Staff Selection Commission Combined Graduate Level Exam
Question : If $\frac{1}{a}(a^2+1)=3$, then the value of $\frac{a^6+1}{a^3}$ is:
Option 1: 9
Option 2: 18
Option 3: 27
Option 4: 1
Correct Answer: 18
Solution : Given: $\frac{1}{a}(a^2+1)=3$ ⇒ $a+\frac{1}{a}=3$ ⇒ $(a+\frac{1}{a})^3=3^3$ ⇒ $a^3+\frac{1}{a^3}+3×a×\frac{1}{a}(a+\frac{1}{a})=27$ ⇒ $a^3+\frac{1}{a^3}+3×3=27$ [as, $a+\frac{1}{a}=3$] ⇒ $a^3+\frac{1}{a^3}=27-9$ $\therefore \frac{a^6+1}{a^3}=18$ Hence, the correct answer is 18.
Question : What is the average circumference of the standard cricket ball in international cricket as of October 2022?
Option 1: 7.89 inches - 8.45 inches
Option 2: 10.46 inches - 10.90 inches
Option 3: 9.45 inches - 10.20 inches
Option 4: 8.81 inches - 9 inches
Correct Answer: 8.81 inches - 9 inches
Solution : The correct answer is 8.81 inches - 9 inches.
In international cricket, the average circumference of a standard cricket ball is typically between 8.81 inches and 9 inches. According to the regulations of the International Cricket Council (ICC), the
Question : Directions: Select the option that is related to the fifth term in the same way as the second term is related to the first term and the fourth term is related to the third term. 121 : 12 :: 225 : 16 :: 441 : ?
Option 1: 21
Option 2: 19
Option 3: 23
Option 4: 22
Correct Answer: 22
Solution : Given: 121 : 12 :: 225 : 16 :: 441 : ?
Like, 121 : 12→√121 = 11; 11 + 1 = 12 225 : 16→√225 = 15; 15 + 1 = 16 Similarly, for 441 : ?→√441 = 21 + 1 = 22
So,
Question : Direction: In the following question, select the one which is different from the other three alternatives.
Option 1: 101
Option 2: 212
Option 3: 326
Option 4: 111
Correct Answer: 101
Solution : Let's check the options —
First option: 101; 101 is a prime number. This option is different from the other options.
Second option: 212; 212 is not a prime number.
Third option: 326; 326 is not a prime number.
Fourth option: 111; 111 is not
Question : A store sells a watch for a profit of 25% of its cost price. Then, the percentage of profit against the selling price is:
Option 1: 22%
Option 2: 20%
Option 3: 18%
Option 4: 15%
Correct Answer: 20%
Solution : Let the cost price (CP) of the watch be 100. The selling price (SP) at a profit of 25% = 125 So, profit = 125 – 100 = 25 When the profit percentage is calculated on SP, Profit % = $\frac{\text{Profit}}{\text{SP}} × 100 = \frac{25}{125}
Question : Select the correct direct form of the given sentence. The old man asked the boy where the postman was.
Option 1: The old man says to the boy, “Where is the postman?”
Option 2: The old man said to the boy, “Where has been the postman?”
Option 3: The old man said to the boy, “Where is the postman?”
Option 4: The old man said to the boy, “Where was the postman?”
Correct Answer: The old man said to the boy, “Where is the postman?”
Solution : The third option is correct.
The given sentence is indirect speech, reporting what the old man said to the boy.
Narration Conversion:
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.
Colonialism had a great impact on the lives of the Aboriginal Australians who were eventually (1) _____ by the whites with all power and privilege. The colonisers turned their land into rubbish pits and (2) _____ sites for their own betterment. The Aborigines were often (3) _____ as sub-humans with low status and dirty habits. The whites not only displaced the tribes of their homeland but also (4) _____ the beauty and balance of the natural world. An increase in deforestation and destruction of traditional land led (5) _____ like emu, eagle, and kangaroo, among many others to dwindle over time.
Select the most appropriate option to fill in the blank number 2.
Option 1: dating
Option 2: construction
Option 3: halting
Option 4: recreation
Correct Answer: construction
Solution : The correct choice is the second option.
Construction means the action of building something that correctly fits in the context of the sentence (construction sites), which was changed for the betterment of the whites.
Question : What is the area of the curved surface of a right circular cone with a height of 8 m and a slant height of 10 m?
Option 1: $60\mathrm{~m}^2$
Option 2: $60\pi \mathrm{~m}^2$
Option 3: $40 \mathrm{~m}^2$
Option 4: $ 40 \pi \mathrm{~m}^2$
Correct Answer: $60\pi \mathrm{~m}^2$
Solution : Given: Height($h$) = 8 m and slant height($l$) = 10 m Radius($r$) = $\sqrt{l^2-h^2}$ = $\sqrt{10^2-8^2}$ = $\sqrt{100-64}$ = $\sqrt{36}$ = 6 m Area of the curved surface of a right circular cone = $ \pi rl$ = $\pi×6×10$ = $60\pi $ Hence, the
Question : Directions: Select the word pair that best represents a similar relationship to the one expressed in the given pair of words. (The words must be considered meaningful English words and must not be related to each other based on the number of letters/number of consonants/vowels in the word.) Police : Protection
Option 1: Minister : Governance
Option 2: Thief : Jail
Option 3: King : Kingdom
Option 4: Teacher : Class
Correct Answer: Minister : Governance
Solution : Given: Police : Protection
Like, the police provide protection to the public.
Let's check the options – First option: Minister : Governance; A minister is responsible for the governance of a country or state. Second option: Thief : Jail; Thief is kept in
Question : A megastore is offering a 20% discount on all grocery items. Sakshi bought one grocery item marked at Rs. 400. What is its cost price if the store earned a profit of 25% after giving the discount?
Option 1: Rs. 256
Option 2: Rs. 280
Option 3: Rs. 380
Option 4: Rs. 320
Correct Answer: Rs. 256
Solution : Let the cost price be $x$. Marked price, MP = Rs. 400 Profit % gained = 25% Selling price, SP after 20% discount = MP – $\frac{20}{100}$MP ⇒ SP = 400 – $\frac{20}{100}\times$ 400 ⇒ SP = Rs. 320 Also, Profit percentage = $\frac{\text{Selling
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