Staff Selection Commission Combined Graduate Level Exam
Question : Select the option that expresses the given sentence in reported speech.
The Chief Minister said, "All exams shall be cancelled this year."
Option 1: The Chief Minister said that all exams should have been cancelled that year.
Option 2: The Chief Minister said that all exams would be cancelled that year.
Option 3: The Chief Minister says that all exams shall be cancelled this year.
Option 4: The Chief Minister said that all exams should be cancelled this year.
Correct Answer: The Chief Minister said that all exams would be cancelled that year.
Solution : The correct choice is the second option.
The steps of conversion are as follows:
Question :
Directions: In the following question, a series is given with one number missing. Choose the correct alternative from the ones given that will complete the series. –0.5, –0.35, –0.2, –0.05, ?, 0.25
Option 1: –0.1
Option 2: 0.1
Option 3: 0.15
Option 4: –0.15
Correct Answer: 0.1
Solution : Given: –0.5, –0.35, –0.2, –0.05, ?, 0.25
Let's apply the pattern – –0.5 + 0.15 = –0.35; –0.35 + 0.15 = –0.2; –0.2 + 0.15 = –0.05; –0.05 + 0.15 = 0.1; 0.1 + 0.15 = 0.25
The missing number is 0.1. Hence, the second
Question : Directions: In the following question, the sentence given with a blank is to be filled in with an appropriate word. Select the correct alternative out of the four. Mother shall return____an hour.
Option 1: in
Option 2: after
Option 3: during
Option 4: within
Correct Answer: within
Solution : The fourth option is the correct answer for the sentence because 'within' which means 'in a period not longer than a particular length of time' contextually fits in the sentence and makes the explanation as 'mother shall return in not more than an hour'.
Therefore,
Question : Directions: Pankaj is taller than Vinod, who is shorter than Pramod. Usha is taller than Priyanka but shorter than Vinod. Pramod is shorter than Pankaj. Who is the tallest?
Option 1: Priyanka
Option 2: Pramod
Option 3: Vinod
Option 4: Pankaj
Correct Answer: Pankaj
Solution : Given: Pankaj is taller than Vinod. Pankaj > Vinod Vinod is shorter than Pramod. Pramod > Vinod Usha is taller than Priyanka but shorter than Vinod. Vinod > Usha > Priyanka Pramod is shorter than Pankaj. Pankaj > Pramod By concluding all the given information,
Question : Simplify the following: $\sin2x+2\sin4x+\sin6x$
Option 1: $4\cos^2x\sin4x$
Option 2: $4\cos^2x\sin x$
Option 3: $2\cos^2x\sin4 x$
Option 4: $4\sin^2 x\sin4 x$
Correct Answer: $4\cos^2x\sin4x$
Solution : Given: $\sin2x+2\sin4x+\sin6x$ $=\sin2x+\sin6x+2\sin4x$ Using the formula: $\sin C+\sin D=2\sin\frac{(C+D)}{2}\cos\frac{(C–D)}{2}$, we get: $= 2\sin\frac{(6x+2x)}{2}\cos\frac{(6x–2x)}{2}+2\sin4x$ $= 2\sin4x\cos2x+2\sin4x$ $=2\sin4x(\cos2x+1)$ Using formula: $2\cos^2x=\cos2x+1$, we get: $=2\sin4x(2\cos^2x)$ $= 4\cos^2x\sin4x$ Hence, the correct answer is $4\cos^2x\sin4x$.
Question : The height and the total surface area of a right circular cylinder are 4 cm and 8$\pi$ sq cm, respectively. The radius of the base of the cylinder is:
Option 1: $\left ( 2\sqrt{2}-2 \right )\ \text{cm}$
Option 2: $\left ( 2-\sqrt{2}\right )\ \text{cm}$
Option 3: $2\ \text{cm}$
Option 4: $\sqrt{2}\ \text{cm}$
Correct Answer: $\left ( 2\sqrt{2}-2 \right )\ \text{cm}$
Solution : Given: Height of the cylinder = 4 cm Total surface area = 8$\pi$ cm2 ⇒ $2\pi r(h+r) = 8\pi$ ⇒ $r(4+r) = 4$ ⇒ $r^2+4r-4=0$ Using quadratic formula: $r= \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ⇒ $r= \frac{-4\pm \sqrt{4^2+4\times1\times4}}{2\times1}$ ⇒ $r= \frac{-4\pm \sqrt{16+16}}{2}$
Question : Between 10 pm and 6 am, a fitness band records the following data. Refer to the following data table and answer the question.
How long was the user in Deep Sleep or was Awake?
Option 1: 3.5 hours
Option 2: 2.5 hours
Option 3: 4.5 hours
Option 4: 4 hours
Correct Answer: 4 hours
Solution : According to the data given, Total time = 10 am to 6 am = 8 hours The user in deep sleep or was awake = 15% + 35% = 50% So, the time spend by user = $\frac{50}{100}×8 = 4$ Hence, the correct answer
Question : A, B, and C can do work separately in 16, 32, and 48 days, respectively. They started the work together, but B left off eight days and C six days before the completion of the work. In what time is the work finished?
Option 1: 10 days
Option 2: 9 days
Option 3: 12 days
Option 4: 14 days
Correct Answer: 12 days
Solution : Given: A, B, and C can do work separately in 16, 32, and 48 days. Let the work be finished in $x$ days. By applying the formula: Using, If a man can do the work in $n$ days, then 1 day's work of the
Question : The cost of an article is Rs. 200. If 20% profit is made after giving a 20% discount on the marked price, the marked price is:
Option 1: Rs. 300
Option 2: Rs. 320
Option 3: Rs. 420
Option 4: Rs. 450
Correct Answer: Rs. 300
Solution : Let the marked price be Rs. 100. Discount = 20% ⇒ Selling Price = (100 – 100 × $\frac{20}{100}$) = (100 – 20) = Rs. 80 Now profit = 20% So, the cost price is = 80 × ($\frac{100}{100+20}$) = Rs. $\frac{200}{3}$ Here, Rs.
Question : Directions: Select the figure that will come next in the following figure series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figure series – 1. The inner right-angle triangle is rotating 90° in an anti-clockwise direction. 2. In each box, the symbols given at the top left and middle of the left side of the box interchange their position and shifted to the
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