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Staff Selection Commission Combined Graduate Level Exam

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Question : If $\operatorname{cosec}\theta+\sin\theta=\frac{5}{2}$, then the value of $(\operatorname{cosec}\theta-\sin\theta)$ is:

Option 1: $-\frac{3}{2}$

Option 2: $\frac{3}{2}$

Option 3: $-\frac{\sqrt{3}}{2}$

Option 4: $\frac{\sqrt{3}}{2}$

Team Careers360 25th Jan, 2024

Correct Answer: $\frac{3}{2}$


Solution : Given:
$\operatorname{cosec}\theta+\sin\theta=\frac{5}{2}$
⇒ $\frac{1}{\sin\theta}+\sin\theta=\frac{5}{2}$
⇒ $\frac{1+\sin^{2}\theta}{\sin\theta}=\frac{5}{2}$
⇒ $2\sin^{2}\theta-5\sin\theta+2=0$
⇒ $2\sin^{2}\theta-4\sin\theta-1\sin\theta+2=0$
⇒ $2\sin\theta (\sin\theta-2)-1(\sin\theta-2)=0$
⇒ $(\sin\theta-2)(2\sin\theta-1)=0$
⇒ $\sin\theta= 2,\frac{1}{2}$
$\sin\theta$'s value can't be 2.
So, $\sin\theta=\frac{1}{2}=\sin30^{\circ}$
⇒ $\theta=30^{\circ}$
$\operatorname{cosec}\theta-\sin\theta$
$=\operatorname{cosec}30^{\circ}-\sin30^{\circ}$
$= 2-\frac{1}{2}$
$=\frac{3}{2}$
Hence, the correct answer is $\frac{3}{2}$.

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Question : Select the option that expresses the given sentence in passive voice.

Mary was cooking the meal.

Option 1: The meal were being cooked by Mary.

Option 2: The meal was already being cooked by Mary.

Option 3: Mary was about to cook the meal.

Option 4: The meal was being cooked by Mary.

Team Careers360 25th Jan, 2024

Correct Answer: The meal was being cooked by Mary.


Solution : The correct choice is the fourth option.

Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in

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Question : Select the most appropriate ANTONYM of the underlined word.

My niece is an amateur artist. I hope she becomes famous one day.

Option 1: Boring

Option 2: Freelancing

Option 3: Expert

Option 4: Decent

Team Careers360 25th Jan, 2024

Correct Answer: Expert


Solution : The most appropriate choice is the third option.

Expert means someone who is very knowledgeable or skilled in a particular area and is an antonym for the word amateur, which means someone who is inept.

The meanings of the other options are as follows:

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Question : The area of a rhombus having one side 10 cm and one diagonal 12 cm is:

Option 1: $48\text{ cm}^2$

Option 2: $96\text{ cm}^2$

Option 3: $144\text{ cm}^2$

Option 4: $192\text{ cm}^2$

Team Careers360 25th Jan, 2024

Correct Answer: $96\text{ cm}^2$


Solution : The area of a rhombus, where $d_1$ and $d_2$ are the lengths of the diagonals,
$ = \frac{1}{2} \times d_1 \times d_2 $
In this case, one side of the rhombus is given as 10 cm and one diagonal is given as 12 cm.

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Question : An emulsion is a colloid of a

Option 1: Gas in a liquid

Option 2: liquid in a liquid

Option 3:  liquid in a gas

Option 4: Gas in a solid

Team Careers360 25th Jan, 2024

Correct Answer: liquid in a liquid


Solution : The correct option is liquid in a liquid.

An emulsion is a colloid composed of one liquid dispersed in liquid. It is a form of colloidal dispersion in which the dispersed phase as well as the dispersion medium are both liquids. Emulsions

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Question : The value of $\left(3^2\right)^2 + 3 \times 3 \div 3 - 3$ is:

Option 1: $3^2$

Option 2: $9^2$

Option 3: $2^3$

Option 4: $3^0$

Team Careers360 25th Jan, 2024

Correct Answer: $9^2$


Solution : $\left(3^2\right)^2 + 3\times 3\div3 - 3$
$=\left(9\right)^2 + 3\times 3\div3 - 3$
$=81 + 3\times 3 \div3 - 3$
$= 81 + 3\times1 - 3$
$=81 + 3 -3$
$=81$
$ = 9^2$
Hence, the correct answer is $9^2$.

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