Staff Selection Commission Combined Graduate Level Exam
Question : A can do a task in 8 days, while B can do it in 18 days. In how many days will the work be completed if they both work on alternate days, starting with B?
Option 1: $11 \frac{1}{3}$ days
Option 2: $12 \frac{1}{3}$ days
Option 3: $10$ days
Option 4: $10 \frac{1}{3}$ days
Correct Answer: $11 \frac{1}{3}$ days
Solution : Given: A can do a task in $8$ days. B can do it in $18$ days. Let the total work be the LCM of $(8, 18)$ i.e. $72$ units. ⇒ Efficiency of A $=\frac{72}{8} = 9$ units ⇒ Efficiency of B $=\frac{72}{18} =
Question : Where in India can 'Mushroom' rock be found?
Option 1: Eastern Ghats
Option 2: Western Ghats
Option 3: Thar Desert
Option 4: Satpura Range
Correct Answer: Thar Desert
Solution : The correct answer is Thar desert.
In India mushroom rocks are found in Thar desert region in Rajasthan. Mushroom rocks are Aeolian landform, i.e they are formed by the action of winds on the rocks. It is an erosional landform and also called as
Question : Match the characteristics with their market structure:
(a) Difficult entry (often due to economies of scale)
(b) Can sell as much as it can at the market price
Option 1: (a) Monopolistic competition,
(b) Pure monopoly
Option 2: (a) Pure monopoly,
(b) Oligopoly
Option 3: (a) Oligopoly,
(b) Pure competition
Option 4: (a) Pure competition,
Correct Answer: (a) Oligopoly,
Solution : The correct answer is (a) Oligopoly,
(b) Pure competition.
Oligopoly: An oligopoly is a market structure where there are only a few suppliers who are competing for the same market for a given commodity. Entry and Exit are difficult.
Pure
Question : Which is the first national park established in India?
Option 1: Velvadan National Park
Option 2: Periyar National Park
Option 3: Bandipur National Park
Option 4: Corbett National Park
Correct Answer: Corbett National Park
Solution : The correct option is - Corbett National Park
The first national park in India, currently known as Jim Corbett National Park, was established in 1936 as Uttarakhand's Hailey National Park. The Project Tiger project was launched with the park as its initial target.
Question : Select the most appropriate synonym of the given word. Answer
Option 1: Recall
Option 2: Reply
Option 3: Remember
Option 4: Query
Correct Answer: Reply
Solution : The second option is the correct choice.
Reply refers to responding to a question, statement, or situation by providing an answer or addressing something that has been asked or communicated.
Answer and reply are often used interchangeably in various contexts, especially when responding to a
Question : What is the value of $64x^{3} + 36x^{2}y + 24xy^{2} + 2y^{3}$, when $x = 3$ and $y = -4?$
Option 1: $304$
Option 2: $1456$
Option 3: $1584$
Option 4: $432$
Correct Answer: $1456$
Solution : Given: $x = 3, y = -4$ So, the value of $64x^{3} + 36x^{2}y + 24xy^{2} + 2y^{3}$ $=x^{2}(64x + 36y) + y^{2}(24x + 2y)$ $=3^{2}[(64 × 3) + (36 × -4)] + (-4)^{2}[(24 × 3) + (2 × -4)]$ $=9 × [192 -144] +
Question : If $\left(\frac{\cos A}{1-\sin A}\right)+\left(\frac{\cos A}{1+\sin A}\right)=4$, then what will be the value of $A$? $\left(0^{\circ}<\theta<90^{\circ}\right)$
Option 1: $90^{\circ}$
Option 2: $45^{\circ}$
Option 3: $60^{\circ}$
Option 4: $30^{\circ}$
Correct Answer: $60^{\circ}$
Solution : Given: $\left(\frac{\cos A}{1-\sin A}\right)+\left(\frac{\cos A}{1+\sin A}\right) = 4$ ⇒ $\frac{\cos A(1+\sin A) + \cos A(1-\sin A)}{(1-\sin A)(1+\sin A)} = 4$ ⇒ $\cos A + \cos A \sin A + \cos A - \cos A \sin A = 4(1-\sin^2A)$ ⇒ $2\cos A = 4 \cos^2 A$
Question : Select the most appropriate option to fill in the blank. Have you ______ with the difficulties you might have to face?
Option 1: considered
Option 2: reckoned
Option 3: discussed
Option 4: pondered
Correct Answer: reckoned
Solution : The correct choice will be the second option.
The word reckoned is the most appropriate option to fill in the blank. In this context, "reckoned" means to consider or take into account. The sentence is asking whether the person has given careful thought or consideration
Question : Select the correct active form of the given sentence.
You are asked to tell the plumber to mend all the pipes.
Option 1: Command the plumber mending all the pipes.
Option 2: Tell the plumber to mend all the pipes.
Option 3: All the pipes must be mend.
Option 4: Tell the plumber mending all the pipes.
Correct Answer: Tell the plumber to mend all the pipes.
Active voice is the voice where the subject performs the action. To convert a sentence from passive to active voice, we identify the subject performing the action and rephrase the sentence
Question : If $\small a^{3}+3a^{2}+9a=1$, then what is the value of $a^{3}+\frac{3}{a}$?
Option 1: 31
Option 2: 26
Option 3: 28
Option 4: 24
Correct Answer: 28
Solution : $a^{3}+3a^{2}+9a=1$ .......(i) Multiply the equation by $\frac{3}{a}$ both sides, ⇒ $3a^{2}+9a+27=\frac{3}{a}$ ......(ii) Subtracting (ii) from (i), ⇒ $a^{3}-27=1-\frac{3}{a}$ $\therefore a^{3}+\frac{3}{a}=28$ Hence, the correct answer is 28.
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