All Questions

Staff Selection Commission Combined Graduate Level Exam

Follow
Showing 531 - 540 out of 16704 Questions
6 Views

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

10 Views

Question : Select the option that can be used as a one-word substitute for the given group of words.

The property left to someone by a will

Option 1: Ledger

Option 2: Legacy

Option 3: Legend

Option 4: Lexical

Team Careers360 26th Jan, 2024

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

12 Views

Question :

Directions: In the following question, select the related word from the given alternatives.
Fingers : Hand :: ? : Feet

Option 1: Nails

Option 2: Toes

Option 3: Ankle

Option 4: Heels

Team Careers360 26th Jan, 2024

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.

The question have been saved in answer later, you can access it from your profile anytime. Access now