Staff Selection Commission Sub Inspector Exam
Question : A can run 250 m in 25 sec and B in 30 sec. How many metres start can A give to B in a 1 km race so that the race may end in a dead heat?
Option 1: 169.53 m
Option 2: 173.82 m
Option 3: 166.67 m
Option 4: 186.34 m
Correct Answer: 166.67 m
Solution : A can run 250 m in 25 seconds. ⇒ A can run 1000 m in $\frac{25}{250} \times 1000$ = 100 seconds B can run 250 m in 30 seconds. ⇒ B can run 1000 m in $\frac{30}{250} \times 1000$ = 120 seconds Distance covered
Question : The curved surface area of a right circular cone is $156 \pi$ and the radius of its base is 12 cm. What is the volume of the cone, in cm3?
Option 1: $192 \pi$
Option 2: $210 \pi$
Option 3: $240 \pi$
Option 4: $180\pi$
Correct Answer: $240 \pi$
Solution : Given: The curved surface area of a right circular cone is $156 \pi$ and the radius of its base is 12 cm. Use the formulas, The curved surface area of the cone = $\pi rl$, The volume of the cone = $\frac{1}{3}\pi r^2h$, The
Question : If the angle of elevation of a balloon from two consecutive kilometre stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be:
Option 1: $\frac{\sqrt{3}}{2}$ km
Option 2: $\frac{1}{2}$ km
Option 3: $\frac{2}{\sqrt{3}}$ km
Option 4: $3\sqrt{3}$ km
Correct Answer: $\frac{\sqrt{3}}{2}$ km
Solution : Let the height of the balloon be $h$. $\tan60°=\frac{h}{x}$ ⇒ $\sqrt{3}=\frac{h}{x}$ ⇒ $x=\frac{h}{\sqrt{3}}$ ------(1) $\tan30°=\frac{h}{x+1}$ ⇒ $\frac{1}{\sqrt{3}}=\frac{h}{\frac{h}{\sqrt{3}}+1}$ ⇒ $\frac{1}{\sqrt{3}}=\frac{\sqrt{3}h}{h+\sqrt{3}}$ ⇒ $3h=h+\sqrt{3}$ ⇒ $2h=\sqrt{3}$ ⇒ $h=\frac{\sqrt{3}}{2}$ km Hence, the correct answer is $\frac{\sqrt{3}}{2}$ km.
Question : The following pie charts show the number of start-ups started in various sectors since 2016 and the number of successful start-ups in those sectors respectively. Find the ratio of the number of successful start-ups in the entertainment sector to the total number of start-ups in entertainment since 2016.
Option 1: 5 : 16
Option 2: 5 : 17
Option 3: 7 : 16
Option 4: 25 : 81
Correct Answer: 5 : 16
Solution : Total number of start-ups in entertainment since 2016 = 175 The number of successful start-ups in entertainment sector = 560 $\therefore$ Required ratio = 175 : 560 = 5 : 16 Hence, the correct answer is 5 : 16.
Question : The following sentence has been divided into parts. One of them may contain an error. Select the part that contains the error from the given options. If you don't find any error, mark 'No error' as your answer.
The research fellow defended / his thesis scholarly / and obtained the degree.
Option 1: No error
Option 2: his thesis scholarly
Option 3: and obtained the degree
Option 4: The research fellow defended
Correct Answer: his thesis scholarly
Solution : The second option is correct.
The Term thesis means a type of research paper based on one's original research, so it is already done scholarly. Hence, the adverb scholarly should be deleted in this case.
Therefore, the correct sentence should be, "The research
Question : Directions: Study the given pattern carefully and select the number that can replace the question mark (?) in it.
Option 1: 16
Option 2: 61
Option 3: 51
Option 4: 15
Correct Answer: 61
Solution : Given:
Solve the figure column-wise. In the column, the difference between the first and second number is divisible by 3 and the difference between the third number and the second number is divisible by 4 In column I; 12 – 9 = 3, 13 –
Question : Directions: Select the option that represents the letters that, when placed from left to right in the blanks below, will complete the letter series. P _ R R _ P Q _ _ S _ Q R _ S P _ R R S
Option 1: R Q P Q R S Q
Option 2: S Q R R Q P R
Option 3: S Q Q R R P Q
Option 4: Q S R R P R Q
Correct Answer: Q S R R P R Q
Solution : Given: P _ R R _ P Q _ _ S _ Q R _ S P _ R R S
To fill the series we have to divide the series – P _ R R _ / P
Question : Elizabeth went to a furniture store and purchased a study table. She received a 20% discount on it. She would have saved Rs.1,000 more if she had received a 25% discount. What was the marked price of the study table?
Option 1: Rs. 21,100
Option 2: Rs. 20,000
Option 3: Rs. 18,900
Option 4: Rs. 19,200
Correct Answer: Rs. 20,000
Solution : Let the marked price of the table be $x$. Selling price of the table $=x×\frac{80}{100}$ Also, if she had received a 25% discount the selling price $=x×\frac{75}{100}$ According to the question, $x×\frac{80}{100}-x×\frac{75}{100}=1000$ ⇒ $\frac{5x}{100}=1000$ $\therefore x=20,000$ Hence, the correct answer is Rs. 20,000.
Question : By what the least number should 4320 be multiplied to obtain a number which is a perfect cube?
Option 1: 40
Option 2: 50
Option 3: 60
Option 4: 80
Correct Answer: 50
Solution : 4320 = 3 × 3 × 3 × 2 × 2 × 2 × 2 × 2 × 5 = 33 × 25 × 5 We need one 2's and two 5's to make a cube. Thus, the numbers should be multiplied as
Question : Directions: A piece of paper is folded and cut as shown below in the question figures. From the given answer figures, indicate how it will appear when opened?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : When the given folded paper is unfolded, it will look like –
Hence, the second option is correct.
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