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Staff Selection Commission Combined Graduate Level Exam

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Question : If $\tan3\theta \tan7\theta = 1$, where $7\theta$ is an acute angle, then find the value of $\cot15\theta$.

Option 1: $1$

Option 2: $-1$

Option 3: $-\sqrt{3}$

Option 4: $\sqrt{3}$

Team Careers360 21st Jan, 2024

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°

11 Views

Question : Which country is the leading producer of jute?

Option 1: Brazil

Option 2: China

Option 3: India

Option 4: Columbia

Team Careers360 23rd Jan, 2024

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

16 Views

Question : Which of the following areas or regions is most prone to earthquakes?

Option 1: Deccan Plateau

Option 2: Ganga-Brahmaputra Valley

Option 3: Plains of Northern India

Option 4: Western Ghats

Team Careers360 22nd Jan, 2024

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

22 Views

Question : Direction: In the following question, select the one which is different from other three alternatives.

Option 1: DCFG

Option 2: FEHI

Option 3: JILM

Option 4: HGJL

Team Careers360 22nd Jan, 2024

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 →

17 Views

Question : Select the most appropriate meaning of the given idiom.

Miss the boat

Option 1: Missing a good opportunity

Option 2: Missing your medium of travel

Option 3: Missing good moments of your life

Option 4: Being too late

Team Careers360 23rd Jan, 2024

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

13 Views

Question : If $\sin5\theta = \cos 20° (0°<\theta<90°)$, then the value of $\theta$ is:

Option 1:

Option 2: 22°

Option 3: 10°

Option 4: 14°

Team Careers360 21st Jan, 2024

Correct Answer: 14°


Solution : Given:
$\sin5\theta = \cos 20° (0°<\theta<90°)$
We know, $\cos 20°=\cos(90°-70°)=\sin70°$
So, $\sin5\theta=\sin 70°$
$⇒5\theta=70°$
$\therefore \theta=14°$
Hence, the correct answer is 14°.

31 Views

Question : What is the smallest number which can be added to 9454351626 so that it becomes divisible by 11?

Option 1: 1

Option 2: 6

Option 3: 5

Option 4: 4

Team Careers360 21st Jan, 2024

Correct Answer: 6


Solution : A number is divisible by 11 if the difference between the sum of the digits at even places and the sum of the digits at odd places of a number is either 0 or divisible by 11.
Now, the difference between the sums = (9

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