Staff Selection Commission Combined Graduate Level Exam
Question : If $2 x^2-7 x+5=0$, then what is the value of $x^2+\frac{25}{4 x^2} ?$
Option 1: $5 \frac{1}{2}$
Option 2: $7 \frac{1}{4}$
Option 3: $9 \frac{1}{2}$
Option 4: $9 \frac{3}{4}$
Correct Answer: $7 \frac{1}{4}$
Solution : $2x^2 – 7x + 5 = 0$ $⇒2x^2 + 5 = 7x$ Dividing by $2x$, we get, $⇒x + \frac{5}{2x} = \frac{7}{2}$ Squaring both sides, we get, $⇒(x + \frac{5}{2x})^2 = (\frac{7}{2})^2$ $⇒x^2 + (\frac{5}{2x})^2 + 2 × x × \frac{5}{2x} = \frac{49}{4}$ $⇒x^2
Question : A 'Market Economy' is one in which
Option 1: is controlled by the government
Option 2: is free from the government control
Option 3: is influenced by international market forces
Option 4: All of these
Correct Answer: is free from the government control
Solution : The correct answer is free from government control.
An economic system known as a market economy is one in which businesses and individual citizens of a nation collectively interact to determine economic policy and the cost of goods and services.
Question : Directions: Select the figure that will come next in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : The pattern followed here is that the figure is rotating by 45° in the clockwise direction. The following figure will complete the given pattern –
Hence, the fourth option is correct.
Question : Directions: Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 39 : 72 :: 217 : 428 :: 135 : ?
Option 1: 153
Option 2: 137
Option 3: 264
Option 4: 298
Correct Answer: 264
Solution : Given: 39 : 72 :: 217 : 428 :: 135 : ?
Like, 39 : 72→(39 × 2) – 6 = 78 – 6 = 72 217 : 428→(217 × 2) – 6 = 434 – 6 = 428 Similarly, for 135 : ?→(135 ×
Question : G is the centroid of $\triangle$ABC. If AG = BC, then measure of $\angle$BGC is:
Option 1: 45°
Option 2: 60°
Option 3: 90°
Option 4: 120°
Correct Answer: 90°
Solution : Here D is the midpoint of BC and AG = BC So, BD = GD ⇒ $\angle$BGD = $\angle$GBD and CD = GD ⇒ $\angle$GCD = $\angle$CGD In $\triangle$BGC, $\angle$GBC + $\angle$GCB + $\angle$BGC = 180° ⇒ $\angle$GBC + $\angle$GCB + ($\angle$BGD + $\angle$CGD) =
Question : Select the most appropriate ANTONYM of the underlined word. The natural environment is in contrast with the 'built environment' which refers to areas that have been fundamentally transformed and influenced by human activity, such as cities, towns, substructures, and so on.
Option 1: Hackneyed
Option 2: Inimical
Option 3: Bipartisan
Option 4: Interested
Correct Answer: Bipartisan
Solution : The third option is the correct choice.
The term influenced denotes the impact of external forces, shaping or altering a situation. In contrast, "bipartisan" implies a collaborative effort involving two political parties. The opposite of influenced here would be something not affected or shaped by
Question : Directions: Select the missing number from the given responses.
Option 1: 377
Option 2: 351
Option 3: 336
Option 4: 306
Correct Answer: 336
Solution : Given:
In each column multiply the first two numbers to obtain the third number. Column 2: 23 × 17 = 391 Column 3: 28 × 27 = 756 Similarly, Column 1: 16 × 21 = 336
Question : Select the most appropriate idiom that can substitute the italicised words in the given sentence. The world needs a global leader who can hold out a gesture of peace.
Option 1: mother wit
Option 2: halcyon days
Option 3: a grass widow
Option 4: an olive branch
Correct Answer: an olive branch
Solution : The fourth option is the correct answer.
The phrase an olive branch is a well-known idiom that symbolises a peaceful offering or gesture, often extended to resolve a conflict or promote harmony. In the context of the sentence, it fits seamlessly, conveying the
Question : Directions: Consider the given statement(s) to be true and decide which of the given conclusions can be drawn from the given statement. Statements: All cycles are ducks. All ducks are swans. Conclusions: I. All swans are cycles. II. Some swans are cycles.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Both conclusion I and conclusion II follow
Option 4: Neither Conclusion I nor Conclusion II follows
Correct Answer: Only conclusion II follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All swans are cycles – From the Venn diagram, it is evident that some parts of the circle representing swans lie outside
Question : Directions: Three statements are given, followed by three conclusions numbered I, II, and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: Some Bangles are Bracelets. All Chains are Rings. Some Bracelets are Chains. Conclusions: (I) Some Bangles are Rings. (II) Some Chains are Bangles. (III) Some Rings are Bracelets.
Option 1: Only Conclusion III follows
Option 2: Both Conclusions I and II follow
Option 3: Both Conclusions I and III follow
Option 4: Only Conclusion I follows
Correct Answer: Only Conclusion III follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some Bangles are Rings – From the Venn diagram, it is evident that there is no direct relation between bangles and rings.
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