Correct Answer: 37 : 36

Solution : Total sales of 1st branch for both the years = 80 + 105 = 185
Total sales of 4th branch for both the years = 85 + 95 = 180
$\therefore$ Ratio of 1st to 4th = 185 : 180 = 37 :

Correct Answer: 6, 4, 2, 3, 5, 1

Solution : Given:
1. Tertiary 2. Terrace 3. Terrain 4. Termite 5. Territory 6. Terminate

Step 1: The first, second, and third letters of each word are the same, so move on to the next letter.
Step 2: The fourth letter of

Correct Answer: India

Solution : The correct option is India.

In 2016, India's defence budget saw a notable increase of 8.5 per cent, reaching a total of $55.9 billion, solidifying its position as the world's fifth-largest contributor to military expenditure. In 2023, India's defence budget of INR 5.94 trillion (equivalent

Correct Answer: Bangladesh

Solution : The correct option is Bangladesh.

Bangladesh is located to the east of India. Bangladesh shares its eastern border with the Indian states of West Bengal, Assam, Meghalaya, and Tripura. To the west, north, and south of Bangladesh, it shares borders with India as well.

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, $2^{3}[(1^{3}+2^{3}+3^{3}+4^{3}+....+15^{3})-(1^{3}+2^{3}+3^{3}+4^{3}+5^{3}+6^{3})]$