Staff Selection Commission Combined Graduate Level Exam
Question : Directions: In an institution where there are 800 students, students use different modes of transport to go to the institution and return. The given pie diagram represents the required data. Study the diagram carefully and answer the question.
The number of students who go to the institute on foot is:
Option 1: 160
Option 2: 170
Option 3: 120
Option 4: 106
Correct Answer: 160
Solution : Given Total students = 800 Total value of the pie chart = 360° Students travelled by foot in pie chart = 360° – (216° + 18° + 54°) = 72° Number of students travelled by foot $=\frac{72}{360}×800=160$ Hence, the correct answer is 160.
Question : If RP and RQ are two tangents to a circle with centre O, such that $\angle POQ=120°$, where P and Q are the points on the circle and R is a point outside the circle, then $\angle PRQ$ is equal to:
Option 1: 90°
Option 2: 75°
Option 3: 60°
Option 4: 45°
Correct Answer: 60°
Solution : Given: $\angle POQ=120°$ We know that the angle formed by the line segment between the point of contact at the centre and the two tangents drawn from an outside point to the circle are supplementary angles. So, $\angle PRQ = 180°- 120° = 60°$ Hence,
Question : Directions: Which letter cluster will replace the question mark (?) to complete the given series? PQST, TOVS, ?, BKBQ, FIEP
Option 1: XMYR
Option 2: XYRM
Option 3: YNZQ
Option 4: XNYQ
Correct Answer: XMYR
Solution : Given: PQST, TOVS, ?, BKBQ, FIEP
First letter of the series→P + 4 = T; T + 4 = X; X + 4 = B; B + 4 = F Second letter of the series→Q – 2 = O; O – 2 = M; M
Question : If 2a + 3b = 10 and ab = 3, then find the value of 4a2 + 9b2.
Option 1: 60
Option 2: 62
Option 3: 64
Option 4: 68
Correct Answer: 64
Solution : Given, 2a + 3b = 10 Squaring both sides, (2a + 3b)2 = 102 ⇒ 4a2 + 9b2 + 2 × 2a × 3b = 100 ⇒ 4a2 + 9b2 + 12ab = 100 ⇒ 4a2 + 9b
Question : Directions: Which of the following letter clusters will replace the question mark (?) in the given series to make it logically complete? WUS, QOM, KIG, ?
Option 1: ACE
Option 2: CAE
Option 3: ECA
Option 4: EAC
Correct Answer: ECA
Solution : Given: WUS, QOM, KIG, ?
In the above-given series, subtract 6 from the place value of the letters of the previous term to get the next term. WUS→W – 6 = Q; U – 6 = O; S – 6 = M QOM→Q – 6
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error.
The number of students / attending their classes / are constantly decreasing / in our university.
Option 1: The number of students
Option 2: attending their classes
Option 3: in our university
Option 4: are constantly decreasing
Correct Answer: are constantly decreasing
Solution : The correct choice is the fourth option.
The subject of the sentence is "the number", which is a singular noun. However, the verb "are" is plural. In English, the subject and verb in a sentence must agree in number. In this case, the
Question : What is dry ice?
Option 1: Solid Carbon dioxide
Option 2: Solid Nitrogen dioxide
Option 3: Solid Sulphur dioxide
Option 4: Solid water
Correct Answer: Solid Carbon dioxide
Solution : The correct option is Solid Carbon dioxide.
Dry ice is solid carbon dioxide (CO2) at a temperature of -78.5°C. It sublimates immediately from a solid to a gas, generating carbon dioxide gas that can displace oxygen in confined environments. Because
Question : If $\sec x- \cos x$ = 4, then what will be the value of $\frac{\left(1+\cos ^2x\right)}{\cos x}?$
Option 1: $\frac{9}{4}$
Option 2: $\frac{1}{4}$
Option 3: $2\sqrt{5}$
Option 4: $\sqrt{5}$
Correct Answer: $2\sqrt{5}$
Solution : $\sec x- \cos x$ = $4$ ⇒ $(\sec x- \cos x)^2$ = $4^2$ ⇒ $\sec^2 x- 2\sec x \cos x+\cos^2 x $ = $16$ ⇒ $\sec^2 x+\cos^2 x $ = $16+2\sec x \cos x$ ⇒ $\sec^2 x+\cos^2 x + 2\sec x \cos x$ = $16+2\sec
Question : Directions: In this question, 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 follows/follow from the statements. Statements: Some roses are yellow. Some yellow are buses. All buses are green. Conclusions: I. All yellow are roses. II. Some buses are yellow. III. All yellow is green.
Option 1: Only conclusion III follows
Option 2: None of the conclusions follows
Option 3: Only conclusion II follows
Option 4: Only conclusion I follows
Correct Answer: Only conclusion II follows
Solution : According to the statements, the following Venn diagram can be drawn –
Let's analyse the conclusions – Conclusion I: All yellow are roses – From the above Venn diagram, it is evident that the circles representing yellow and roses overlap each other
Question : A and B have an annual average income of Rs. 80,000. B and C have an annual average income of Rs. 75,000. C and A have an annual average income of Rs. 78,000. The annual income of A is:
Option 1: Rs. 81,000
Option 2: Rs. 82,000
Option 3: Rs. 83,000
Option 4: Rs. 84,000
Correct Answer: Rs. 83,000
Solution : Average of annual income of (A + B) = Rs. 80,000 Total income of (A + B) = 2 × 80,000 = 1,60,000..................(equation 1) Average of annual income of (B + C) = Rs. 75,000 Total income of (B + C) = 2 ×
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