Staff Selection Commission Combined Graduate Level Exam
Question : The ratio of the monthly incomes of X and Y is 5 : 4 and that of their monthly expenditures is 9 : 7. If the income of Y is equal to the expenditure of X, then what is the ratio of the savings of X and Y?
Option 1: 9 : 8
Option 2: 6 : 7
Option 3: 8 : 9
Option 4: 7 : 6
Correct Answer: 9 : 8
Solution : The ratio of the monthly income of X and Y = 5 : 4 The ratio of monthly expenditures of X and Y = 9 : 7 Let the income ratio of X and Y be 5a and 4a. Let the expenditure ratio
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer. She has finished writing the article, ___.
Option 1: has she?
Option 2: isn't it?
Option 3: hasn't she?
Option 4: is it ?
Correct Answer: hasn't she?
Solution : The third option is the correct answer: hasn't she?
The sentence is in the present perfect tense and is a positive statement. So, the question tag must be negative in nature.
Therefore, the answer is "She has finished writing the article, hasn't she?."
Question : Assume that a drop of water is spherical and that its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely, then the height of the glass (in cm) is:
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 4
Solution : Height of the glass $=h$ cm Radius of the glass $=\frac{h}{2}$ Volume of the glass $=\frac{1}{3}\pi r^2 h=\frac{1}{3}\pi (\frac{h}{2})^2 h$ Radius of the spherical drop $=\frac{1}{2\times10}=\frac{1}{20}$ cm Volume of a spherical drop $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (\frac{1}{20})^3$ Volume of 32,000 spherical drops $=32000\times\frac{4}{3}\pi (\frac{1}{20})^3$ Now, the volume
Question : If $\tan^4\theta + \tan^2\theta=1$, what is the value of $11(\cos^4\theta+\cos^2\theta)$?
Option 1: – 11
Option 2: 8
Option 3: 0
Option 4: 11
Correct Answer: 11
Solution : Given: $\tan^4\theta + \tan^2\theta=1$ ⇒ $\tan^2\theta(\tan^2\theta+1)=1 [\because \sec^2\theta-\tan^2\theta=1]$ ⇒ $\tan^2\theta \sec^2\theta=1$ $\therefore \tan^2\theta=\cos^2\theta$ $11(\cos^4\theta+\cos^2\theta)$ = $11[(\cos^2\theta)^2+\cos^2\theta]$ = $11(\tan^4\theta + \tan^2\theta)$ = $11×1$ = $11$ Hence, the correct answer is 11.
Question : The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 8 : 5. The ratio of their volumes is equal to:
Option 1: 9 : 10
Option 2: 8 : 9
Option 3: 9 : 11
Option 4: 7 : 10
Correct Answer: 9 : 10
Solution : Given: The radii of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 8 : 5. Let the radii of two cylinders be $3x$ and $4x$ and their heights be $8y$ and $5y$. Use the formulas,
Question : Directions: In a certain code language, PLIERS is coded as MMAFJO, and SHOVEL is coded as FZRLFR. How will WRENCH be coded in the same language?
Option 1: CXJBQU
Option 2: BXJBPV
Option 3: BXJBQU
Option 4: CXIBPV
Correct Answer: BXJBPV
Solution : Given: PLIERS is coded as MMAFJO and SHOVEL as FZRLFR.
Like, PLIERS; PLIERS→SREILP (Reverse the letters); S – 6 = M; R – 5 = M; E – 4 = A; I – 3 = F; L – 2 = J; P – 1 =
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.
Swaminathan had a table on which all his things, his coat, cap, slate, ink bottle, and books, were thrown in a confused (1)______ He sat on his stool and shut his eyes to (2) ________ what work he had for the day: first of course there was arithmetic – those five (3)_______ in profit and loss; then there was English – he had to copy down a page from his English lesson and write dictionary meanings of (4) _______ words; and then there was geography. And only two hours before him to do all this heap of work and get (5) ______ for school.
Question:
Select the most appropriate option to fill in the blank number 3.
Option 1: disputes
Option 2: puzzles
Option 3: debates
Option 4: conditions
Correct Answer: puzzles
Solution : The correct choice is the second option.
In the context of the passage, the word "puzzles" fits best to describe the five tasks in profit and loss under arithmetic. The term puzzle implies a sense of complexity or difficulty, which aligns with the nature
Question : 'O' is the circumcentre of triangle ABC lying inside the triangle, then $\angle$OBC + $\angle$BAC is equal to:
Option 1: 90°
Option 2: 60°
Option 3: 110°
Option 4: 120°
Correct Answer: 90°
Solution : Let $\angle$OBC and $\angle$OCB be $\theta$. In $\triangle$OBC, $\angle$OBC + $\angle$OCB + $\angle$BOC = 180° ⇒ $\theta + \theta + \angle$BOC = 180° ⇒ $\angle$BOC = 180° – 2$\theta$ We know that in a circle, the angle subtended by an arc at the centre is
Question : Select the correct active form of the given sentence.
Has the villa been occupied by them?
Option 1: Did they occupied the villa?
Option 2: Had they occupied the villa?
Option 3: Have they occupied the villa?
Option 4: Do they occupied the villa?
Correct Answer: Have they occupied the villa?
Solution : The correct choice is the third option.
Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.
The structure of the
Question : Directions: Given below is a question followed by two statements I and II. Read both statements carefully to decide which one of them is sufficient to answer the question. Six people - A, B, C, D, E and F are sitting in a straight line facing north. Who sits to the immediate left of D? (I) A sits second from one of the extreme ends of the line. Only two people sit between A and B. E sits to the immediate right of C. (II) C sits third from the left end of the line. Only one person sits between C and F. E sits third to the right of F.
Option 1: Data in statement II alone is sufficient to answer the question while data in statement I is not
Option 2: Data in statement I alone is sufficient to answer the question while data in statement II is not
Option 3: Data in statements I and II together are not sufficient to answer the question
Option 4: Data in statements I and II together are sufficient to answer the question
Correct Answer: Data in statements I and II together are not sufficient to answer the question
Solution : Given: (I) A sits second from one of the extreme ends of the line. Only two people sit between A and B. E sits to the immediate right of C.
(II) C
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