Staff Selection Commission Combined Graduate Level Exam
Question : What will be the value of $\sin 10^{\circ}- \frac{4 }{ 3} \sin ^3 10^{\circ}?$
Option 1: $\frac{1}{3 \sqrt{3}}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{2 \sqrt{3}}$
Option 4: $\frac{\sqrt{3}}{6}$
Correct Answer: $\frac{1}{6}$
Solution : $\sin 10^{\circ}- \frac{4 }{ 3} \sin ^3 10^{\circ}$ $=\frac{1}{3}(3\sin 10^{\circ}- 4 \sin ^3 10^{\circ})$ $=\frac{\sin3(10^{\circ})}{3}$ [$\because \sin 3 \theta = 3\sin \theta - 4 \sin 3 \theta$] $=\frac{\sin30^{\circ}}{3}$ $=\frac{\frac{1}{2}}{3}$ $=\frac{1}{6}$ Hence, the correct answer is $\frac{1}{6}$.
Question : Select the option that will improve the underlined part of the sentence. In case no improvement is needed, select 'No Improvement'.
I reached at London only this morning.
Option 1: reach
Option 2: reached
Option 3: No improvement
Option 4: am reaching
Correct Answer: reached
Solution : The correct choice is the second option.
The verb reach is a transitive verb, and it takes an object directly. Hence, the preposition used after the reached, which is the past form of the verb is not required, and thus should be omitted.
Therefore,
Question : Directions: Select the option that is related to the fifth letter cluster in the same way as the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster. BULL : CDVWMNMN :: SHOT : TUIJPQUV :: TENS : ?
Option 1: UVFGOPTU
Option 2: OPTUUVFG
Option 3: OPTUOPTU
Option 4: UVFGUVFG
Correct Answer: UVFGOPTU
Solution : Given: BULL : CDVWMNMN :: SHOT : TUIJPQUV :: TENS : ?
Add 1 and 2 to the place value of each letter of BULL, to obtain their related letter cluster –
Thus, BULL is related to CDVWMNMN. And, SHOT : TUIJPQUV –
Thus, SHOT
Question : Which of the following books is not written by Munshi Premchand?
Option 1: Gaban
Option 2: Godan
Option 3: Guide
Option 4: Nirmala
Correct Answer: Guide
Solution : The correct answer is Guide.
Indian author R. K. Narayan published his English-language first book, The Guide, in 1958. The Sahitya Akademi, India's National Academy of Letters, awarded Narayan the 1960 Sahitya Akademi Award for English for the book. Like most of his works, this
Question : Directions: Select the option that is related to the fifth letter cluster in the same way as the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster. SCOOTER : SGWSTIZ :: AEROPLANE : FPDPUUYMJ :: HELICOPTER : ?
Option 1: RETPOCILEH
Option 2: SGWTTIPTNR
Option 3: SFUQPDJMFI
Option 4: SGWTTIPLEH
Correct Answer: SGWTTIPTNR
Solution : Given: SCOOTER : SGWSTIZ :: AEROPLANE : FPDPUUYMJ :: HELICOPTER : ?
Like, for SCOOTER; S + 7 = Z; C + 6 = I; O + 5 = T; O + 4 = S; T + 3 = W; E + 2 = G;
Question : Directions: In the following question, find the odd number pair from the given alternatives.
Option 1: 6 – 612
Option 2: 5 – 521
Option 3: 4 – 46
Option 4: 7 – 543
Correct Answer: 7 – 543
Solution : Taking the cube of the first number and reversing the digits to obtain the second number.
First option: 6 – 612→63 = 216; On reversing the digits, 216 becomes 612. Second option: 5 – 521→53 = 125; On reversing the digits,
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.
We believe our value is in direct proportion to the value of our accomplishments. If we cannot accomplish certain results, we tend to feel (1)_____ about ourselves. Some of us try too hard and become workaholics and over-achievers. With a few genuine feelings of self-worth, we try to create some and prove that we are somebody by our successes and (2)_____. Because our desire for perfection is so great, we (3)_____ to set unrealistic goals and place unreasonable demands on ourselves. Failing, rather than encouraging us to have realistic aspirations, only leads to a mere punishing round of self-blame and a resolve to drive ourselves harder next time. If we do not finally achieve our goals, we are (4)____; despite everything we have done, we still feel (5)_____ inside.
Question:
Select the most appropriate option to fill in the blank number 1.
Option 1: high
Option 2: good
Option 3: low
Option 4: better
Correct Answer: low
Solution : The correct choice is the third option.
In this context, "low" suggests a feeling of disappointment, sadness, or reduced self-esteem when one is unable to achieve specific goals or results.
The meanings of other words are:
Question : The average of 15 numbers is 7. If the average of the first 8 numbers is 6.5 and the average of the last 8 numbers is 8.5, then the middle number is:
Option 1: 10
Option 2: 23
Option 3: 13
Option 4: 15
Correct Answer: 15
Solution : Given: Average of 15 results = 7 Average of first seven = 6.5 Average of last seven = 7.5 According to the question, Sum of all results = 15 × 7 = 105 Sum of first seven results = 8 × 6.5 = 52 Sum
Question : Direction: In the given question, select the related letters from the given alternatives.
DLIP : FNKR :: JROV : ?
Option 1: MURY
Option 2: LTQX
Option 3: NVSZ
Option 4: KSPW
Correct Answer: LTQX
Solution : Given:
Like, D + 2 = F; L + 2 = N; I + 2 = K; P + 2 = R
Similarly, J + 2 = L; R + 2 = T;
Question : In a trapezium ABCD, AB and DC are parallel to each other with a perpendicular distance of 8 m between them. Also, AD = BC = 10 m, and AB = 15 m < DC. What is the perimeter (in m) of the trapezium ABCD?
Option 1: 50
Option 2: 66
Option 3: 62
Option 4: 58
Correct Answer: 62
Solution : ⇒ AD = BC = 10 m ⇒ AB = EF = 15 m ⇒ AE = BF = 8 m In $\triangle$ADE, By Pythagoras theorem, AD2 = AE2 + DE2 DE = $\sqrt{10^2-8^2}$ = $\sqrt{100-64}$ = $\sqrt{36}$ = 6 m ⇒
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