Staff Selection Commission Combined Graduate Level Exam
Question : If $\cos A+\cos^2 A=1$, then the value of $\sin^4 A+\sin^6 A$ is:
Option 1: $2$
Option 2: $\cos \mathrm{A}$
Option 3: $1$
Option 4: $\sin A$
Correct Answer: $\cos \mathrm{A}$
Solution : Given: $\cos A+\cos^2 A=1$ ⇒ $\cos A=1 - \cos^2 A$ ⇒ $\cos A= \sin^2 A$ Squaring both sides, ⇒ $\cos^2 A= \sin^4 A$ ⇒ $1-\sin^2 A= \sin^4 A$ Multiplying both sides by $\sin^2 A$, $\sin^2 A-\sin^4 A=\sin^6 A$ ⇒ $\sin^2 A=\sin^6 A+\sin^4 A$ ⇒
Question : River Indus originates from :
Option 1: Hindukush range
Option 2: Himalayan range
Option 3: Karakoram range
Option 4: Kailash range
Correct Answer: Kailash range
Solution : The correct answer is Kailash range
The Indus River originates from mountain springs northeast of Mount Kailash in Western Tibet, flows through the conflict region of Kashmir to the north, makes a sharp left turn after the Nanga Parbat massif, and then flows through
Question : If $a+b=3$, then the value of $a^{3}+b^{3}+9ab-27$ is:
Option 1: 24
Option 2: 25
Option 3: 0
Option 4: 27
Correct Answer: 0
Solution : Given: $a+b=3$ Cubing both sides, we get $(a+b)^3=3^3$ ⇒ $a^3+b^3+3ab(a+b)=27$ Putting, $(a+b)=3$ ⇒ $a^3+b^3+3ab×3=27$ ⇒ $a^3+b^3+9ab=27$ Thus, $a^3+b^3+9ab–27=0$ Hence, the correct answer is 0.
Question : Direction: In the following question, select the one which is different from other three alternatives.
Option 1: LNOR
Option 2: TRPS
Option 3: CEFI
Option 4: GIJM
Correct Answer: TRPS
Solution : Given:
First option:LNOR ; Follows alphabetical order
Second option:TRPS ; Does not follows alphabetical order
Third option:CEFI ; Follows alphabetical order
Fourth option:GIJM ; Follows alphabetical order
Hence, second option is correct.
Question : At a Christmas sale, all the goods in a shop are on sale at a 30% discount. If Jasmine buys a skirt marked at 800, how much would she need to pay?
Option 1: 476
Option 2: 400
Option 3: 770
Option 4: 560
Correct Answer: 560
Solution : Marked price = 800 Discount = 30% of marked price = 30% of 800 = 240 Selling price = 800 – 240 = 560 Hence, the correct answer is 560.
Question : Directions: Select the option that represents the letters that, when placed from left to right in the blanks below, will complete the letter series. ZYR_Z_RRZY_R_YR _
Option 1: R Y R Z R
Option 2: Z R Y Z R
Option 3: R Z R Y Z
Option 4: Z R R Y Z
Correct Answer: R Y R Z R
Solution : Given: ZYR_Z_RRZY_R_YR _
To fill the series, we have to divide the series – ZYR_/ Z_RR/ ZY_R/ _YR _
Let's check each option – First option: R Y R Z R; ZYRR / ZYRR / ZYRR
Question : What is the value of $\operatorname{cos}\left(-\frac{17 \pi}{3}\right)$?
Option 1: $1$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\frac{1}{2}$
Option 4: $0$
Correct Answer: $\frac{1}{2}$
Solution : $\operatorname{cos}\left(-\frac{17 \pi}{3}\right)$ $=\operatorname{cos}\left(\frac{17 \pi}{3}\right)$ $=\operatorname{cos}\left(\frac{17\times 180º}{3}\right)$ $=\operatorname{cos}\left(17\times 60º\right)$ $=\operatorname{cos}\left(1020º\right)$ $=\operatorname{cos}\left(90º\times 11+30º\right)$ $=\operatorname{sin}\left(30º\right)$ $=\frac{1}{2}$ Hence, the correct answer is $\frac{1}{2}$.
Question : Select the correct passive form of the given sentence.
The government will build an amphitheatre.
Option 1: An amphitheatre will be build by the government.
Option 2: An amphitheatre will be built by the government.
Option 3: An amphitheatre would be built by the government.
Option 4: An amphitheatre be build by the government.
Correct Answer: An amphitheatre will be built by the government.
Solution : The correct choice is the second 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 the subject in
Question : Identify the sentence with correct spellings.
Option 1: There was not enouf food in the beggar's house.
Option 2: There was not enough food in the beggar's house.
Option 3: There was not enauf food in the beggar's house.
Option 4: There was not enoufh food in the beggar's house.
Correct Answer: There was not enough food in the beggar's house.
Solution : The sentence with correct spelling is the second option.
The word enough is correctly spelt in this sentence, which means an adequate or sufficient quantity or amount of something. This sentence conveys that the beggar's house did
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 child is the father of the man. Childhood is a (1)______ of what one is going to be when one (2)______ maturity. The natural instincts of a man are (3)______ in his childhood. Time modifies them but cannot (4)______ them. History contains numerous examples of great men who gave (5)______ of their future when they were children. A child’s mind is (6)______ and flexible. The mould he receives before his clay (7)______ becomes his permanent mark. The values and standards of (8)______ which will determine his life as a man (9)______ in childhood itself. There may be certain (10)______ of course. A bright morning may end in a storm!
Question:
Select the most appropriate option to fill in the blank no. 4.
Option 1: finish
Option 2: delete
Option 3: efface
Option 4: cancel
Correct Answer: efface
Solution : The correct choice is the third option.
Efface means to erase a mark from a surface. It helps convey the intended meaning time can modify the instincts of a man, but it cannot erase them.
The Question containing Inaapropriate or Abusive Words
Question lacks the basic details making it difficult to answer
Topic Tagged to the Question are not relevant to Question
Question drives traffic to external sites for promotional or commercial purposes
The Question is not relevant to User
And never miss an important update
