Staff Selection Commission Combined Graduate Level Exam
Question : The number of solid spheres, each of diameter 6 cm, that could be moulded to form a solid metal cylinder of height 90 cm and diameter 4 cm is:
Option 1: 10
Option 2: 14
Option 3: 16
Option 4: 13
Correct Answer: 10
Solution : We have, The radius of the sphere, $R$ = 3 cm The radius of the cylinder, $r$ = 2 cm The height of the cylinder, $h$ = 90 cm Now, the required number of solid spheres = $\frac{\text{ Volume of the cylinder}}{\text{Volume of the Sphere}}$
Question : Directions: In the following question below, some statements are followed by some conclusions. Taking the given statements to be true, even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusions logically follows from the given statements. Statements: I. No student is a teacher. II. All students are children. III. Some girls are students. Conclusions: I. Some children are not teachers. II. Some girls are not teachers. III. No girl is a teacher.
Option 1: Only conclusions I and II follow
Option 2: All conclusions follow
Option 3: Only conclusions II and III follow
Option 4: Only conclusions I and III follow
Correct Answer: Only conclusions I and II follow
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion I: Some children are not teachers – From the Venn diagram, it is evident that some children are students and no
Question : A sum of money amounts to INR 767 in 3 years, and to INR 806 in 4 years on simple interest at 6% per annum. What is the sum?
Option 1: INR 600
Option 2: INR 560
Option 3: INR 675
Option 4: INR 650
Correct Answer: INR 650
Solution : Given, A sum of money amounts to INR 767 in 3 years, and to INR 806 in 4 years on simple interest at 6% annum. Interest for 1 year = 806 – 767 = INR 39 ⇒ Interest in 3 years = 39 ×
Question : Directions: Three different positions of the same dice are shown (figures 1 to 3). Find the number on the face opposite to the face having 1.
Option 1: 3
Option 2: 6
Option 3: 5
Option 4: 4
Correct Answer: 4
Solution : Taking dice positions 1 and 3 with 4 as the common face –
Moving clockwise from the common face with 4 –
Pairs of opposite faces –
So, the opposite face to the face containing 1 is 4. Hence, the fourth option is correct.
Question : A train, 500 metres long and running at a uniform speed, passes a station in 35 seconds. If the length of the platform is 221 metres, the speed of the train in km/h is:
Option 1: $72\frac{1}{35}$
Option 2: $74.16$
Option 3: $24.76$
Option 4: $78.54$
Correct Answer: $74.16$
Solution : Given: The distance of the train is 500 m and the length of the platform is 221 m. The time taken by the train is 35 seconds. We know that, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$. Total distance = 500 + 221 = 721 m $\text{Speed}=\frac{721}{35}$ m/s To convert m/s
Question : Directions: Consider the given statements to be true, even if they seem to be at variance from commonly known facts. You have to decide which of the following conclusions or assumptions be drawn from the given statement. Statements: I. All that glitter is not gold. II. Sujatha wears gold ornament. Conclusions: I. Sujatha's ornament glitters. II. Sujatha's ornament does not glitter.
Option 1: Only conclusion I follows
Option 2: Only conclusion II follows
Option 3: Both conclusions I and II follow
Option 4: Neither conclusion I nor II follows
Correct Answer: Neither conclusion I nor II follows
Solution : Let's analyse the conclusions – Conclusion I: Sujatha's ornament glitters. According to the statement, all that glitters is not gold. Here, Sujatha wears a gold ornament which may or may not glitter. Therefore, this conclusion doesn't follow. Conclusion II: Sujatha's
Question : Which of the following elements is more reactive than copper?
Option 1: Gold
Option 2: Zinc
Option 3: Silver
Option 4: Platinum
Correct Answer: Zinc
Solution : The correct option is Zinc.
Reactivity in metals is often related to their position in the reactivity series. The reactivity series is a list of metals arranged in order of their tendency to lose electrons and form positive ions. In this series, zinc is
Question : In which year did Kyoto Protocol came into force?
Option 1: 2004
Option 2: 2005
Option 3: 2006
Option 4: 2007
Correct Answer: 2005
Solution : The correct option is 2005
The Kyoto Protocol is an international agreement that sets legally binding goals for industrialised nations to cut their emissions of greenhouse gases to combat climate change. It was enacted in Kyoto, Japan, on December 11, 1997, and became operative from
Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct? 13 − 65 ÷ 45 × 21 + 2 = 82
Option 1: 65 and 13, × and +
Option 2: 45 and 13, × and +
Option 3: 45 and 21, × and +
Option 4: 45 and 13, − and +
Correct Answer: 45 and 13, × and +
Solution : Given: 13 − 65 ÷ 45 × 21 + 2 = 82
Replace the given numbers and symbols in the options one by one with the original numbers and symbols in the given equation. First option: 65 and 13, ×
Question : ABCD is a quadrilateral. The length of the diagonal AC is 24 cm. The sum of the perpendicular drawn from vertex B and D on the diagonal AC is 10 cm. What is the area of the quadrilateral?
Option 1: 240 cm2
Option 2: 180 cm2
Option 3: 120 cm2
Option 4: 90 cm2
Correct Answer: 120 cm2
Solution : Given: $d=24$ cm and $h_1+h_2=10$ cm. The area of the quadrilateral $=\frac{1}{2}\times(h_1+h_2)\times d$ where $d$ and $(h_1+h_2)$ are its diagonals and sum of heights. So, the area $=\frac{1}{2}\times10\times 24=120$ cm2 Hence, the correct answer is 120 cm2.
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