Staff Selection Commission Sub Inspector Exam
Question : Study the given graph and answer the question that follows. The graph shows data related to the number of students enrolled for a vocational course in two institutes (X and Y) during three years. What is the difference between the average number of students enrolled in Institute X in 2010 and 2011 and that in Institute Y in 2011 and 2012?
Option 1: 20
Option 2: 15
Option 3: 18
Option 4: 22
Correct Answer: 20
Solution : Students enrolled in institute X in 2010 and 2011 = 320 + 240 = 560 Average = $\frac{\text{Sum of all the observations}}{{\text{Total number of observations}}}=\frac{560}{2} = 280$ Students enrolled in Institute Y in 2011 and 2012 = 320 + 200 = 520 Average = $\frac{520}{2}=
Question : Aarush and Maahi together can do a piece of work in 10 days. If Aarush alone can do the same work in 15 days, then how many days Maahi alone will take to do the same work?
Option 1: 25
Option 3: 30
Option 4: 20
Correct Answer: 30
Solution : Let us assume the total unit of work to be 30, which is the LCM of 15 and 10. Efficiency of Aarush and Maahi = $\frac{30}{10}$ = 3 units/day Efficiency of Aarush = $\frac{30}{15}$ = 2 units/day Efficiency of Maahi = 3 – 2 =
Question : Directions: If 27 * 4 = 77 and 31 * 9 = 239, then 21 * 6 = ?
Option 1: 94
Option 2: 107
Option 3: 99
Option 4: 106
Correct Answer: 99
Solution : Given: 27 * 4 = 77 and 31 * 9 = 239
Like, 27 * 4 = 77→27 × 4 = 108; 27 + 4 = 31; 108 – 31 = 77 And, 31 * 9 = 239→31 × 9 = 279; 31 + 9
Question : Select the most appropriate idiom for the underlined segment in the given sentence. The dacoit was shot from up close by the police officer.
Option 1: Milksop
Option 2: smell a rat
Option 3: Point blank
Option 4: Bullet proof
Correct Answer: Point blank
Solution : The correct choice will be the third option.
The idiom point blank is used to describe a shot or an action that occurs at very close range, typically without any intervening distance. In the context of the given sentence, the use of "point blank"
Question : The ratio of inradius and circumradius of an equilateral triangle is:
Option 1: $1:2$
Option 2: $2:1$
Option 3: $1:\sqrt2$
Option 4: $\sqrt2:1$
Correct Answer: $1:2$
Solution : In equilateral triangle, Inradius $= \frac{\text{side}}{2\sqrt3}$ Circumradius $= \frac{\text{side}}{\sqrt3}$ Ratio of inradius and circumradius $= \frac{\text{side}}{2\sqrt3}: \frac{\text{side}}{\sqrt3} = 1:2$ Hence, the correct answer is $1:2$.
Question : Select the most appropriate one-word substitution of the given group of words. A notice of the death of a person, often with a biographical sketch, as in a newspaper.
Option 1: Obituary
Option 2: Oblivion
Option 3: Elegy
Option 4: Advertisement
Correct Answer: Obituary
Solution : The correct answer is the first option.
Explanation: An obituary is a written notice or article that announces the death of a person. It often includes details about the person's life, achievements, and other relevant information. Obituaries are commonly found in newspapers and serve
Question : The second most used language on the World Wide Web is
Option 1: German
Option 2: French
Option 3: Chinese
Option 4: English
Correct Answer: Chinese
Solution : The correct option is Chinese.
The World Wide Web (WWW) is a worldwide network of interconnected hypertext texts and multimedia material that users may traverse using web browsers. This language is the most spoken in the world.
Question : If $x\left(5-\frac{2}{x}\right)=\frac{5}{x}$, then the value of $x^2+\frac{1}{x^2}$ is:
Option 1: $\frac{54}{25}$
Option 2: $\frac{53}{28}$
Option 3: $\frac{53}{27}$
Option 4: $\frac{54}{23}$
Correct Answer: $\frac{54}{25}$
Solution : Given: $x\left(5-\frac{2}{x}\right)=\frac{5}{x}$ ⇒ $5x-2 = \frac{5}{x}$ ⇒ $5x-\frac{5}{x} =2$ ⇒ $5(x-\frac{1}{x})=2$ ⇒ $x- \frac{1}{x} = \frac{2}{5}$ Squaring both sides. ⇒ $x^2+\frac{1}{x^2}-2 = \frac{4}{25}$ ⇒ $x^2+\frac{1}{x^2} = \frac{4}{25}+2$ ⇒ $x^2+\frac{1}{x^2} = \frac{54}{25}$ Hence, the correct answer is $\frac{54}{25}$.
Question : The average of 25 results is 20. The average of the first 12 results is 15 and that of the last 12 results is 18. Then, the 13th result is:
Option 1: 100
Option 2: 101
Option 3: 104
Option 4: 103
Correct Answer: 104
Solution : Given: The average of 25 results is 20. The average of the first 12 results is 15 and that of the last 12 results is 18. The sum of 25 result = (25 × 20) = 500 The sum of the first 12 results =
Question : Let the HCF of m and n be "a" and let n = ab, LCM of m and n is given by:
Option 1: bm
Option 2: am
Option 3: ab
Option 4: mn
Correct Answer: bm
Solution : Given: HCF = a n = ab We know that, The product of the two numbers = HCF × LCM ⇒ m × n = HCF × LCM Putting the values, we get: ⇒ m × ab = a × LCM Thus, LCM = bm
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