Staff Selection Commission Combined Graduate Level Exam
Question : If $x+y+z=0$ and $x^2+y^2+z^2=40$, then what is the value of $x y+y z+z x?$
Option 1: –20
Option 2: 5
Option 3: –5
Option 4: –10
Correct Answer: –20
Solution : Given: $x + y + z = 0$ and $x^2+y^2+z^2=40$ ⇒ $(x+ y + z)^2= 0$ ⇒ $x^2 + y^2 + z^2 + 2(xy + yz + zx) = 0$ ⇒ $40 + 2(xy + yz + zx) = 0$ ⇒ $2(xy + yz +
Question : Find the value of $\sqrt{30+\sqrt{30+\sqrt{30+...}}}$ :
Option 1: 5
Option 2: $3\sqrt{10}$
Option 3: 6
Option 4: 7
Correct Answer: 6
Solution : Let $x = \sqrt{30+\sqrt{30+\sqrt{30+...}}}$ So, ${x = }\sqrt{30+x}$ By squaring both sides, we get, $⇒x^{2}=(\sqrt{30+x})^{2}$ $⇒x^{2}=30+x$ $⇒x^{2}–x–30=0$ $⇒x^{2}– 6x+5x–30=0$ $⇒x(x–6)+5(x–6) = 0$ $⇒(x–6)(x+5)=0$ $⇒x=6,–5$ A square root cannot be negative. Thus, $x$ cannot be –5. So, $x = 6$ Hence, the correct answer is 6.
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error."
You shall get (1) / all the informations (2) / if you read this book carefully. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (2)
Solution : The error lies in the second part of the sentence.
Information is an uncountable noun that does not take an "s" at the end to indicate pluralisation. The correct word to use in this context is information, which is not used in plural form.
Question : Parts of the following sentence are given as options. Identify the segment that contains a grammatical error.
This is the album who I found in the garage.
Option 1: in the garage
Option 2: the album
Option 3: who I found
Option 4: This is
Correct Answer: who I found
Solution : The correct choice is the third option.
The pronoun who is an interrogative pronoun and a relative pronoun, which is used to refer to persons. That can be used for people, animals, or things.
Therefore, the correct sentence is: This is the
Question : The Paris Indian Society was an Indian nationalist organisation founded in ______.
Option 1: 1907
Option 2: 1905
Option 3: 1909
Option 4: 1900
Correct Answer: 1905
Solution : The correct option is 1905.
The Paris Indian Society was an organisation founded in Paris in 1905 to promote Indian nationalist and anti-colonial activities. Zoroastrianism was founded by the prophet Zoroaster (or Zarathustra) in ancient Persia around the 6th century BCE.
Question : Select the option that expresses the given sentence in passive voice.
The Event Management team organised the wedding.
Option 1: The wedding is organised by the Event Management team.
Option 2: The Event Management has organised the wedding.
Option 3: The Event Management team is organising the wedding.
Option 4: The wedding was organised by the Event Management team
Correct Answer: The wedding was organised by the Event Management team
Solution : The correct choice is the fourth option.
Explanation:
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 voice becomes
Question : A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. How many hours will it take him to row three-fifths of the same distance in still water?
Option 1: 9.5
Option 2: 7.2
Option 3: 10
Option 4: 12
Correct Answer: 7.2
Solution : Given: Time taken for upstream = 18 hours Time taken for downstream = 9 hours LCM of 9 and 18 is 18. Let the distance be 18 km. Downstream speed = $\frac{\text{Distance}}{\text{Time}}$ = $\frac{18}{9}$ = 2 km/hr Upstream speed = $\frac{18}{18}$ = 1 km/hr Speed
Question : Direction: Which one of the given responses is the meaningful order of the following?
1. Fruit 2. Pollen 3. Corolla 4. Stamen
Option 1: 2, 4, 3, 1
Option 2: 2, 3, 4, 1
Option 3: 3, 1, 4, 2
Option 4: 2, 1, 3, 4
Correct Answer: 2, 4, 3, 1
Solution : Given:
As, Stamen is made from Pollen, Corolla is made from Stamen, Fruit is made from Corolla.
So, the meaningful order is as follows –
Pollen → Stamen → Corolla → Fruit
Therefore, the
Question : Select the most appropriate meaning of the underlined idiom in the given sentence. Nobody in the conference seemed to believe the cock and bull story about such a major movie star.
Option 1: Factual story.
Option 2: Wildly exaggerated or falsified story.
Option 3: Interesting story.
Option 4: Secretive story.
Correct Answer: Wildly exaggerated or falsified story.
Solution : The correct option is the second option.
Explanation: Cock and bull story refers to a highly improbable, unbelievable, or fabricated tale that lacks credibility. In the context of the sentence, it suggests that the story about the major movie star was
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error".
I don't have (1) / any money to (2) / spend for luxuries. (3) / No error (4)
Correct Answer: (3)
Solution : The error lies in the third part of the sentence.
Explanation: The preposition ''for'' should be replaced with ''on'' to make the sentence grammatically accurate and convey the intended meaning that the speaker doesn't have any money available for spending on luxury items.
Therefore,
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