Staff Selection Commission Combined Graduate Level Exam
Question : The value of $\tan θ + \cot θ − \sec θ \operatorname{cosec} θ$ is:
Option 1: $2$
Option 2: $−2$
Option 3: $0$
Option 4: $\frac{1}{2}$
Correct Answer: $−2$
Solution : $\tan^2\theta+\cot^2\theta-\sec^2\theta \operatorname{cosec}^2\theta$ = $\frac{\sin^2\theta}{\cos^2\theta}+\frac{\cos^2\theta}{\sin^2\theta}-\frac{1}{\sin^2\theta\cos^2\theta}$ = $\frac{\sin^4\theta+\cos^4\theta-1}{\sin^2\theta\cos^2\theta}$ = $\frac{(\sin^2\theta+\cos^2\theta)^2-2\sin^2\theta\cos^2\theta-1}{\sin^2\theta\cos^2\theta}$ = $\frac{1-2\sin^2\theta\cos^2\theta-1}{\sin^2\theta\cos^2\theta}$ = $–2$ Hence, the correct answer is $–2$.
Question : Select the option that can be used as a one-word substitute for the given group of words.
One who has the ability to do many different things
Option 1: Versatile
Option 2: Adaptable
Option 3: Expert
Option 4: Specialist
Correct Answer: Versatile
Solution : The first option is the correct choice.
The one-word substitute for the given group of words is versatile.
Versatile encapsulates the idea of possessing a wide range of skills and being adaptable to various tasks or situations. It implies a capability to excel in diverse
Question : Directions: Which two signs should be interchanged to make the given equation correct? 117 ÷ 13 + 16 × 540 – 40 = 644
Option 1: ÷ and +
Option 2: + and ×
Option 3: – and +
Option 4: ÷ and –
Correct Answer: + and ×
Solution : Given: 117 ÷ 13 + 16 × 540 – 40 = 644
Replace the given symbols in the options one by one with the original symbols in the given equation – First option: ÷ and + = 117 + 13 ÷ 16 ×
Question : What sum will give Rs. 244 as the difference between simple interest and compound interest at 10% in $1\frac{1}{2}$ years compounded half-yearly?
Option 1: Rs. 40,000
Option 2: Rs. 36,000
Option 3: Rs. 32,000
Option 4: Rs. 28,000
Correct Answer: Rs. 32,000
Solution : As interest is compounded, half-yearly T = $\frac{3}{2}$×2 = 3 half-yearly R = $\frac{10}{2}$ = 5% half-yearly By applying the formula: Difference = Principal$(\frac{R}{100})^2(3+\frac{R}{100})$, where $R$ is the rate of interest per six months compounded half-yearly. Putting the value, we get: 244 = Principal$[(\frac{5}{100})^2(3+
Question : Direction: In the following question, select the related number from the given alternatives.
4 : 64 :: 2 : ?
Option 1: 16
Option 2: 8
Option 3: 22
Option 4: 12
Correct Answer: 8
Solution : Given:
Here,
4³= 64
Similarly, 2³= 8
Hence, second option is correct.
Question : The least preferred technique in the disposal of Municipal Solid Waste is
Option 1: Incineration
Option 2: Composting
Option 3: Land filling
Option 4: Bricketting
Correct Answer: Bricketting
Solution : The correct option is Bricketting.
Due to difficulty in managing varied waste compositions, possible environmental concerns, and energy-intensive procedures, bricketting, or briquetting, is a less widely employed technology for Municipal Solid Waste (MSW) disposal. Waste materials are crushed and moulded into compact, dense, and solid
Question : Select the sentence which does NOT have a spelling error.
Option 1: The art and science of designing buildings is called architecchure.
Option 2: The art and science of designing buildings is called architecture.
Option 3: The art and science of designing buildings is called archtiecture.
Option 4: The art and science of designing buildings is called architectrue.
Correct Answer: The art and science of designing buildings is called architecture.
Solution : The second option is the correct answer.
The correct spelling is architecture which refers to the art and science of designing and constructing buildings, including the planning, design, and coordination of spaces and structures to meet
Question : Directions: Which of the following letter clusters will replace the question mark (?) in the given series to make it logically complete? ADZ, GJF, MPL, SVR, ?
Option 1: XYB
Option 2: YBX
Option 3: XBY
Option 4: YXB
Correct Answer: YBX
Solution : Given: ADZ, GJF, MPL, SVR, ?
Add 6 to each letter cluster to get the next term in the given series – ADZ→A + 6 = G, D + 6 = J, Z + 6 = F→GJF GJF→G + 6 = M, J + 6
Question : Select the correct direct form of the given sentence. The surgeon says that I should get anaesthesia for the surgery.
Option 1: The surgeon says, “You should get anaesthesia for the surgery.”
Option 2: The surgeon says, “I should get anaesthesia for the surgery.”
Option 3: The surgeon said, “You should get anaesthesia for the surgery.”
Option 4: The surgeon says, “You could get anaesthesia for the surgery.”
Correct Answer: The surgeon says, “You should get anaesthesia for the surgery.”
Solution : The correct choice is the first option.
We know that the reporting verb remains unchanged when it is in the present tense, but the first-person pronoun is changed to the second-person in the direct speech.
Question : An isosceles triangle ABC is right-angled at B. D is a point inside the triangle ABC. P and Q are the feet of the perpendicular drawn from D on the sides AB and AC respectively of ABC. If $AP = a$ cm , $AQ = b$ cm and $\angle$BAD = 15°, $\sin$ 75°= ?
Option 1: $\frac{2b}{\sqrt 3 a }$
Option 2: $\frac{a}{2b}$
Option 3: $\frac{\sqrt 3a}{2b}$
Option 4: $\frac{2a}{\sqrt 3b}$
Correct Answer: $\frac{\sqrt 3a}{2b}$
Solution : Since $\triangle$ABC is a right-angled isosceles triangle, $\angle$A = $\frac{180 - 90}{2}$ = 45° $\angle$DAQ = $\angle$A–$\angle$BAD = 45° – 15° = 30° $\sin$ $\angle$ADQ = $\sin$ 60° = $\frac{AQ}{AD}$ $\frac{b}{AD}$ = $\frac{\sqrt3}{2}$ AD = $\frac{2b}{\sqrt3}$ From $\triangle$APD, $\sin$ 75° = $\frac{AP}{AD}$ = $\frac{a}{\frac{2b}{\sqrt3}}$
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