Staff Selection Commission Combined Graduate Level Exam
Question : If $4x^{2}=15^{2}–9^{2}$, then the value of $x$ is:
Option 1: 9
Option 2: 6
Option 3: 3
Option 4: 12
Correct Answer: 6
Solution : Given: $4x^{2}=15^{2}–9^{2}$ According to the formula of $a^{2}–b^{2}=(a–b)(a+b)$, ⇒ $4x^{2}=(15–9)(15+9)$ ⇒ $4x^{2}=6×24$ ⇒ $x^{2}=6×6$ ⇒ $x=\sqrt{36}$ ⇒ $x=6$ Hence, the correct answer is 6.
Question : If $xy(x+y)=m$, then the value of $(x^3+y^3+3m)$ is:
Option 1: $\frac{m^3}{xy}$
Option 2: $\frac{m^3}{(x+y)^3}$
Option 3: $\frac{m^3}{x^3y^3}$
Option 4: $mx^3y^3$
Correct Answer: $\frac{m^3}{x^3y^3}$
Solution : Given: $xy(x+y)=m$ We know that the algebraic identity is $(x+y)^3=x^3+y^3+3xy(x+y)$. $xy(x+y)=m$ ⇒ $(x+y)=\frac{m}{xy}$ Take the cube on both sides of the above equation, we get, $(x+y)^3=(\frac{m}{xy})^3$ ⇒ $x^3+y^3+3xy(x+y)=\frac{m^3}{x^3y^3}$ Substitute the value of $xy(x+y)=m$ in above equation, we get, $x^3+y^3+3m=\frac{m^3}{x^3y^3}$ Hence, the correct answer is $\frac{m^3}{x^3y^3}$.
Question : The sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph.
A. Tigers are the largest members of the cat family. They are found in many parts of Asia. B. They mostly live in dark forests and sleep during the day. They come out for hunting pigs and deer by night. C. It is assumed that, probably, around 3,000 tigers live in the wild. This species looks spectacular and grand, and they are very graceful in their movements. D. It is almost impossible for us to see them against a jungle background, especially when they are standing still, because of their striped coats. Unlike, most cats, the tiger likes bathing very much.
Option 1: ABCD
Option 2: CDBA
Option 3: ACBD
Option 4: ADBC
Correct Answer: ACBD
Solution : The third option is the correct choice.
The paragraph starts by introducing tigers and their habitat (A), followed by information about the estimated population and characteristics of tigers (C). The mention of their nocturnal hunting habits is then presented (B), and the paragraph concludes with
Question : If $\sin (x+y) = \cos (x–y)$, then the value of $\cos^2 x$ is:
Option 1: $\frac{1}{2}$
Option 2: $3$
Option 3: $5$
Option 4: $\frac{1}{4}$
Correct Answer: $\frac{1}{2}$
Solution : Given: $\sin (x+y) = \cos (x–y)$ If $\theta_1+\theta_2=90^{\circ}$, then If $\sin \theta _1=\cos \theta_2$. $\sin (x+y) = \cos (x–y)$ ⇒ $x+y+x–y=90^{\circ}$ ⇒ $2x=90^{\circ}$ ⇒ $x=45^{\circ}$ The value of $\cos^2 x=\cos^245^{\circ}$ = $(\frac{1}{\sqrt2})^2$ = $\frac{1}{2}$ Hence, the correct answer is $\frac{1}{2}$.
Question : Identify the segment in the sentence which contains a grammatical error.
Three hours will have passed when the bell will ring.
Option 1: will ring
Option 2: will have passed
Option 3: Three hours
Option 4: when the bell
Correct Answer: will ring
Solution : The correct choice is the first option.
The error is in using will ring instead of the simple present tense rings after the conjunction when. In this context, it's more appropriate to use the simple present tense to indicate an action that
Question : Which Article of the Indian Constitution deals with the Right against Exploitation?
Option 1: Article 22
Option 2: Article 23
Option 3: Article 21
Option 4: Article 20
Correct Answer: Article 23
Solution : The correct answer is Article 23.
The right against exploitation is mentioned in Articles 23 and 24 of the Indian Constitution, and these are the Fundamental Rights which guarantee every citizen protection from any kind of forced labour or human trafficking. The right against
Question : Directions: In the following question, select the related number from the given alternatives. 4 : 17 :: 7 : ?
Option 1: 49
Option 2: 50
Option 3: 51
Option 4: 52
Correct Answer: 50
Solution : Given: 4 : 17 :: 7 : ?
4 : 17→(4)2 = 16; 16 + 1 = 17 Similarly, 7 : ?→(7)2 = 49; 49 + 1 = 50
Hence, the second option is correct.
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 have passed (1) / the examination (2) / two years ago. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The error lies in the first part of the sentence.
The action occurred "two years ago". The use of the present perfect tense (have passed) in a sentence with a clear time reference (two years ago) is incorrect. Instead, the past simple tense should be
Question : Directions: Select the option that is related to the fourth term in the same way as the first term is related to the second term and the fifth term is related to the sixth term. 8 : 496 :: ? : 204 :: 9 : 711
Option 1: 5
Option 2: 13
Option 3: 6
Option 4: 11
Solution : Given: 8 : 496 :: ? : 204 :: 9 : 711
Here, 8 : 496→(8)3 – (8 × 2) = 512 – 16 = 496 9 : 711→(9)3 – (9 × 2) = 729 – 18 = 711
Now, let's
Question : Directions: Which letter cluster will replace the question mark (?) to complete the given series? CBOM, FCQN, ?, LEUP, OFWQ
Option 1: HDSO
Option 2: IDSO
Option 3: IDSP
Option 4: IDTO
Correct Answer: IDSO
Solution : Given: CBOM, FCQN, ?, LEUP, OFWQ
Add 3 to the positional value of the first letter, 1 to the positional value of the second letter, 2 to the positional value of the third letter, and 1 to the positional value of the fourth letter of
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