Staff Selection Commission Combined Graduate Level Exam
Question : The income of A is $\frac{2}{3}$ of B's income and the expenditure of A is $\frac{3}{4}$ of B's expenditure. If $\frac{1}{3}$ of the income of B is equal to the expenditure of A, then the ratio of the savings of A to those of B is:
Option 1: 5 : 3
Option 2: 3 : 5
Option 3: 4 : 3
Option 4: 3 : 4
Correct Answer: 3 : 5
Solution : Income of A = $\frac{2}{3}$ of B's income Let the income of A = $2x$ and income of B = $3x$ Expenditure of A = $\frac{3}{4}$ of B's expenditure Let expenditure of A = $3y$ and expenditure of B = $4y$ $\frac{1}{3}$ of
Question : Select the option that will improve the underlined part of the given sentence. In case no improvement is needed, select 'No improvement required'.
Unless we are not sure of our goals, we cannot achieve them.
Option 1: No improvement required
Option 2: Unless we are sure
Option 3: Not until we are sure
Option 4: Except if we are not sure
Correct Answer: Unless we are sure
Solution : The correct choice is the second option.
The phrase unless we are not sure should be replaced with unless we are sure to make the sentence grammatically accurate. In the sentence, the use of a double negative (are not sure) creates
Question : Which one of the following is the infective stage of the Malarial Parasite ?
Option 1: schigozoite
Option 2: trophozoite
Option 3: sporoblast
Option 4: sporozoite
Correct Answer: sporozoite
Solution : The correct option is sporozoite.
The sporozoite is the infectious stage of the malarial parasite. An infected female Anopheles mosquito injects sporozoites into the bloodstream along with its saliva when it bites a human host. Once in the liver, these sporozoites infect hepatocytes (liver cells)
Question : In the given figure, the diameter AB and chord CD of a circle meet at P. PT is tangent to the circle at T. If CD = 8 cm, PD = 10 cm, and PB = 8 cm, find AB.
Option 1: 14.5 cm
Option 2: 22.5 cm
Option 3: 12 cm
Option 4: 8 cm
Correct Answer: 14.5 cm
Solution : Given: CD = 8 cm, PD = 10 cm, and PB = 8 cm $\therefore$ PC = CD + PD = 8 + 10 = 18 cm If two chords, AB and CD, of a circle intersect at a point P outside the circle,
Question : Select the correct passive voice form for the given sentence.
Rashi was writing a letter to her husband.
Option 1: A letter was being written by Rashi to her husband.
Option 2: A letter were being written by Rashi to her husband.
Option 3: A letter was been written by Rashi to her husband.
Option 4: A letter were been written by Rashi to her husband.
Correct Answer: A letter was being written by Rashi to her husband.
Solution : The correct choice is the first 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
Question : An article is listed at Rs. 2375. A man purchases it at two successive discounts of 50% and 25% and spends Rs. 165 on the repair of the article. If he sells the article at a profit of 62.5%, what is the selling price (in rupees) of the article?
Option 1: 1467.6
Option 2: 1492.6
Option 3: 1715.39
Option 4: 1460.6
Correct Answer: 1715.39
Solution : Marked price = Rs. 2375 Price after two successive discounts of 50% and 25% = Rs. 2375 × $\frac{50}{100}$×$\frac{75}{100}$ = Rs. 890.625 Amount spent on the repair of the article = Rs. 165 So, cost price = Rs. 890.625 + Rs.165 = Rs. 1055.625 Profit
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. I went on (1) _____ trying to 'find out how to'; but I wrote two or three novels without feeling that I had made (2) _____ progress. It was not until I wrote 'Ethan Frome' that I suddenly felt the artisan's full (3) _____ of his implements. When 'Ethan Frome' first appeared, I was (4) _____ criticised by the reviewers for what was considered the clumsy structure of the tale. I had pondered long on this structure, had felt its peculiar difficulties, and possible awkwardness, but could think of no (5) _____ which would serve as well in the given case: and though I am far from thinking 'Ethan Frome' is my best novel, and am bored and even exasperated when I am told that it is, I am still sure that its structure is not its weak point.
Question:
Select the most appropriate option to fill in the blank no. 2.
Option 1: no sooner
Option 2: barely
Option 3: much
Option 4: so
Correct Answer: much
Solution : The correct alternative is the third option.
It indicates that the writer wrote two or three novels without feeling that they had made a significant amount of progress, which aligns with the writer's sentiment in the passage.
Question : Select the INCORRECT formula from the following options.
Option 1: $\operatorname{cosec}^2 \theta-\cot ^2 \theta=1$
Option 2: $\sin ^2 \theta+\cos ^2 \theta=1$
Option 3: $\sec ^2 \theta+\cos ^2 \theta=1$
Option 4: $\sec ^2 \theta-\tan ^2 \theta=1$
Correct Answer: $\sec ^2 \theta+\cos ^2 \theta=1$
Solution : $\sec^2 \theta = \frac{1}{\cos^2 \theta}$ But, $\sec ^2 \theta+\cos ^2 \theta\neq1$ Hence, the correct answer is $\sec ^2 \theta+\cos ^2 \theta=1$.
Question : $(113^2+ 115^2 + 117^2- 113×115 - 115×117 -117×113)$ is equal:
Option 1: 0
Option 2: 4
Option 3: 8
Option 4: 12
Correct Answer: 12
Solution : Use the formula: $a^2 + b^2 + c^2 - ab - bc - ca = \frac{1}{2}((a-b)^2 + (b-c)^2 + (c-a)^2)$ Now, $(113^2+ 115^2 + 117^2- 113×115 - 115×117 -117×113)$ $=\frac{1}{2}[(113-115)^2 + (115-117)^2 + (117-113)^2]$ $=\frac{1}{2}[(-2)^2 + (-2)^2 + (4)^2]$ $=\frac{1}{2}(4 + 4 + 16)$ $=\frac{1}{2}(24)$
Question : If the measure of one angle of a right triangle is 30º more than the measure of the smallest angle, then the measure of the smallest angle is:
Option 1: 90º
Option 2: 60º
Option 3: 30º
Option 4: 75º
Correct Answer: 30º
Solution : Given: The measure of one angle of a right triangle is 30º more than the measure of the smallest angle. Let the smallest angle be $x$. So, the other angle = $(x+30°)$ According to the question, $x+(x+30°)+90°=180°$ ⇒ $2x=180°–120°$ ⇒ $x=\frac{60°}{2}$ ⇒ $x=30°$ Hence, the
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