Staff Selection Commission Combined Graduate Level Exam
Question : Two pipes, S1 and S2, can alone fill an empty tank in 15 hours and 20 hours, respectively. Pipe S3 alone can empty that filled tank in 40 hours. Firstly, both pipes, S1 and S2, are opened and after 2 hours, pipe S3 is also opened. In how much time will the tank be filled after S3 is opened?
Option 1: $\frac{90}{17}\ \text{hours}$
Option 2: $\frac{89}{12}\ \text{hours}$
Option 3: $\frac{90}{13}\ \text{hours}$
Option 4: $\frac{92}{11}\ \text{hours}$
Correct Answer: $\frac{92}{11}\ \text{hours}$
Solution : Let the capacity of the tank be 120 units (LCM of 15, 20, and 40) Pipe A fills = $\frac{120}{15}$ = 8 units per hour Pipe B fills = $\frac{120}{15}$ = 6 units per hour Pipe C empties = $\frac{120}{40}$ = 3 units per hour A and B in 2 hours fill (8 + 6) × 2 units of the tank = 28 units of the tank Remaining units of the tank to be filled = 120 – 28 = 92 units/hour After 2 hours, C joins. So, units of the tank filled by A, B, and C = (8 + 6 – 3) = 11 units/hour So, the time needed to fill the remaining tank = $\frac{92}{11}$ hours Hence, the correct answer is $\frac{92}{11}\ \text{hours}$.
Question : Washing of peeled vegetables removes the vitamin
Option 1: A
Option 2: C
Option 3: D
Option 4: E
Correct Answer: C
Solution : The correct option is Vitamin C.
Some vitamin C is lost when vegetables are washed. Because vitamin C is a water-soluble vitamin, it dissolves in water. When you wash vegetables, part of the vitamin C is washed away. The quantity of vitamin C lost during washing is determined by several factors, including the kind of vegetable, the length of time it is washed, and the temperature of the water. Leafy vegetables, such as spinach and kale, lose more vitamin C than root vegetables, such as carrots and potatoes.
Question : If $14 : 30 :: 7 : x$, then what is the value of $x$?
Option 1: 15
Option 2: 21
Option 3: 9
Option 4: 12
Correct Answer: 15
Solution : $14 : 30 :: 7 : x$ ⇒ $\frac{14}{30}=\frac{7}{x}$ ⇒ $x = \frac{7\times 30}{14}$ ⇒ $x= 15$ Hence, the correct answer is 15.
Question : The perimeter of an isosceles triangle is 100 cm. If the base is 36 cm, find its semi-perimeter (in centimetres).
Option 1: 64 cm
Option 2: 60 cm
Option 3: 45 cm
Option 4: 50 cm
Correct Answer: 50 cm
Solution : Semi-perimeter of a triangle $= (\frac{\text{Perimeter}}{2})$ = $\frac{100}{2}$ = 50 cm Hence, the correct answer is 50 cm.
Question : The length, breadth, and height of a wooden box with a lid are 10 cm, 9 cm, and 7 cm, respectively. The total inner surface of the closed box is 262 cm2. The thickness of the wood (in cm) is:
Option 1: $2$
Option 2: $3$
Option 3: $\frac{23}{3}$
Option 4: $1$
Correct Answer: $1$
Solution : Given: Inner surface area = 262 cm2 The length, breadth, and height are 10 cm, 9 cm, and 7 cm, respectively. Let the thickness of the wood be $x$ cm. Surface area of the cuboid = 2(length × breadth + length × height + breadth × height) Area of inner surface $= 2(9 - 2x)(10 - 2x) + 2(9 -2x)(7 - 2x) + 2(10- 2x)(7 - 2x)$ $⇒ 262 = 2(9 - 2x)(10 - 2x) + 2(9 -2x)(7 - 2x) + 2(10 - 2x)(7- 2x)$ Putting the value of $x = 1,$ the above equation is satisfied. Hence, the correct answer is $1$.
Question : Which of the following statements are correct regarding the composition of the State Legislative Council as of December 2023? A. The maximum strength of the Council is fixed at one-third of the total strength of the Assembly. B. The minimum strength of the Council is fixed at 40. C. A total of 5/6 of the total number of members of a Legislative Council are indirectly elected and 1/6 members are nominated. D. The nominations (nominated members) made by the Governor can be challenged in the court.
Option 1: B, C and D only
Option 2: A, B and C only
Option 3: A, B, C and D
Option 4: A, B and D only
Correct Answer: A, B and C only
Solution : The correct answer is A, B and C only.
A state's Legislative Council may not have fewer than 40 members or more than one-third of the State Assembly's total membership, as stated in Article 171 of the Constitution. One-third or less of the State Legislative Assembly's members may comprise the State Legislative Council. Its membership must, however, be less than forty. The State Legislative Council's Chairman and Deputy Chairman are chosen by these members.
Question : Directions: If 4 × 9 × 3 = 4 and 5 × 3 × 1 = 3, then 9 × 9 × 7 = ?
Option 1: 5
Option 2: 6
Option 3: 7
Option 4: 9
Correct Answer: 5
Solution : Given: 4 × 9 × 3 = 4, 5 × 3 × 1 = 3
The pattern in the equation→4 × 9 × 3 = 4 is 4 + 9 + 3 = 16 = 42 The pattern in the equation→5 × 3 × 1 = 3 is 5 + 3 + 1 = 9 = 32
Here, the sign × means +. Using the same pattern in equation 9 × 9 × 7 The equation becomes – 9 + 9 + 7 = 25 = 52 Therefore, the square root of 25 is equal to 5.
Hence, the first option is correct.
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error.
He was unable / to help me because / he had been failed / to arrange the money.
Option 1: to help me because
Option 2: to arrange the money
Option 3: he had been failed
Option 4: he was unable
Correct Answer: he had been failed
Solution : The error lies in the third option.
The error is in the phrase he had been failed. The verb failed in this context should be used in its active form, not in the passive form with been. The correct form should be he had failed, which means he did not succeed in arranging the money.
Therefore, the correct sentence is: "He was unable to help me because he had failed to arrange the money."
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
In case of a natural calamity, the shortage of essential things must be overcome in a short time.
(1) commodities
(2) consignments
(3) material
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The sentence can be improved using the first option.
This option is the correct choice because "commodities" is a more precise and appropriate term for essential items or goods, especially when discussing overcoming shortages during a natural calamity. It is a suitable replacement that enhances clarity and specificity.
The meanings of the other options are as follows:
Therefore, the correct sentence is: In case of a natural calamity, the shortage of essential commodities must be overcome in a short time.
Question : Direction: In the following question, select the missing number from the given responses.
Option 1: 17
Option 2: 18
Option 3: 19
Option 4: 21
Correct Answer: 21
Solution : Given:
In the first column, 6 × 6 = 36 → 6 × 4 = 24 → 6 × 3 = 18
In the second column, 8 × 8 = 64 → 8 × 6 = 48 → 8 × 3 = 24
In the third column, 7 × 7 = 49 → 7 × 5 = 35 → 7 × 3 = 21
So, the missing number is 21.
Hence, fourth option is correct.
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