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Staff Selection Commission Combined Graduate Level Exam

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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

Team Careers360 25th Jan, 2024

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

12 Views

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 ?

Team Careers360 23rd Jan, 2024

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?."

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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

Team Careers360 22nd Jan, 2024

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

20 Views

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

Team Careers360 24th Jan, 2024

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.

14 Views

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

Team Careers360 25th Jan, 2024

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,

156 Views

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

Team Careers360 24th Jan, 2024

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 =

15 Views

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°

Team Careers360 25th Jan, 2024

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

84 Views

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?

Team Careers360 23rd Jan, 2024

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

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