Correct Answer: 60

Solution :
Given, $\overline{\mathrm{BD}} \perp \overline{\mathrm{AC}}$
$\mathrm{BD}=12 \mathrm{~cm}$, $\mathrm{m}(\overline{\mathrm{AD}})=6 \mathrm{~cm}$ and $\mathrm{m}(\overline{\mathrm{CD}})=4 \mathrm{~cm}$
$AC = AD + CD = 10$ cm
Area of $\Delta ABC$ = $\frac{1}{2}\times \text{base}\times \text{height}$
= $\frac{1}{2}\times AC\times BD$
= $\frac{1}{2}\times (6+4)\times 12$
= $60$ cm²
Hence, the correct answer is 60.

Correct Answer: Charles Cornwallis

Solution : The correct option is Charles Cornwallis.

The Permanent Settlement in Bengal was introduced in 1793 during the governorship of Lord Cornwallis. Lord Cornwallis was the Governor General of Bengal from 1786 to 1793. The Permanent Settlement, also known as the Cornwallis Code, aimed to

Correct Answer: isosceles trapezium

Solution : In an isosceles trapezium, the two non-parallel sides are equal and at least two pairs of consecutive angles are congruent.
Hence, the correct answer is isosceles trapezium.

Correct Answer: 43.75%

Solution : Marks of division F = 45
Marks of Division C = 80
Difference = 80 – 45 = 35
So, the required percentage = $\frac{35}{80}\times100$ = 43.75%
Hence, the correct answer is 43.75%.

Correct Answer: 900

Solution : The marked price (MP) = Selling price (SP) × $\frac{100}{(100-\text{discount percentage})}$
The trousers were purchased for INR 765 after a 15% discount, which means that INR 765 is 85% of the marked price (MP) (because 100% – 15% = 85%).
MP = 765 × $\frac{100}{85}$

Correct Answer: (3)

Solution : The third option is the correct choice. 

''Doing sightseeing'' should be replaced with ''sightseeing'', thereby indicating the idea of spending time visiting places of interest in the historical city.

The use of '"doing" before ''sightseeing'' is redundant since ''sightseeing'' in the sentence already implies the

Correct Answer: Nirbhaya Fund

Solution : The correct option is the Nirbhaya Fund

The One Stop Centre (OSC) Scheme for women is funded by the Nirbhaya Fund. The Nirbhaya Fund was set up in India to support initiatives that enhance the safety, and security of women, especially in the context

Correct Answer: 100

Solution : Given:
5, 10, 20, 37, 63, X

Here, the pattern is as follows –

So, 100 is the missing number of the series. Hence, the first option is correct.

Correct Answer: Three

Solution : Given:
AMPLIFY

When the letters of AMPLIFY are arranged in alphabetical order, the letter cluster formed is AFILMPY.

So, 3 letters i.e. A, L, and Y are in the same position as before. Hence, the first option is correct.

Correct Answer: (10, 25, 100)

Solution : Given:
(12, 24, 144)

Like, 12 = 12 × 1, 24 = 12 × 2, 144 = 12 × 12
Let's check the options –
First option: (10, 25, 100); 10 = 10 × 1, 25 = 5 × 5, 100 = 10