Staff Selection Commission Sub Inspector Exam
Question : If $\left(5 \sqrt{5} x^3-3 \sqrt{3} y^3\right) \div(\sqrt{5} x-\sqrt{3} y)=\left(A x^2+B y^2+C x y\right)$, then the value of $(3 A+B-\sqrt{15} C)$ is:
Option 1: 8
Option 2: 5
Option 3: 3
Option 4: 12
Correct Answer: 3
Solution : Given: $\left(5 \sqrt{5} x^3-3 \sqrt{3} y^3\right) \div(\sqrt{5} x-\sqrt{3} y)=\left(A x^2+B y^2+C x y\right)$ ⇒ $((\sqrt{5} x)^3-(\sqrt{3} y)^3) \div(\sqrt{5} x-\sqrt{3} y)=\left(A x^2+B y^2+C x y\right)$ ⇒ $((\sqrt{5} x-\sqrt{3} y)((\sqrt{5} x)^2+(\sqrt{3} y)^2+(\sqrt{5} x)×(\sqrt{3} y)) \div(\sqrt{5} x-\sqrt{3} y)=\left(A x^2+B y^2+C x y\right)$ ⇒ $(\sqrt{5} x)^2+(\sqrt{3} y)^2+(\sqrt{5} x)×(\sqrt{3} y)=\left(A
Question : Directions: Which number will replace the question mark (?) in the following series? 82, ?, 119, 142, 168, 197
Option 1: 99
Option 2: 95
Option 3: 85
Option 4: 107
Correct Answer: 99
Solution : Given: 82, ?, 119, 142, 168, 197
The pattern is as follows –
So, 99 is the missing number. Hence, the first option is correct.
Question : Select the most appropriate word, which means the same as the group of words given. An exact or a very close copy of something substitute
Option 1: artificial
Option 2: forgery
Option 3: replica
Option 4: substitute
Correct Answer: replica
Solution : The correct choice is the third option.
Explanation: A "replica" refers to a precise or extremely close copy of something, often replicating its appearance, characteristics, or features. It stands out among the other options as it specifically denotes an accurate duplication or imitation of an
Question : The radius of the base of a cylinder is 14 cm and its curved surface area is 880 cm2. Its volume (in cm3) is: (Take $\pi=\frac{22}{7}$)
Option 1: 3080
Option 2: 1078
Option 3: 6160
Option 4: 9240
Correct Answer: 6160
Solution : Radius, $r$ = 14 cm The curved surface area of the cylinder = 880 cm2. $2\pi r h$ = 880 $⇒\pi r h$ = 440 ---------(i) $\therefore$ Volume of the cylinder = $\pi r^2 h=\pi r h × r= 440 × 14= 6160$
Question : During one of the five-year plans, which of the following politicians gave the slogan "Garibi Hatao"?
Option 1: Charan Singh
Option 2: Gaini Zail Singh
Option 3: Morarji Desai
Option 4: Indira Gandhi
Correct Answer: Indira Gandhi
Solution : The correct answer is Indira Gandhi.
Indira Gandhi introduced the "Garibi Hatao" slogan in the Fifth Five-Year Plan. The slogan was given for the objective of poverty elimination and employment generation. Indira Gandhi was the first and the only female Prime Minister of
Question : If house tax is paid before the due date, one gets a reduction of 12% on the amount of the bill. By paying the tax before the due date, a person got a reduction of Rs. 2,100. The amount (in Rs.) of house tax was:
Option 1: 21,000
Option 2: 17,500
Option 3: 25,000
Option 4: 18,000
Correct Answer: 17,500
Solution : The reduction of Rs. 2,100 represents 12% of the original house tax amount. Let the original house tax amount as A. According to the question, 0.12A = 2100 ⇒ A = $\frac{2100}{0.12}$ = Rs. 17,500 Hence, the correct answer is 17,500.
Question : Study the given pie chart and answer the question that follows. The pie chart shows the expenditure of a family on different items and their savings throughout the year 2021.
If the total income of the family was INR 1,00,000, how much money (in INR) was spent on the education of the children?
Option 1: 12,500
Option 2: 12,000
Option 3: 13,500
Option 4: 13,000
Correct Answer: 12,000
Solution : The total income of the family was = INR 1,00,000 Spent on the education of the children = 12% of 1,00,000 = $\frac{12}{100}\times 1,00,000$ = INR 12,000 Hence, the correct answer is 12,000
Question : Directions: Which number will replace the question mark (?) to complete the given series? 85, 64, 51, 44, 41, ?
Option 1: 37
Option 2: 40
Option 3: 38
Option 4: 39
Correct Answer: 40
Solution : Given: 85, 64, 51, 44, 41, ?
So, 40 is the required missing number in the series. Hence, the second option is correct.
Question :
Directions: In the following question, select the related word from the given alternatives. Heat : Calorie :: Sound : ?
Option 1: Decibel
Option 2: Joule
Option 3: Knot
Option 4: Richter
Correct Answer: Decibel
Solution : Given: Heat : Calorie :: Sound : ?
Like, calorie is the unit of heat. Similarly, decibel is the unit of sound.
Hence, the first option is correct.
Question : If $N= \frac{(\sqrt6-\sqrt5)}{(\sqrt6+\sqrt5)}$, then what is the value of $(N+\frac{1}{N})$?
Option 1: 10
Option 2: 11
Option 3: 12
Option 4: 22
Correct Answer: 22
Solution : Given: $N= \frac{(\sqrt6-\sqrt5)}{(\sqrt6+\sqrt5)}$ $\frac{1}{N}= \frac{(\sqrt6+\sqrt5)}{(\sqrt6-\sqrt5)}$ To find: $(N+\frac{1}{N})$ Putting the values, we get: = $\frac{(\sqrt6-\sqrt5)}{(\sqrt6+\sqrt5)}+\frac{(\sqrt6+\sqrt5)}{(\sqrt6-\sqrt5)}$ = $\frac{(\sqrt6-\sqrt5)^2+(\sqrt6+\sqrt5)^2}{(\sqrt6+\sqrt5)(\sqrt6-\sqrt5)}$ = $\frac{6+5-2\sqrt6\sqrt5+6+5+2\sqrt6\sqrt5}{6-5}$ = 22 Hence, the correct answer is 22.
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