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Staff Selection Commission Combined Graduate Level Exam

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Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".

(Any of) these two options could be the correct answer.

(1) Either one of

(2) Any two of

(3) Either of

(4) No Improvement

Option 1: (1)

Option 2: (2)

Option 3: (3)

Option 4: (4)

Team Careers360 26th Jan, 2024

Correct Answer: (3)


Solution : The correct choice is the third option.

Explanation:

"Either of" is the most appropriate choice, conveying the idea that one of the two options could be correct.

So, the correct sentence would be: "Either of these two options could be the correct answer."

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Question : $\frac{1}{1+\cos(90^{\circ}- \theta)}$ + $\frac{1}{1-\cos(90^{\circ}- \theta)}$ =?

Option 1: $2\sec^2 \theta$

Option 2: $1$

Option 3: $2$

Option 4: $2 \tan^2 \theta$

Team Careers360 27th Jan, 2024

Correct Answer: $2\sec^2 \theta$


Solution : $\frac{1}{1+\cos(90^{\circ}- \theta)}$ + $\frac{1}{1-\cos(90^{\circ}- \theta)}$
= $\frac{1}{1+\sin \theta}$ + $\frac{1}{1-\sin \theta}$
= $\frac{(1-\sin \theta)+(1+\sin \theta)}{(1-\sin \theta)(1+\sin \theta)}$
= $\frac{2}{1-\sin ^2 \theta}$
= $\frac{2}{\cos ^2 \theta}$
= $2\sec^2 \theta$
Hence, the correct answer is $2\sec^2 \theta$.

27 Views

Question : If $4x=\sqrt5+2$, then the value of $(x-\frac{1}{16x})$ is:

Option 1: 1

Option 2: –1

Option 3: 4

Option 4: $2\sqrt5$

Team Careers360 26th Jan, 2024

Correct Answer: 1


Solution : Given:
$4x=\sqrt5+2$
⇒ $\frac{1}{4x}=\sqrt5-2$ (by rationalising)
⇒ $4x - \frac{1}{4x}=(\sqrt5+2)-(\sqrt5-2)$
⇒ $4x - \frac{1}{4x}=\sqrt5+2-\sqrt5+2$
⇒ $4x - \frac{1}{4x}=4$
Dividing both sides by 4, we get,
⇒ $\frac{4x}{4}-\frac{1}{4x×4}=\frac{4}{4}$
$\therefore x - \frac{1}{16x}=1$
Hence, the correct answer is 1.

32 Views

Question : Directions: Introducing a woman, a man said, "Her mother is the only daughter of my mother-in-law". How is the man related to the woman?

Option 1: Son

Option 2: Brother

Option 3: Husband

Option 4: Father

Team Careers360 27th Jan, 2024

Correct Answer: Father


Solution : As per the given information, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.

So, from the above family tree, the man is the father of that woman. Hence, the 

10 Views

Question : ABC is an equilateral triangle with a side of 12 cm. What is the length of the radius of the circle inscribed in it?

Option 1: $2 \sqrt{3}$ cm

Option 2: $8 \sqrt{3}$ cm

Option 3: $4 \sqrt{3} $ cm

Option 4: $6 \sqrt{3}$ cm

Team Careers360 27th Jan, 2024

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.

16 Views

Question : Gandhi's inspiration for Civil Disobedience came from the writings of 

Option 1: Henry David Thoreau 

Option 2: David Ricardo 

Option 3: Henry Kissinger

Option 4: Bertrand  Russell 

Team Careers360 26th Jan, 2024

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

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