Staff Selection Commission Combined Graduate Level Exam
Question : $\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}$ and the perimeters of these triangles are 32 cm and 12 cm, respectively. If $\mathrm{DE}=6 \mathrm{~cm}$, then what will be the length of AB?
Option 1: 16 cm
Option 2: 14 cm
Option 3: 12 cm
Option 4: 18 cm
Correct Answer: 16 cm
Solution : If two triangles are similar, then their perimeters are directly proportional to the length of their corresponding sides. So, $\frac{\text{Perimeter of $\triangle$ABC}}{\text{Perimeter of $\triangle$ABC}}= \frac{AB}{DE} = \frac{32}{12}$ ⇒ $AB = \frac{32}{12}\times 6$ ⇒ $AB = 16\ \mathrm{cm}$ Hence, the correct answer is 16 cm.
Question : If $a+\frac{1}{a-2}=4$, then the value of $(a-2)^{2}+(\frac{1}{a-2})^{2}$ is:
Option 1: 0
Option 2: 2
Option 3: –2
Option 4: 4
Correct Answer: 2
Solution : Given: $a+\frac{1}{a-2}=4$ Subtracting 2 from both sides, ⇒ $a-2+\frac{1}{a-2}=2$ Squaring both sides, ⇒ $( a-2)^2+\frac{1}{( a-2)^2} + 2=2^2$ ⇒ $( a-2)^2+\frac{1}{( a-2)^2}=2^2-2$ ⇒ $( a-2)^2+\frac{1}{( a-2)^2}=2$ Hence, the correct answer is 2.
Question : The Rourkela steel plant was set up in collaboration with Germany in which the state of India?
Option 1: Jharkhand
Option 2: Bihar
Option 3: Assam
Option 4: Odisha
Correct Answer: Odisha
Solution : The correct option is Odisha.
One of India's biggest steel production sites is the Rourkela Steel Plant. It is located in the city of Rourkela in the Sundargarh district of Odisha. One of India's earliest integrated steel factories, the Rourkela Steel Plant was founded in
Question : In a 1500 m race, Anil beats Bakul by 150 m, and in the same race, Bakul beats Charles by 75 m. By what distance does Anil beat Charles?
Option 1: 217.50 m
Option 2: 200.15 m
Option 3: 293.50 m
Option 4: 313.75 m
Correct Answer: 217.50 m
Solution : In 1500 m race, Anil beats Bakul by 150 m. When Anil completes the race, Bakul covers 1500 – 150 = 1350 m Bakul beats Charles by 75 m in 1500 m race. So in a 1350 m race, Bakul is ahead of Charles
Question : Select the correct passive form of the given sentence.
May you achieve success in all your endeavours.
Option 1: May success will be achieved by you in all your endeavours.
Option 2: Success might be achieved by you in all your endeavours.
Option 3: May success be achieved by you in all your endeavours.
Option 4: Success has been achieved by you in all your endeavours.
Correct Answer: May success be achieved by you in all your endeavours.
Solution : The correct choice is the third option.
Explanation: In a passive voice construction, the subject of the sentence receives the action, and the focus is on the action rather than the doer. The verb "achieve" becomes
Question : If $4x^2-12x+k$ is a perfect square, then the value of $k$ is:
Option 1: 2
Option 2: 9
Option 3: 12
Option 4: 10
Correct Answer: 9
Solution : Given: $4x^2-12x+k$ is a perfect square. $4x^2-12x+k=(2x)^2-2×2x×3+k$ Since this a perfect, So, $(2x)^2-2×2x×3+k=(2x)^2-2×2x×3+3^2=(2x–3)^2$ Value of $k$ is 32 = 9 Hence, the correct answer is 9.
Question : Which among the following rocks may contain fossils of plants, animals and other microorganisms that once lived on them?
Option 1: Metamorphic rocks
Option 2: Intrusive igneous rocks
Option 3: Sedimentary rocks
Option 4: Extrusive igneous rocks
Correct Answer: Sedimentary rocks
Solution : The correct option is Sedimentary rocks.
The type of rock that may contain fossils of plants, animals, and other microorganisms that once lived on or in them is called sedimentary rock. Sedimentary rocks are formed from the accumulation and cementation of sediments, which
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error.
When the train pulled in / at the station, it take / Joseph some time / to get off.
Option 1: When the train pulled in
Option 2: at the station, it take
Option 3: Joseph some time
Option 4: to get off.
Correct Answer: at the station, it take
Solution : The segment that contains a grammatical error is the second option.
Explanation: The error lies in the tense consistency as per zero conditional. The correct form should be "it took" instead of "it take". In this context, took is the correct
Question : The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?
Option 1: $6 \sqrt{3}\ \text{cm}$
Option 2: $4\sqrt{3}\ \text{cm}$
Option 3: $9 \sqrt{3}\ \text{cm}$
Option 4: $5\sqrt{3}\ \text{cm}$
Correct Answer: $4\sqrt{3}\ \text{cm}$
Solution : Given: Side of the equilateral triangle = 12 cm We know that, The radius of a circle circumscribing in an equilateral triangle = $\frac{\text{side}}{\sqrt3}$ = $\frac{12}{\sqrt3}$ = $4\sqrt3\ \text{cm}$ Hence, the correct answer is $4\sqrt3\ \text{cm}$.
Question : Directions: From the given options, which answer figure can be formed by folding the figure given in the question?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : In a 3D view of dice, 1. Each face out of the three faces in the 3D view should be from all the pairs. 2. Two opposite faces cannot appear adjacently in the 3D view of a folded cube figure. So, the opposite pairs of faces
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