Correct Answer: centroid

Solution : In a $\triangle ABC$, AD, BE and CF are the medians from vertices A, B, and C.
The point of intersection of AD, BE and CF is called the centroid.
Hence, the correct answer is the centroid.

Correct Answer: 9

Solution : Given: $(x+\frac{1}{x})\neq 0$ and $(x^3+\frac{1}{x^3})=0$
$(x+\frac{1}{x})^3=x^3+\frac{1}{x^3}+3×x×\frac{1}{x}(x+\frac{1}{x})$
Substitute the value of $(x^3+\frac{1}{x^3})=0$ in above equation, we get,
⇒ $(x+\frac{1}{x})^3=0+3(x+\frac{1}{x})$
⇒ $(x+\frac{1}{x})^3=3(x+\frac{1}{x})$
⇒ $(x+\frac{1}{x})^{3–1}=3$
⇒ $(x+\frac{1}{x})^2=3$
On squaring both sides of the above equation, we get,
⇒ $((x+\frac{1}{x})^2)^2=3^2$
⇒ $(x+\frac{1}{x})^4=9$
Hence, the correct answer is 9.

Correct Answer: 4

Solution : The correct answer is the fourth option as the sentence is grammatically perfect and addresses its meaning.

In the first option 'raised' is the past(v₂) form of the verb 'raise' while the main verb used in the sentence is 'rise' making it inappropriate.

Correct Answer: $-1$

Solution : $\tan3\theta \cdot \tan7\theta = 1$
⇒ $\tan 7\theta = \frac{1}{\tan 3\theta}$
⇒ $\tan7\theta = \cot3\theta$
⇒ $\tan7\theta = \tan(90° - 3\theta)$
⇒ $7\theta + 3\theta = 90°$
⇒ $10\theta = 90°$
⇒ $\theta = 9°$
$\therefore$ $\cot15\theta = \cot (15\times 9)°=\cot135° = \cot(90° + 45°)=-\tan45°

Correct Answer: India

Solution : The correct option is India.

India is the world's largest producer of raw and jute goods, contributing over 50 and 40 per cent to global production. Jute is a significant agricultural product, and India has a long history of the cultivation and processing of

Correct Answer: each

Solution : The correct choice is the first option.

The word each is used to emphasise the importance of considering and valuing every individual moment and detail.

Each is a determiner, which in the context of a sentence signifies that care and compassion should be

Correct Answer: Ganga-Brahmaputra Valley

Solution : The correct answer is Ganga-Brahmaputra Valley.

Ganga-Brahmaputra Valley is the choice most likely to experience earthquakes out of all of the possibilities provided because of its proximity to the Himalayan foothills. According to the most recent version of India's seismic zone map (2002), the

Correct Answer: HGJL

Solution : Split the given letter clusters in the group of 2 and then swap the letters of the first group –

First option: DCFG 

DCFG → DC FG → CD FG

Both the letter groups are consecutive alphabets.

Second option: FEHI 

FEHI → FE HI →

Correct Answer: Missing a good opportunity

Solution : The correct choice is the first option.

The reason for this answer is that to miss the boat means to lose an opportunity by being slow to react and act. It implies that someone failed to take advantage of a situation or

Correct Answer: (3)

Solution : The error lies in the third part of the sentence.

The reason for the error is the incorrect usage of subject-verb agreement. "User" is a singular noun, so the verb should be "is" instead of "are" to match in singular form.

So, the correct sentence