Staff Selection Commission Combined Graduate Level Exam
Question : If $(x+\frac{1}{x})^{2}=3$, then the value of $(x^{3}+\frac{1}{x^{3}})$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: –1
Correct Answer: 0
Solution : Given: $(x+\frac{1}{x})^{2}=3$, Taking square root on both sides, we get $(x+\frac{1}{x})=\sqrt{3}$ Now, Cubing both sides we get $(x+\frac{1}{x})^3=(\sqrt{3})^3$ ⇒ $x^3+\frac{1}{x^3}+3×x×\frac{1}{x}(x+\frac{1}{x})=(3\sqrt{3})$ ⇒ $x^3+\frac{1}{x^3}=3\sqrt{3}–3(x+\frac{1}{x})$ $\because x+\frac{1}{x}=\sqrt{3}$ Thus, $x^3+\frac{1}{x^3}=3\sqrt{3}–3\sqrt{3} = 0$ Hence, the correct answer is 0.
Question : Directions: Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 98 : 7 :: 162 : 9 :: 242 : ?
Option 1: 11
Option 2: 12
Option 3: 14
Option 4: 13
Correct Answer: 11
Solution : Given: 98 : 7 :: 162 : 9 :: 242 : ?
Like, (7)2 × 2 = 49 × 2 = 98 (9)2 × 2 = 81 × 2 = 162 Similarly, (?)2 × 2 = 242 ⇒ (?)2 = 242
Question : M is three times as good a worker as N and together they finish a piece of work in 30 days. In how many days will M alone finish the work?
Option 1: 50
Option 2: 40
Option 3: 60
Option 4: 45
Correct Answer: 40
Solution : Given: M is three times as good as N. Let the efficiency of N and M be $x$ and $3x$ respectively. So, total work $=30×(x+3x)=120x$ units Therefore, the time required by A to finish the work alone = $\frac{120x}{3x}$ = 40 days Hence, the correct
Question : Directions: In a certain language, the word CLOCK is written as 4 – 13 – 17 – 4 – 12. How will you write PHONE in the same language?
Option 1: 17 – 10 – 16 – 15 – 6
Option 2: 17 – 9 – 16 – 17 – 6
Option 3: 17 – 9 – 17 – 15 – 6
Option 4: 16 – 9 – 15 – 16 – 5
Correct Answer: 17 – 9 – 17 – 15 – 6
Solution : Given: CLOCK is written as 4 – 13 – 17 – 4 – 12.
Write the position values of the letters of CLOCK, and then add 2 to the position value of O, and add 1 to
Question : Select the option that expresses the given sentence in passive voice. The first-year students are bidding farewell to their seniors.
Option 1: Farewell is to be bid to their seniors by the first-year students.
Option 2: Farewell was being bid to their seniors by the first-year students.
Option 3: Farewell is being bid to their seniors by the first-year students.
Option 4: Their seniors is being bid farewell by the first-year students.
Correct Answer: Farewell is being bid to their seniors by the first-year students.
Solution : The correct choice is the third 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
Question : Comprehension: In the following passage, some words have been deleted. Fill in the blanks with the help of the options given. Select the most appropriate option for each number. The air has become very dirty in (1)______ parts of the world. This is of course (2)______ to your health. Experts say many people die (3)______ it each year. There is a new study on (4)______ pollution which comes from the experts of the World Health Organization (WHO) (5)______ is an agency of the United Nations. If you (6)______ unhealthy air for long periods of time, you could (7)______ sick. Air pollution has been linked to many diseases (8)______stroke and cancer. The WHO says that seven million (9)______ die each year as a result of the (10)______ air. Question: Select the most appropriate option to fill in the blank no. 2.
Option 1: harmful
Option 2: wasteful
Option 3: useful
Option 4: helpful
Correct Answer: harmful
Solution : The right choice is the first option.
The word harmful in the sentence indicates that whatever is being discussed (likely poor air quality, based on the previous context) is detrimental to health. It's the appropriate choice among the options because it correctly describes a
Question : If $2x+\frac{2}{x}=3$, then the value of $x^{3}+\frac{1}{x^{3}}+2$ is:
Option 1: $\frac{3}{4}$
Option 2: $\frac{4}{5}$
Option 3: $\frac{5}{8}$
Option 4: $\frac{7}{8}$
Correct Answer: $\frac{7}{8}$
Solution : Given: $2x+\frac{2}{x}=3$ $2(x+\frac{1}{x})=3$ $(x+\frac{1}{x})=\frac{3}{2}$ Cubing both sides, we get: $(x+\frac{1}{x})^3=(\frac{3}{2})^3$ ⇒ $x^3+\frac{1}{x^3}+3×x×\frac{1}{x}(x+\frac{1}{x})=\frac{27}{8}$ ⇒ $x^3+\frac{1}{x^3}+3×\frac{3}{2}=\frac{27}{8}$ ⇒ $x^3+\frac{1}{x^3}=\frac{27}{8}–\frac{9}{2}$ ⇒ $x^3+\frac{1}{x^3}=–\frac{9}{8}$ To get the value of $x^{3}+\frac{1}{x^{3}}+2$, we need to add 2 both sides. Thus, $x^{3}+\frac{1}{x^{3}}+2 = –\frac{9}{8}+2$ $\therefore x^{3}+\frac{1}{x^{3}}+2 = \frac{7}{8}$ Hence, the correct answer is $\frac{7}{8}$.
Question : A thief steals an item and escapes, running at 20 km/hr. A policeman arrives at the spot of the crime after 6 minutes and immediately starts chasing the thief. 24 minutes after the policeman started to chase the thief, there is still a gap of 400 m between the two. At what distance from the spot of crime would the policeman catch up with the thief and what is the speed at which the policeman ran?
Option 1: 15 km; 25 km/hr
Option 2: 14.4 km; 24 km/hr
Option 3: 10 km; 25 km/hr
Option 4: 12 km; 24 km/hr
Correct Answer: 12 km; 24 km/hr
Solution : Speed of the thief = 20 km/hr Let the speed of the policeman be $x$ km/hr. Time after the policeman starts chasing the thief = 6 minutes Distance between them 30 minutes after the crime = 400 m = 0.4 km According
Question : Three bells ring at intervals of 36 seconds, 40 seconds, and 48 seconds, respectively. They start ringing together at a particular time. They will ring together after every:
Option 1: 6 minutes
Option 2: 12 minutes
Option 3: 18 minutes
Option 4: 24 minutes
Correct Answer: 12 minutes
Solution : 36 = 3 × 3 × 2 × 2 40 = 2 × 2 × 2 × 5 48 = 2 × 2 × 2 × 2 × 3 So, LCM = 2 × 2 × 2 × 2 × 3 × 3 ×
Question : What is 'net neutrality'?
Option 1: Internet Service Providers and governments should treat all data on the internet equally.
Option 2: Piracy on the internet must be curbed.
Option 3: Internet users must give out balanced opinions on social media sites.
Option 4: Internet should be kept free from malware and viruses.
Correct Answer: Internet Service Providers and governments should treat all data on the internet equally.
Solution : The correct answer is Internet service providers and governments should treat all data on the Internet equally.
Net neutrality is the principle that all internet traffic should be treated equally, without discrimination or
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