frac{23}{25})^2$
⇒ $x =84640 \times \frac{25\times 25}{23 \times 23}$
$\therefore x= 1,00,000$
Present Value = Rs. 1,00,000
Hence, the correct answer is 1,00,000.

Correct Answer: 13

Solution : Given:
The number which when added to itself 14 times gives 195.

Let the number be x
According to the question –
x + 14x = 195
15x = 195
x = 13

Therefore, the number is 13. Hence, the second option is correct.

Correct Answer: C

Solution : Given:
(I) Only 2 people sit to the right of D. G is an immediate neighbour of D. Only 3 people sit between A and G. F sits to the immediate right of G.

(II) Only 2 people sit between B and C. E is not an immediate neighbour of C.

So, C sits to the immediate left of A. Hence, the second option is correct.

Correct Answer: SRUF

Solution : Given:
BEST : WVHE :: CROP : ?

Follow the pattern to obtain the required code –

Thus, BEST is coded as WVHE.
Similarly, follow the same pattern for CROP –
 

Thus, CROP is coded as SRUF. Hence, the second option is correct. 

Correct Answer: INR 2 lakh

Solution : The correct option is INR 2 lakh.

The amount of insurance coverage available for accidental death under the Pradhan Mantri Suraksha Bima Yojana (PMSBY) is INR 2 lakh. The PMSBY is a government-backed insurance scheme that provides accidental death and disability coverage at an affordable premium.

Correct Answer: 15 overs/h

Solution : The correct option is 15 overs/h.

In Test cricket, the International Cricket Council (ICC) has set a minimum required over rate of 15 overs per hour. According to the ICC playing conditions, if a team fails to meet this required overrate, they may face penalties, including fines for the captain and potential suspension for repeat offences.

Correct Answer: $2 \sqrt{5}$

Solution : Given: 
$a-\frac{1}{a}=4$
Squaring both sides, we get,
⇒ $a^2+\frac{1}{a^2}-2=16$
⇒ $a^2+\frac{1}{a^2}=16+2$
⇒ $a^2+\frac{1}{a^2}=18$
Adding 2 on both sides, we get,
⇒ $a^2+\frac{1}{a^2}+2=18+2$
⇒ $(a+\frac{1}{a})^2=20$
$\therefore a+\frac{1}{a}=2\sqrt5$
Hence, the correct answer is $2\sqrt5$.

Correct Answer: $\frac{\sqrt3}{2}$

Solution : $\frac{\tan\theta +\cot\theta }{\tan\theta -\cot\theta }=2$
Use rule of componendo and dividendo i.e. If $\frac{a}{b}=\frac{c}{d}$ then, $\frac{a+b}{a-b}=\frac{c+d}{c-d}$. we have,
⇒ $\frac{\tan\theta +\cot\theta +\tan\theta -\cot\theta}{\tan\theta +\cot\theta -\tan\theta +\cot\theta}=\frac{2+1}{2-1}$
⇒$\frac{2\tan\theta}{2\cot\theta} = 3$
⇒ $\tan^2\theta=3$
⇒ $\sin^2\theta= 3\cos^2\theta$
⇒ $\sin^2\theta= 3(1-\sin^2\theta)$
⇒ $4\sin^2\theta= 3$
⇒ $\sin\theta=\frac{ \sqrt3 }{2}$
Hence, the correct answer is $\frac{ \sqrt3 }{2}$.