Staff Selection Commission Combined Graduate Level Exam
Question : If $\theta$ is an acute angle and $\sin(\theta +18^{\circ} )=\frac{1}{2}$, then the value of $\theta$ in circular measure is:
Option 1: $\frac{\pi}{12}$ radians
Option 2: $\frac{\pi}{15}$ radians
Option 3: $\frac{2\pi}{5}$ radians
Option 4: $\frac{3\pi}{13}$ radians
Correct Answer: $\frac{\pi}{15}$ radians
Solution : Given that $\sin(\theta +18^{\circ})=\frac{1}{2}$, we need to find the value of $\theta$ in radians. We know that $\sin30^{\circ}=\frac{1}{2}$, $\sin(\theta +18^{\circ})=\sin30^{\circ}$ $⇒\theta +18^{\circ}=30^{\circ}$ $⇒\theta=12^{\circ}$ To convert degrees to radians, we use the formula ⇒ Radians = Degrees × $\frac{\pi}{180^{\circ}}$ So, $\theta=12^{\circ}×\frac{\pi}{180}=\frac{\pi}{15}$ radians Hence, the correct
Question : Who among the following wrote Sanskrit grammer?
Option 1: Kalidasa
Option 2: Charaka
Option 3: Panini
Option 4: Aryabhat
Correct Answer: Panini
Solution : The correct answer is Panini.
Panini wrote a book called Ashtadhyai. It is an ancient treatise on Sanskrit grammar. He lived between 4th and 5th century BC during the advent of Mauryan empire. Ashtadhyayi means eight texts which is an Sanskrit grammar book which gives
Question : If $a = 64$ and $b = 289$, then the value of $\sqrt{\sqrt{\sqrt{a}+\sqrt{b}}-\sqrt{\sqrt{b}-\sqrt{a}}}$ is:
Option 1: $2^{\frac{1}{2}}$
Option 2: $2$
Option 3: $4$
Option 4: $–1$
Correct Answer: $2^{\frac{1}{2}}$
Solution : Given: $a = 64$ and $b = 289$ The given expression is $\sqrt{\sqrt{\sqrt{a}+\sqrt{b}}-\sqrt{\sqrt{b}-\sqrt{a}}}$. Substitute the value of $a = 64$ and $b = 289$ in the above equation, we get, $=\sqrt{\sqrt{\sqrt{64}+\sqrt{289}}-\sqrt{\sqrt{289} - \sqrt{64}}}$ $=\sqrt{\sqrt{8+17}-\sqrt{17-8}}$ $=\sqrt{\sqrt{25}-\sqrt{9}}$ $=\sqrt{5-3}$ $=2^{\frac{1}{2}}$ Hence, the correct answer is $2^{\frac{1}{2}}$.
Question : The value of $\frac{4 \tan ^2 30^{\circ}+\sin ^2 30^{\circ} \cos ^2 45^{\circ}+\sec ^2 48^{\circ}-\cot ^2 42^{\circ}}{\cos 37^{\circ} \sin 53^{\circ}+\sin 37^{\circ} \cos 53^{\circ}+\tan 18^{\circ} \tan 72^{\circ}}$ is:
Option 1: $\frac{35}{48}$
Option 2: $\frac{59}{48}$
Option 3: $\frac{49}{24}$
Option 4: $\frac{35}{24}$
Correct Answer: $\frac{59}{48}$
Solution : Given: $\frac{4 \tan ^2 30^{\circ}+\sin ^2 30^{\circ} \cos ^2 45^{\circ}+\sec ^2 48^{\circ}-\cot ^2 42^{\circ}}{\cos 37^{\circ} \sin 53^{\circ}+\sin 37^{\circ} \cos 53^{\circ}+\tan 18^{\circ} \tan 72^{\circ}}$ We know that $\tan 30^{\circ} = \frac{1}{\sqrt{3}}$ $\sin 30^{\circ} = \frac{1}{2}$ $\cos 45^{\circ} = \frac{1}{\sqrt{2}}$ $\cos 37^{\circ} = \cos (90^{\circ} - 53^{\circ})
Question : Given below are four sentences in jumbled order. Pick the option that gives their correct order.
A. Very soon, he bought a young goat. B. When all his goats left him, Abdul was very lonely. C. He simply couldn't do without his pets. D. He thought, "A young goat will stay with me for long."
Option 1: CADB
Option 2: CDBA
Option 3: BCAD
Option 4: BDAC
Correct Answer: BCAD
Solution : The third option is the correct choice.
The sequence begins with Abdul experiencing loneliness after all his goats leave him (B), highlighting his emotional connection to the animals. This loneliness is further emphasised in sentence C, explaining that Abdul couldn't do without his pets. Following
Question : Who amongst the following got a Nobel Prize in recognition of his discoveries of how salts and water transported in and out of cells in the human body?
Option 1: Roderick MacKinnon
Option 2: Kurt Wuethrich
Option 3: John E. Sultan
Option 4: H. Robert Horvitz
Correct Answer: Roderick MacKinnon
Solution : The correct answer is Roderick MacKinnon.
Nobel Prize in Chemistry is awarded by the Royal Swedish Academy of Sciences every year. The 2003 Nobel Prize was conferred to Peter Agre and Roderick MacKinnon. They have demonstrated how ions and water are transported through cell
Question : Which of the following pairs of "dynasty-ruled region" is correctly matched?
I. Shakas: Northwest and North India.
II. Vakatakas: Central and Western India.
Option 1: Neither I nor II
Option 2: Only I
Option 3: Only II
Option 4: Both I and II
Correct Answer: Both I and II
Solution : The correct option is Both I and II.
Shakas belonged to the Scythian ethnic group. The Shakas migrated into northwest India after being driven out of the plains of Syr Darya (Jaxartes) by the Great Yueh Chi tribe (a Chinese tribe)
Question : Choose the incorrectly spelt word.
Option 1: Innocense
Option 2: Governance
Option 3: Enforcement
Option 4: Insufficient
Correct Answer: Innocense
Solution : The correct choice is the first option.
There is an error in the spelling of "innocense" because the correct spelling is innocence, which means the fact of not being guilty of a crime.
The meanings of other words are as follows:
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. 9 : 79 :: 11 : 119 :: 7 : ?
Option 1: 41
Option 2: 49
Option 3: 47
Option 4: 51
Correct Answer: 47
Solution : Given: 9 : 79 :: 11 : 119 :: 7 : ?
Like, 9 : 79→(9)2 – 2 = 81 – 2 = 79 11 : 119→(11)2 – 2 = 121 – 2 = 119 Similarly, for 7 : ?→(7)2 – 2
Question : Select the most appropriate option that can substitute the underlined segment in the given sentence. The question was raised for discussion before the members during the assembly session.
Option 1: came up
Option 2: came off
Option 3: came round
Option 4: came out
Correct Answer: came up
Explanation:
Came off means successfully detached or separated from a surface or object.
Came round means regained consciousness or changed one's opinion or viewpoint.
Came out is emerged or became publicly known, often referring to information,
The Question containing Inaapropriate or Abusive Words
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