Staff Selection Commission Combined Graduate Level Exam
Question : If $\theta$ is an acute angle and $\tan \theta+\cot \theta=2$, then the value of $\tan ^{200} \theta+\cot ^{200} \theta$ is:
Option 1: 1
Option 2: 2
Option 3: –1
Option 4: 0
Correct Answer: 2
Solution : Given $\theta$ is an acute angle Also, $\tan \theta+\cot \theta=2$ $\frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta} = 2$ ⇒ $\frac{\sin^2\theta + \cos^2\theta}{\sin\theta \cos\theta} = 2$ ⇒ $1 = 2\sin\theta \cos\theta$ ⇒ $\sin2\theta = 1$ ⇒ $2\theta = 90°$ ⇒ $\theta = 45°$ Now, $\tan ^{200} \theta+\cot ^{200} \theta$ $= (\tan
Question : Vajira Chitrasena of Sri Lanka was conferred the Padma Shri award 2020 for which of the following?
Option 1: Enriching India-Sri Lanka ties through Indian classical dance
Option 2: Enriching India- Sri Lanka ties through education
Option 3: Enriching India- Sri Lanka ties through social work
Option 4: Enriching India-Sri Lanka ties through Indian classical music
Correct Answer: Enriching India-Sri Lanka ties through Indian classical dance
Solution : The correct option is Enriching India-Sri Lanka ties through Indian classical dance.
Vajira Chitrasena of Sri Lanka was conferred the Padma Shri award in 2020 for her contributions to dance. Renowned as a pioneering figure in Sri Lankan
Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) which may improve the sentence. Choose the correct alternative. In case, no improvement is needed your answer is (4).
The farmers work at the fields.
(1) on the fields
(2) through the fields
(3) in the fields
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The correct option is the third option.
In the fields correctly conveys the idea that the farmers are working inside the fields, which is what the sentence intends to convey.
Therefore, the correct sentence is, "The farmers work in the fields."
Question : The simple interest on a sum for five years is two-fifths of the sum. The rate of interest per annum is:
Option 1: 1%
Option 2: 8%
Option 3: 6%
Option 4: 4%
Correct Answer: 8%
Solution : Time = 5 years Let the principal be $x$ Rate = $r$ So, simple interest = $\frac{2x}{5}$ Simple interest =$\frac{\text{Principal×Rate×Time}}{100}$ ⇒ $\frac{2x}{5}$ =$\frac{x×r×5}{100}$ ⇒ $r = \frac{2x×100}{5×5x}$ ⇒ $r = \frac{200x}{25x}$ $\therefore r = 8\%$ per annum Hence, the correct answer is 8%.
Question : The respective ratio between the height of the tower and the point at some distance from its foot is $5\sqrt{3}:5$. What will be the angle of elevation of the top of the tower?
Option 1: 30°
Option 2: 60°
Option 3: 90°
Option 4: 45°
Correct Answer: 60°
Solution : It is given that the respective ratio between the height of the tower and the point at some distance from its foot is $5\sqrt{3}:5$. So, AB : BC = $5\sqrt{3}:5$ In ΔABC, $\frac{AB}{BC}=\tan\theta$ ⇒ $\frac{5\sqrt{3}}{5}=\tan\theta$ ⇒ $\tan\theta=\sqrt{3}$ $\therefore \theta=60°$ Hence, the correct answer is 60°.
Question : A Navy captain is going away from a lighthouse at the speed of $4(\sqrt3–1)$ m/s. He observed that it took him 1 minute to change the angle of elevation of the top of the lighthouse from 60° to 45°. What is the height (in meters) of the lighthouse?
Option 1: $240\sqrt{3}$
Option 2: $480(\sqrt{3}–1)$
Option 3: $360\sqrt{3}$
Option 4: $280\sqrt{2}$
Correct Answer: $240\sqrt{3}$
Solution : Given: A Navy captain is going away from a lighthouse at the speed of $4(\sqrt3-1)$m/s. Let the base length be $B_{1}$ when the elevation is 60° and the base length be $B_{2}$ when the elevation is 45° and the height of the lighthouse be H.
Question : Directions: In this question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) which may improve the sentence. Choose the correct alternative in case no improvement is needed your answer is (4).
There are many species of parakeets in India, the recognisable being the Rose-ringed parakeet.
(1) more recognisable
(2) more recognised
(3) most recognisable
(4) No improvement
Solution : The sentence can be improved using the third option.
Since the sentence is comparing the Rose-ringed parakeet to other species of parakeets in India, "most recognisable" is the correct choice, indicating that it is the most easily recognised among them. Most recognisable is used for
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error.
She always / invite me / to / dinner.
Option 1: She always
Option 2: to
Option 3: dinner
Option 4: invite me
Correct Answer: invite me
Solution : The correct choice is the fourth option.
The error is in the verb form. In this context, "invite" should be replaced with "invites" as per the subject-verb agreement rule. We use the base form of the verb + "s/es" with a singular noun
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits, e.g. 13 - operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (9, 6, 25) (14, 5, 29)
Option 1: (27, 8, 29)
Option 2: (18, 4, 42)
Option 3: (13, 9, 32)
Option 4: (12, 8, 20)
Correct Answer: (13, 9, 32)
Solution : Given: (9, 6, 25); (14, 5, 29)
In the given sets, add the first and second numbers. Then add 10 to the resultant to get the third number. (9, 6, 25)→9 + 6 = 15; 15 + 10 = 25 (14, 5, 29)→14
Question : Who built the Konark's Sun Temple?
Option 1: Anantavarman Chodaganga Deva
Option 2: Narasingha Deva I
Option 3: Kapilendra Deva
Option 4: Purushottam Deva
Correct Answer: Narasingha Deva I
Solution : The correct answer is Narasingha Deva I.
The Konark Sun Temple, constructed around 1250 under the rule of King Narasingha Deva I of the Eastern Ganga dynasty, is a 13th-century Hindu temple dedicated to the deity Surya, or the Sun God. It is
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