Staff Selection Commission Sub Inspector Exam
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
Question : Directions: In the given question, select the related letter from the given alternatives. AFKP : DINS :: WBGL : ?
Option 1: ORUX
Option 2: OSWA
Option 3: OTYD
Option 4: OQSU
Correct Answer: OTYD
Solution : Given: AFKP : DINS :: WBGL : ?
Add 5 to the place value of the previous letter to get the next letter – A + 5 = F; F + 5 = K; K + 5 = P and D + 5 = I;
Question : The 10 per cent reservation in central government jobs under the economically weaker sections (EWS) category is available to the persons whose family income is below:
Option 1: INR 8 lakh
Option 2: INR 5 lakh
Option 3: INR 6 lakh
Option 4: INR 7 lakh
Correct Answer: INR 8 lakh
Solution : The correct option is INR 8 lakh.
The annual family income serves as the basis for the 10% reservation in central government posts under the Economically Weaker Sections (EWS) category. Those whose family income is less than Rs. 8 lakhs annually are
Question : Study the graph and answer the question. The number of workers in the factory whose weekly earnings are INR 5,500 or more but less than INR 7,500 is:
Option 1: 375
Option 2: 285
Option 3: 345
Option 4: 240
Correct Answer: 375
Solution : The number of workers in the factory whose weekly earnings are INR 5,500 or more but less than INR 7,500 = 85 + 95 + 105 + 90 = 375 Hence, the correct answer is 375.
Question : Directions: In the given question, select the related letter cluster from the given alternatives. UASC : YEWG :: DHLO : ?
Option 1: LHUS
Option 2: HSPL
Option 3: HLPS
Option 4: HLOD
Correct Answer: HLPS
Solution : Given: UASC : YEWG :: DHLO : ?
Add 4 to the place value of each letter of UASC to obtain the required code – U + 4 = Y; A + 4 = E; S + 4 = W; C + 4 = G
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