Correct Answer: (125, 25, 100)

Solution : Given:
(23, 14, 9); (37, 19, 18)

Here, (23, 14, 9)→14 + 9 = 23
(37, 19, 18)→19 + 18 = 37

Let's check the options –
First option: (125, 25, 5)→25 + 5 = 30 ≠ 125
Second option: (125, 100, 5)→100

Correct Answer: $2 \sqrt{3}$ cm

Solution : Given: ABC is an equilateral triangle with a side of 12 cm.
The length of the inradius of the equilateral triangle = $\frac{\text{side}}{2\sqrt3}=\frac{12}{2\sqrt3}=2\sqrt3$ cm
Hence, the correct answer is $2\sqrt3$ cm.

Correct Answer: 15 : 9

Solution : Let's check the options –
First option: 20 : 11; (11 × 2) – 2 = 22 – 2 = 20
Second option: 6 : 4; (4 × 2) – 2 = 8 – 2 = 6
Third option: 15 : 9; (9

Correct Answer: Henry David Thoreau 

Solution : Correct Answer is Henry David Thoreau 

Civil disobedience began after the British ignored Gandhi’s 11 demands. In response, Gandhi allied himself with young activists to lead a movement known as the ‘Civil Disobedience’ Movement. During Gandhi’s anti-British protests, he called on all Indians

Correct Answer: Legacy

Solution : The second option is the correct answer.

A legacy is the property or money that is left to someone in a will. It is a bequest or inheritance that is passed down from one generation to another.

The meanings of the other options are as

Correct Answer: Toes

Solution : Given:
Fingers : Hand :: ? : Feet

Like, fingers are the extensions of our hands.
Similarly, toes are the extensions of our feet.

Hence, the second option is correct.

Correct Answer: $\frac{\sqrt{b^2-a^2}}{a}$

Solution : Given,
$\operatorname{cosec} \theta=\frac{b}{a}$
⇒ $\sin\theta=\frac ab$
We have to find the value of $\frac{\sqrt{3} \cot \theta+1}{\tan \theta+\sqrt{3}}$
We know, $\cot\theta=\frac{\cos\theta}{\sin\theta}$ and $\tan\theta=\frac{\sin\theta}{\cos\theta}$
$\frac{\sqrt{3} \cot \theta+1}{\tan \theta+\sqrt{3}}=\frac{\sqrt3\times\frac{\cos\theta}{\sin\theta}+1}{\frac{\sin\theta}{\cos\theta}+\sqrt3}$
= $\frac{\cos\theta(\sqrt3\cos\theta+\sin\theta)}{\sin\theta(\sin\theta+\sqrt3\cos\theta)}$
= $\frac{\cos\theta}{\sin\theta}$
= $\frac{\sqrt{1-\sin^2\theta}}{\sin\theta}$ [As $\sin^2\theta+\cos^2\theta=1$]
= $\frac{\sqrt{1-(\frac ab)^2}}{\frac ab}$
= $\frac{\sqrt{b^2-a^2}}{a}$
Hence, the correct answer is

Correct Answer: Two

Solution : Given:
Each vowel in the word CAPSULE is changed to the previous letter in the English alphabetical series and each consonant is changed to the following letter in the English alphabetical series.

In the newly formed word, Q is 3^rd from left and T

Correct Answer: IDMHDQNVCT

Solution : Given: 
TELEVISION is coded as UDMDWKQKMP
PUNISHMENT is coded as QTOHTJKGLV

Add and subtract 1 alternatively from the place values of the first 5 letters, and add and subtract 2 alternatively from the place values of the remaining letters.
Like, TELEVISION ⇒ T + 1

Correct Answer:

Solution : According to the given figures –
1. A figure at the centre rotates 90° in the anti-clockwise direction.
2. The letters are placed diagonally –
In Box 1, the letters M and N are placed diagonally in the southwest and northeast directions.
In Box 2, the