Correct Answer: 6

Solution : Let the quotient when the number is divided by 45 be $x$.
Then, the number should be 45$x$ + 21
= (15 × 3$x$) + 21
Let 3$x$ = P.
So, 45$x$ + 21 = 15P + 21
So, it is clear that 15P is

Correct Answer: 5295

Solution : Given:
17 + 17 = 2895; 19 + 19 = 3615

Like, 17 + 17 = 2895→17² = 289
Now, on adding 5 at the unit place the result will be 2895.
And, 19 + 19 = 3615→19² = 361
Now, on adding

Correct Answer: ripen

Solution : The second option is correct as 'ripen' means to become mature and is ready to be plucked, which contextually fits in the sentence, while plucking of mangoes doesn't go contextually well with other options namely 'germinate', 'age' and 'grow'.

Therefore, the correct statement should

Correct Answer: 2

Solution : The correct choice is the second option.

In passive constructions, the present continuous tense often employs being, followed by the past participle of the main verb. In this context, being used independently is the appropriate structure.

So, the correct sentence is: It also indicates

Correct Answer: 28 days

Solution : Total work = 14 × 60 = 840 units.
Number of days required for 30 people = $\frac{840}{30} = 28$ days.
Hence, the correct answer is 28 days.

Correct Answer: 111672

Solution : Given:
$14^{3}+16^{3}+18^{3}+.....+30^{3}$
$= 2^{3}\times7^{3}+2^{3}\times8^{3}+2^{3}\times9^{3}+.....+2^{3}\times15^{3}$
$= 2^{3}(7^{3}+8^{3}+9^{3}+.....+15^{3})$
$= 2^{3}[(1^{3}+2^{3}+3^{3}+4^{3}+....+15^{3})-(1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3})]$
The sum of cubes of $n$ natural numbers$ =\left[\frac{n(n+1)}{2}\right]^2$
For $n = 6$, we have
$1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3}=\left[\frac{6(6+1)}{2}\right]^2 = \left[\frac{42}{2}\right]^2 = (21)^{2} =$ 441
For $n = 15$, we have
$1^{3}+2^{3}+3^{3}+4^{3}+....+15^{3}=\left[\frac{15(15+1)}{2}\right]^2 = \left[\frac{240}{2}\right]^2 = (120)^{2} =$ 14400
Now, $2^{3}[(1^{3}+2^{3}+3^{3}+4^{3}+....+15^{3})-(1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3})]$

Correct Answer: Alpine grassland

Solution : The Correct Answer is-  Alpine grassland 

Alpine grassland dominates the Himalayan mountains' typical natural vegetation above 3600 meters. Silver fur, pine birch, and other important trees are listed. A natural alpine grassland at a high elevation, the Alpine-steppe is a subregion of the Montane

Correct Answer: 7

Solution : Given: $p^2+q^2=7pq$
Divide the above equation by $pq$ on both sides, we get,
⇒ $\frac{p^2+q^2}{pq}=\frac{7pq}{pq}$
⇒ $\frac{p}{q}+\frac{q}{p}=7$
Hence, the correct answer is 7.

Correct Answer: pursue

Solution : "Pursue" means to actively and diligently work towards a goal or objective, which is exactly the action one should take with their career. Therefore, the correct word to fill in the blank is "pursue."

Correct Answer: (46, 92, 414)

Solution : Given:
(28, 65, 261), (37, 83, 342)

(28, 65, 261); 261 – 65 = 196; 196 ÷ 7 = 28
(37, 83, 342); 342 – 83 = 259; 259 ÷ 7 = 37
Let's check the options –
First option: (39, 42, 393);