Staff Selection Commission Combined Graduate Level Exam
Question : If $x \sin 45° = y\operatorname{cosec} 30°$, then $\frac{x^4}{y^4}$ is equal to:
Option 1: $4^3$
Option 2: $6^3$
Option 3: $2^3$
Option 4: $8^3$
Correct Answer: $4^3$
Solution : Given: If $x \sin \ 45° = y \operatorname{cosec} 30°$. $⇒\frac{x}{y} = \frac{\operatorname{cosec}30°}{\sin 45°}$ Substitute the values of the given trigonometric ratios, we get, $⇒\frac{x}{y} = \frac{2}{\frac{1}{\sqrt{2}}}$ $⇒\frac{x}{y} = (2\sqrt{2})$ On both sides of the above equation, taking the fourth power gives us, $⇒\frac{x^{4}}{y^{4}} =
Question : Two donkeys are standing 400 metres apart. The first donkey can run at a speed of 3 m/sec and the second can run at 2 m/sec. If two donkeys run towards each other, after how much time (in seconds) will they bump into each other?
Option 1: 60
Option 2: 80
Option 3: 400
Option 4: 40
Correct Answer: 80
Solution : Here the distance between two donkeys = 400 metres. Speed of the first donkey = 3 m/sec. Speed of the second donkey = 2 m/sec. If both running in opposite directions relative speed = (3 + 2) = 5 m/sec. So, the time taken to
Question : A unit price elastic demand curve will touch
Option 1: Both price and quantity axis .
Option 2: Neither price axis , nor quantity axis.
Option 3: Only price axis .
Option 4: Only quantity axis .
Correct Answer: Neither price axis , nor quantity axis.
Solution : The correct option is Neither price axis, nor quantity axis.
The price (vertical axis) or quantity (horizontal axis) axis will never be touched by a unit price elastic demand curve during its entire length. This implies that if a
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.
Redwing had read (1)_____that one of his favourite writers, Ernest Hemingway, had been asked what was the best (2)_______for a novelist. He had said "an unhappy childhood". Redwing had enjoyed a fine time growing up, but he (3)_______if this whole (4)_______was unfolding more like a novel and would be (5)_______on one person, one character, the guy in charge: him. Maybe you had a happy childhood and then an unhappy adulthood, and that's how novels worked.
Question: Select the most appropriate option to fill in blank no. 3.
Option 1: wasted
Option 2: wondered
Option 3: wandered
Option 4: welded
Correct Answer: wondered
Solution : The correct choice is the second option.
In this context, wondered means that Redwing was contemplating or thinking about whether the unfolding events resembled a novel. He was pondering or questioning this possibility. The word wondered means to have thoughts of curiosity or doubt,
Question : Select the most appropriate ANTONYM of the underlined word.
She will probably come tonight for a party.
Option 1: definitely
Option 2: perhaps
Option 3: apparently
Option 4: possibly
Correct Answer: definitely
Solution : The correct answer is the first option.
Probably suggests a likelihood but not a certainty of the event happening. The most appropriate antonym is definitely, which means without a doubt and with certainty.
The meanings of the other options are as follows:
Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series. I, V, ?, L
Option 1: C
Option 2: D
Option 3: M
Option 4: X
Correct Answer: X
Solution : Given: I, V, ?, L
The Roman numeral system contains seven numbers. They are I, V, X, L, C, D, and M.
The next term after V has to
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
I forbid you not to go there again.
(1) there again.
(2) No Error
(3) not to go
(4) I forbid you
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The error lies in the third option.
Forbid is a verb that means refusing to allow something. It is already a negative word, and the use of not to go makes the sentence have double negatives, which is incorrect. Thus, not to go should be
Question : Select the correct direct form of the given sentence. She said that she could not believe him.
Option 1: She said, “You cannot believe him.”
Option 2: She said, “I may not believe him.”
Option 3: She said, “I cannot believe him.”
Option 4: She says, “I could not believed him.”
Correct Answer: She said, “I cannot believe him.”
Solution : The correct option is the third option.
Explanation: In the direct form, the reported speech is directly quoted, and the pronouns may change based on the context.
In this case, she (third-person) changes to "I" (first-person), and him remains unchanged.
Question : Select the most appropriate direct form of the given sentence. Father told Avika to stop watching the TV and eat her food.
Option 1: Father said to Avika, “ Stop eating the TV and watch your food.”
Option 2: Father said, “Avika, Why can’t you stop watching the TV and eat your food?”
Option 3: Father said, “Avika, stop watching the TV and eat her food.”
Option 4: Father said, “Avika, stop watching the TV and eat your food.
Correct Answer: Father said, “Avika, stop watching the TV and eat your food.
Solution : The fourth option is correct.
Direct speech is a form of speech or writing where the actual words spoken by a person are quoted within quotation marks and attributed to the speaker. Narration conversion:
Question : ' O ' is a point in the interior of an equilateral triangle. The perpendicular distance from ' O ' to the sides are $\sqrt{3}~cm, 2 \sqrt{3}~cm, 5 \sqrt{3}~cm$. The perimeter of the triangle is:
Option 1: 48 cm
Option 2: 32 cm
Option 3: 24 cm
Option 4: 64 cm
Correct Answer: 48 cm
Solution : Perpendicular distance = $p{_1} = \sqrt{3}$ $p{_2} =2\sqrt{3}$ $p{_3} = 5\sqrt{3}$ Height of an equilateral triangle = $\frac{\sqrt{3} \times (a)}{2}$ Height of an equilateral triangle = sum of perpendicular distance with point The perimeter of an equilateral triangle = $3\times a$ Height of equilateral
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