Staff Selection Commission Sub Inspector Exam
Question : If the perimeter of circle A is equal to the perimeter of semicircle B, what is the ratio of their areas?
Option 1: $\left (x+ 2\right)^{2} : 2\pi ^{2}$
Option 2: $2\pi ^{2} : \left ( x+2 \right)^{2}$
Option 3: $\left (\pi +2 \right )^{2} : 4\pi ^{2}$
Option 4: $4\pi ^{2}:\left ( \pi +2 \right)^{2}$
Correct Answer: $\left (\pi +2 \right )^{2} : 4\pi ^{2}$
Solution : Let the radius of circle A be r1 units and the radius of semicircle B is r2 units. According to the question, 2$\pi$r1 = $\pi$r2 + 2r2 ⇒ 2$\pi$r1 = r2
Question : The income of Raju is 25% more than that of Manju. Raju got a 25% rise in his income, and Manju got a 40% rise in his income, the percentage increase in their combined incomes is:
Option 1: 51.72%
Option 2: 31.67%
Option 3: 22.43%
Option 4: 41.26%
Correct Answer: 31.67%
Solution : Let the income of Manju be 100. The income of Raju is 25% more than Manju = 125 After increment of 25% in Raju's income = $125+\frac{25}{100}\times125=156.25$ After increment of 40% in Manju's income = $100+\frac{40}{100}\times100=140$ Their's combined previous income = 100 + 125 =
Question : Khelo India University Games – 2021 were hosted by ____________.
Option 1: Kerala
Option 2: Tamil Nadu
Option 3: Telangana
Option 4: Karnataka
Correct Answer: Karnataka
Solution : The correct option is Karnataka.
The state of Karnataka served as the host for the 2021 Khelo India University Games. On April 1, 2022, the Khelo India University Games 2021 logo, jersey, mascot, and anthem were unveiled at the event's opening ceremony in Bengaluru
Question : The value of equipment depreciates by 20% each year. How much less will the value of the equipment be after 3 years?
Option 1: 48.8%
Option 2: 51.2%
Option 3: 54%
Option 4: 60%
Correct Answer: 48.8%
Solution : Assume the initial value as $P$ and calculate the depreciation value by using the formula $P(1-\frac{R}{100})^n$ where $R$ is the rate and $n$ is the time. So, the value after 3 years = $P(1-\frac{20}{100})^3$ = $P(1-\frac{1}{5})^3$ = $P(\frac{4}{5})^3$ = $P(0.8)^3$ = $0.512P$ So, the required
Question : Which state of India is given the popular name of "India's bread basket"?
Option 1: Assam
Option 2: Maharashtra
Option 3: Uttar Pradesh
Option 4: Punjab
Correct Answer: Punjab
Solution : The correct answer is Punjab.
Punjab is the state which contributes the most to the production of main crops in India. It is also famously known as the "bread basket" due to its high contribution to the agricultural industry. Despite occupying only 1.5% of
Question : Directions: In a certain code language, ACTOR is coded as ROYCA, and NURSE is coded as ESWUN. How will JUDGE be coded in the same language?
Option 1: EGJUI
Option 2: GEIUJ
Option 3: EGUIJ
Option 4: EGIUJ
Correct Answer: EGIUJ
Solution : Given: ACTOR is coded as ROYCA, and NURSE is coded as ESWUN.
Change the position of the first two and last two letters and add 5 to the positional value of the third letter of ACTOR, to obtain the required code –
Thus, ACTOR is
Question : Directions: In the following number series, two numbers have been put within brackets. Select the most appropriate option for these numbers in relation to their inclusion in the series. 21, 24, 19, (29), 17, 28, (15), 30
Option 1: The first bracketed number (from the left) is correct and the second bracketed number (from the left) is incorrect.
Option 2: Both the bracketed numbers are correct.
Option 3: The first bracketed number (from the left) is incorrect and the second bracketed number (from the left) is correct.
Option 4: Both the bracketed numbers are incorrect.
Correct Answer: The first bracketed number (from the left) is incorrect and the second bracketed number (from the left) is correct.
Solution : Given: 21, 24, 19, (29), 17, 28, (15), 30
The pattern is as follows –
Therefore, the first bracketed number (from the left) is incorrect it should
Question : Directions: Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: 1. Some dancers are singers. 2. No singer is an actor. Conclusions: I. Some actors are singers. II. All singers are dancers.
Option 1: Neither conclusion I nor II follows
Option 2: Only conclusion I follows
Option 3: Either conclusion I or II follows
Option 4: Only conclusion II follows
Correct Answer: Neither conclusion I nor II follows
Solution : The possible Venn diagram, according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): Some actors are singers – From the Venn diagram, it is evident that there is a negative relation between actors
Question : $7 \sin ^2 A+3 \cos ^2 A=4$, then find $\cot A$:
Option 1: $\sqrt{3}$
Option 2: $\sqrt{2}$
Option 3: $\frac{1}{\sqrt{2}}$
Option 4: $\frac{1}{\sqrt{3}}$
Correct Answer: $\sqrt{3}$
Solution : $7 \sin ^2 A+3 \cos ^2 A=4$ $7 \sin ^2 A+3(1-\sin ^2 A)=4$ $7 \sin ^2 A+3-3 \sin ^2 A=4$ $4 \sin ^2 A=1$ $ \sin ^2 A=\frac{1}{4}$ $ \sin A=\frac{1}{2}$ $\therefore A = 30^{\circ}$ $\cot A = \cot 30^{\circ} = \sqrt3 $ Hence, the
Question : In a big garden, 60% of the trees are coconut trees, 25% of the coconut trees are mango trees and 20% of the mango trees are apple trees. If the number of apple trees is 1500, the number of trees in the garden is:
Option 1: 48000
Option 2: 50000
Option 3: 51000
Option 4: 45000
Correct Answer: 50000
Solution : Let us assume that the total number of trees in the garden is 100 units. Coconut trees = 60 units Mango trees = 60 × 0.25 = 15 units Apple trees = 15 × 0.2 = 3 units As per the question, 3 units =
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