Correct Answer: $(4,–9)$

Solution : Given: The point is $(4,7)$ and the line is $y=–1$.
The formula for the reflection of the point $(x_1, y_1)$ over the line $ax+by+c=0$ is $\frac{x–x_1}{a}=\frac{y–y_1}{b}=\frac{–2(ax_1+by_1+c)}{a^2+b^2}$.
Here, are the values of $a=0$, $b=1$, and $c=1$.
$(x–4)=0$ and $(y–7)=\frac{–2(7+1)}{1}$
⇒ $x=4$ and $y=–16+7$
⇒ $x=4$ and

Correct Answer: 729

Solution : Given:
64 : 4 :: ? : 9

Like, 64 : 4→4³ = 64
Similarly, follow the same pattern for (?) : 9→9³ = 729

So, 729 is related to 9. Hence, the third option is correct.

Correct Answer: Lord Dalhousie

Solution : The correct option is - Lord Dalhousie

The Doctrine of Lapse was introduced by Lord Dalhousie, who served as the Governor-General of India from 1848 to 1856. It allowed the British to annex a princely state if it lacked a natural heir, and the

Correct Answer: 2 hours

Solution : The ratio of the speed of the boat in still water to the speed of the stream is 8 : 3.
The boat can travel 22 km downstream in 24 minutes.
Let the speed of the boat in still water be 8x and the

Correct Answer: Conclusion I follows

Solution : According to the above given statement,

Conclusion I: Ram is admitted – It is given that only first-division holders are admitted, and Ram is a first-division holder. So, Ram is admitted. Therefore, this conclusion logically follows.
Conclusion II: Only Ram is admitted –

Correct Answer: 36

Solution : The correct answer is 36.

Lakshadweep Island is the smallest union territory of India and is located in the Arabian Sea on the Western Coast of India. There are 36 islands in the Lakshadweep archipelago. They are coral islands and are rich in diversity. Among

Correct Answer: $\frac{12}{13}$

Solution : $\sec \theta+\tan \theta=5$---(1)
We know, $\sec^2 \theta-\tan^2 \theta=1$
⇒ $(\sec \theta+\tan \theta)(\sec \theta-\tan \theta)=5$
⇒ $\sec \theta-\tan \theta=\frac{1}{5}$---(2)
Solving equations 1 and 2, we get,
$\sec \theta=\frac{13}{5}$, $\tan\theta=\frac{12}{5}$
So, $\cos\theta=\frac{1}{\sec\theta}=\frac{5}{13}$
$\tan\theta=\frac{12}{5}$
⇒ $\frac{\sin\theta}{\cos\theta}=\frac{12}{5}$
⇒ $\frac{\sin\theta}{\frac{5}{13}}=\frac{12}{5}$
$\therefore \sin \theta=\frac{12}{13}$
Hence, the correct answer is $\frac{12}{13}$.

Correct Answer: enumerate

Solution : The second option is the correct choice.

Itemise means to detail or list items, tasks, or things individually. Enumerate means to list things one by one, which makes it the correct synonym.

The meanings of the other options are as follows:

• Impart: This means to

Correct Answer: essential

Solution : The correct answer is the fourth option.

Explanation: The word essential, which means crucial or extremely important, fits best in the context, suggesting that upgrading the higher education sector is crucial or necessary for improving India's global ranking.

The meanings of the other options are

Correct Answer: Mouse

Solution : Given:
Ant : Fly : Bee :: Hamster : Squirrel : ?

Like, Ant, Fly, and Bee are all insects.
Similarly, Hamsters and Squirrels are rodents and Mouse is also a rodent.

Hence, the third option is correct.