Staff Selection Commission Combined Graduate Level Exam
Question : If $\sin\left ( 2a+45^{\circ} \right )=\cos\left ( 30^{\circ}-a \right )$ where $0^{\circ}< a< 90^{\circ}$, then the value of a is:
Option 1: $0^{\circ}$
Option 2: $15^{\circ}$
Option 3: $45^{\circ}$
Option 4: $60^{\circ}$
Correct Answer: $15^{\circ}$
Solution : $\sin\left ( 2a+45^{\circ} \right )=\cos\left ( 30^{\circ}-a \right )$ ⇒ $\sin\left ( 2a+45^{\circ} \right )=\sin\left ( 90^{\circ}–(30^{\circ}-a \right ))$ ⇒ $2a+45^{\circ} = 90^{\circ}–(30^{\circ}–a)$ ⇒ $2a+45^{\circ} = 90^{\circ}–30^{\circ}+a$ ⇒ $a = 60^{\circ}–45^{\circ}$ ⇒ $a = 15^{\circ}$ Hence, the correct answer is $15^{\circ}$.
Question : Which of the following is not a component of the expenditure of the Government?
Option 1: Expenditure on the acquisition of machinery
Option 2: Expenditure on the acquisition of land
Option 3: Expenditure on the acquisition of the building
Option 4: Interest payments
Correct Answer: Interest payments
Solution : The correct option is Interest payments.
Interest payments are often not part of the government's capital budget. Rather than being a capital expense, interest payments are a component of revenue expenditure.
Question : A retailer marks up his goods by 150% and offers a 40% discount. What will be the selling price (in Rs.), if the cost price is Rs. 800?
Option 1: 1200
Option 2: 1500
Option 3: 1000
Option 4: 2000
Correct Answer: 1200
Solution : Cost price = Rs. 800 Marked price = cost price + 150% of cost price = Rs. 800 + Rs. 1200 = Rs. 2000 Discount = 40% of marked price = 40% of 2000 = Rs. 800 $\therefore$ Selling price = Marked price – discount
Question : Rearrange the parts of the sentence in the correct order.
Jobseekers are not
P. being unemployed are a test of faith Q. self-purification, where the difficulties of R. relentlessly to a pilgrimage of S. fatalistic but reapply themselves
Option 1: SPQR
Option 2: PQSR
Option 3: SRQP
Option 4: RPSQ
Correct Answer: SRQP
Solution : The correct choice is the third option.
The sentence describes jobseekers' mindset and approach towards unemployment. They view unemployment as an opportunity for personal growth. They approach their job search with relentless effort and despite challenges, they recognise the difficulties but continue to strive.
Question : Directions: In the following question, select the related number from the given alternatives. 18 : 30 :: 36 : ?
Option 1: 78
Option 2: 64
Option 3: 66
Option 4: 68
Correct Answer: 66
Solution : Given: 18 : 30 :: 36 : ?
Like, (2 × 18) – 6 = 36 – 6 = 30 Similarly, (2 × 36) – 6 = 72 – 6 = 66
66 is related to 36. Hence, the third option is correct.
Question : Comprehension:
In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
The Sun is the star at the centre of (1) __________ Solar System. It is a nearly perfect ball of hot plasma. The Sun has inspired us since ancient times. It’s central to mythology and religion in (2) ____________ around the world. It keeps our planet warm enough for living things to grow. It gives us light so we can see. It is by far the most important (3) _________of energy for life on Earth. It is about a hundred times as wide (4)________ the Earth. If there were no sun, many things wouldn’t occur like photosynthesis or the presence of oxygen, which would have caused no (5) __________ of life.
Select the most appropriate option to fill in the blank number 3.
Option 1: gesture
Option 2: source
Option 3: control
Option 4: symbol
Correct Answer: source
Solution : The correct choice is the second option.
The source correctly fits into the sentence and conveys the intended meaning. The passage discusses the importance of the Sun. In the context of the sentence, the term source refers to the origin or provider of energy.
The
Question : If $\mathrm{D}$ is the midpoint of $\mathrm{BC}$ in $\triangle \mathrm{ABC}$ and $\angle A=90^{\circ}$, then $AD=$ ______.
Option 1: $\frac{\mathrm{BC}}{4}$
Option 2: $2 \mathrm{BC}$
Option 3: $\frac{\mathrm{BC}}{2}$
Option 4: $\mathrm{BC}$
Correct Answer: $\frac{\mathrm{BC}}{2}$
Solution :
Given: In $\triangle \mathrm{ABC}$, the midpoint of $\mathrm{BC}$ is $\mathrm{D}$ and $\angle A=90^{\circ}$. AD is the median to the BC. We know that the median to the hypotenuse of a right-angled triangle is half of the hypotenuse. $AD = \frac{1}{2} BC$ Hence, the correct answer
Question : A galvanometer can be converted into a voltmeter by connecting with it a
Option 1: high resistance in parallel
Option 2: low resistance on parallel
Option 3: high resistance in series
Option 4: low resistance in series
Correct Answer: high resistance in series
Solution : The correct option is high resistance in series.
To transform a galvanometer into a voltmeter, a high-resistance element in series with the galvanometer, often referred to as a multiplier or shunt resistor is used. This additional resistor serves the purpose of controlling
Question : The country where drip irrigation is more efficiently used is
Option 1: India
Option 2: Israel
Option 3: Sri Lanka
Option 4: England
Correct Answer: Israel
Solution : The correct answer is Israel
Israel is widely regarded as a pioneer in the invention and application of drip irrigation technology. Because of its dry environment and limited water supplies, Israel has widely used drip irrigation to maximise agricultural water efficiency.
Question : In a College, the number of students with different majors is as follows.
Find the average number of students in each subject.
Option 1: 55
Option 2: 49
Option 3: 42
Option 4: 35
Correct Answer: 49
Solution : No. of students in mathematics = 45 No. of students in Physics = 60 No. of students in History = 30 No. of students in Hindi = 65 No. of students in Sanskrit = 45 Total sum of students all numbers = 45 + 60
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