Staff Selection Commission Combined Graduate Level Exam
Question : A sum of money becomes INR 11,880 after 4 years and INR 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in INR)?
Option 1: 2,410
Option 2: 2,530
Option 3: 2,640
Option 4: 2,750
Correct Answer: 2,640
Solution : Let the rate of interest per annum be $R$ and principal $P$ According to the question, (Amount after 4 years): (Amount after 6 years) = 11880 : 17820 = 2 : 3 ⇒ [$(1+\frac{R}{100})^{4}$]: [$(1+\frac{R}{100})^{6}$] = 2 : 3 ⇒ $(1+\frac{R}{100})^{2}$ = $\frac{3}{2}$ Amount after
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at MN as shown below.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per the mirror image properties, closer things appear closer to the mirror in the reflection. According to the information provided, the mirror is placed on the bottom side of the figure (on line MN). So, the bottom side of the reflected image will appear as
Question : Study the given graph and answer the question that follows.
The ratio of the total production of cement by Company A in 2016 and Company C in 2018 to the total production of cement by Company B in 2017 and 2019 is:
Option 1: 9 : 8
Option 2: 7 : 6
Option 3: 8 : 7
Option 4: 10 : 9
Correct Answer: 9 : 8
Solution : As per the graph, The total production in A in 2016 = 280 million tonnes The total production in C in 2018 = 350 million tonnes Total production = 280 + 350 = 630 million tonnes The total production in B in 2017
Question : Directions: The weight of the four boxes is 20, 40, 80, and 90 kilograms. Which of the following cannot be the total weight, in kilograms, of any combination of these boxes, and in a combination, a box can be used only once?
Option 1: 220
Option 2: 230
Option 3: 150
Option 4: 210
Correct Answer: 220
Solution : Given: The weight of the four boxes is 20, 40, 80, and 90 kilograms.
The total weight of all possible combinations of boxes is as follows – 20 + 40 = 60; 20 + 80 = 100; 20 + 90 = 110; 40 + 80
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
Due to the fall in real estate prices builders have (stopped from constructing) multi-storeyed office buildings
(1) at constructing
(2) to constructing
(3) stopped constructing
(4) No Improvement
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 3
Solution : The correct choice to improve the sentence is the third option.
Explanation: This option is the correct improvement. It uses the verb "stopped constructing," which is the appropriate way to convey that builders have ceased their construction activities. This option adheres to proper verb usage
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
Tired I was I had to (1) / keep on working till (2) / the wee hours of the morning. (3) / No Error (4).
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The error lies in the first part of the sentence.
The sentence has a structural error. Though should be added at the beginning of the sentence as it is used as a subordinating conjunction, which helps in indicating contrast in the sentence so the phrase,
Question : (N + 18) persons, each working for 7.5 hours a day, can complete 48% of the work in 20 days. (N + 12) persons can complete the remaining work in 30 days if each works 6.5 hours per day. Determine the value of N.
Option 1: 18
Option 2: 16
Option 3: 20
Option 4: 22
Correct Answer: 18
Solution : Number of hours (N + 18) people worked in a day, $T_1$ = 7.5 hours Number of days they worked for, $D_1$ = 20 days Fraction of work completed by them, $W_1$ = 0.48 Number of hours (N + 12) people worked in a day,
Question : From two points, lying on the same horizontal line, the angles of elevation of the top of the pillar are $\theta$ and $\phi$ ($\theta<\phi$). If the height of the pillar is $h$ m and the two points lie on the same sides of the pillar, then the distances between the two points are:
Option 1: $h(\tan\theta-\tan\phi)$ metre
Option 2: $h(\cot\phi-\cot\theta)$ metre
Option 3: $h(\cot\theta-\cot\phi)$ metre
Option 4: $h\frac{(\tan\theta \tan\phi)}{(\tan\phi-\tan\theta)}$ metre
Correct Answer: $h(\cot\theta-\cot\phi)$ metre
Solution : Let AB = height of pole = $h$ metre $\angle$ACB = $\theta$, $\angle$ADB = $\phi$ In ∆ABD, $\tan\phi=\frac{AB}{BD}$ ⇒ $BD=h\cot\phi$ In ∆ABC, $\tan\theta=\frac{AB}{BC}$ ⇒ $BC=h\cot\theta$ ∴ Required distance, CD $=h\cot\theta-h\cot\phi$ $= h(\cot\theta-\cot\phi)$ metre Hence, the correct answer is $h(\cot\theta-\cot\phi)$ metre.
Question : Successive discounts of 10% and 10% are equivalent to a single discount of:
Option 1: 18%
Option 2: 19%
Option 3: 20%
Option 4: 21%
Correct Answer: 19%
Solution : Single equivalent discount of 10% and 10% $=10+10-\frac{10×10}{100}=19\%$ Hence, the correct answer is 19%.
Question : The area of a sector of a circle is 88 sq. cm., and the angle of the sector is 45°. Find the radius of the circle. (Use $\pi=\frac{22}{7}$)
Option 1: $3 \sqrt{ 11} \mathrm{~cm}$
Option 2: $4 \sqrt{ 14} \mathrm{~cm}$
Option 3: $6 \sqrt{ 13} \mathrm{~cm}$
Option 4: $5 \sqrt{ 14} \mathrm{~cm}$
Correct Answer: $4 \sqrt{ 14} \mathrm{~cm}$
Solution : Given, that the angle of the sector is 45°. The area of a sector of a circle is 88 sq. cm. Let the radius of the circle be $r$ cm. We know that Area of sector = $\frac{\theta}{360^{\circ}}\times \pi r^2$ According to
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