Staff Selection Commission Combined Graduate Level Exam
Question : Find the value of: $\sqrt{\frac{1 - \sin 3 \theta}{1 + \sin 3 \theta}}$
Option 1: $\sec 3 \theta - \tan 3 \theta$
Option 2: $(\sec 3 \theta - \tan 3 \theta)^3$
Option 3: $(\sec 3 \theta - \tan 3 \theta)^2$
Option 4: $\sec 3 \theta + \tan 3 \theta$
Correct Answer: $\sec 3 \theta - \tan 3 \theta$
Solution : $\sqrt{\frac{1 – \sin 3 \theta}{1 + \sin 3 \theta}}$ = $\sqrt{\frac{(1 – \sin 3 \theta)(1 – \sin 3\theta)}{(1 + \sin 3\theta)(1 – \sin 3\theta)}}$ = $\sqrt{\frac{(1 – \sin 3\theta)^{2}}{1 – \sin^{2}3\theta}}$ = $\sqrt{\frac{(1 – \sin 3\theta)^{2}}{\cos^{2}3\theta}}$ = $\frac{1 -
Question : If $\left (x+\frac{1}{x}\right )=5$, find the value of $\frac{6x}{x^{2}+x+1}$.
Option 1: 3
Option 2: 2
Option 3: 1
Option 4: 0
Correct Answer: 1
Solution : Given: $\left (x+\frac{1}{x} \right)=5$ ⇒ $\frac{x^2+1}{x}=5$ ⇒ $x^2+1=5x$ Adding $x$ on both sides, ⇒ $x^2+1+x=5x+x$ ⇒ $x^2+x+1=6x$ Now, put the value of $x^2+x+1=6x$ in the expression $\frac{6x}{x^{2}+x+1}$ So, $\frac{6x}{x^{2}+x+1}=\frac{6x}{6x}=1$ Hence, the correct answer is 1.
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
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
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 +
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
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→
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
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