Staff Selection Commission Sub Inspector Exam
Question : The value of $99\frac{95}{99} × 99$ is:
Option 1: 9798
Option 2: 9997
Option 3: 9898
Option 4: 9896
Correct Answer: 9896
Solution : Given: $99\frac{95}{99}×99$ = $\frac{99×99+95}{99}×99$ = 99 × 99 + 95 = 9801 + 95 = 9896 Hence, the correct answer is 9896.
Question : If $W_{1}:W_{2}= 2:3$ and $W_{1}:W_{3}= 1:2$, then $W_{2}:W_{3}$ is:
Option 1: 3 : 4
Option 2: 4 : 3
Option 3: 2 : 3
Option 4: 4 : 5
Correct Answer: 3 : 4
Solution : $W_{1}:W_{2}= 2:3$ and $W_{1}:W_{3}= 1:2$ Equalising the ratio as $W_1$ is common in both, 2 is multiplied in $W_{1}:W_{3}= 2:4$ The ratio becomes $W_{1}:W_{2}:W_3= 2:3:4$ So, the ratio of $W_{2}:W_{3}$ is $3:4$. Hence, the correct answer is 3 : 4.
Question : Directions: In the following question, choose the correct alternative which will improve the part of the sentence given in quotes.
Sumathi was "a industriously" and willing worker.
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The correct choice is the first option.
Explanation: The word "a industriously" should be replaced with "an industrious" to convey the intended meaning that Sumathi was a hardworking and willing worker. Adverbs modify verbs, adjectives, or other adverbs, but in this sentence, we
Question : Select the most appropriate ANTONYM of the given word. DIVERGE
Option 1: branch
Option 2: divide
Option 3: stray
Option 4: collect
Correct Answer: collect
Solution : The correct choice is the fourth option.
Explanation: Diverge means to move or extend in different directions from a common point. Its opposite would be to come together or gather, which aligns with the meaning of collect.
The meanings of the other options are
Question : Directions: Shalu walks 30 m north, then she turns right and walks 30 m then she turns right and walks 55 m. Then she turns left and walks 20 m. Then she again turns left and walks 25 m. How many meters away and in which direction is she from her original position?
Option 1: 20 m, South
Option 2: 10 m, North
Option 3: 30 m, North
Option 4: 50 m, East
Correct Answer: 50 m, East
Solution : Firstly, we will draw the diagram as per the given instructions –
From the above diagram, the distance between the starting and the endpoint is 50 m and the endpoint is in the East direction from the starting point.
So, Shalu is in
Question : Directions: Which answer figure will complete the question figure?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : On comparing the question figure and all the answer figures, the following figure will combine and make the complete pattern –
Hence, the first option is correct.
Question : Select the option that will improve the underlined part of the given sentence. In case no improvement is needed, select 'No improvement required'. Lily has dedicate her life towards becoming a doctor.
Option 1: had dedicate
Option 2: is dedicate
Option 3: No improvement required
Option 4: has dedicated
Correct Answer: has dedicated
Solution : The correct answer is the fourth option.
"Dedicate" should be in the past participle form, which is "dedicated" in this case, to match the auxiliary verb "has". The given sentence is in the present perfect tense indicating that Lily has already completed the action
Question : What is the average of the squares of the first 19 natural numbers?
Option 1: 124
Option 2: 127.5
Option 3: 130
Option 4: 133.5
Correct Answer: 130
Solution : Given: 19 natural numbers. Sum of first n natural numbers = $\frac{\text{n(n+1)(2n+1)}}{6}$ Sum of first 19 natural numbers = $\frac{\text{19(19+1)(2×19+1)}}{6}$ = $\frac{\text{14820}}{6}$ = 2470 Average of these numbers = $\frac{\text{Sum of first 19 natural numbers}}{19}$ = $\frac{\text{2470}}{19}$ = 130 Hence, the correct answer is 130.
Question : What is the simplified value of: $7 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}-\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)-\frac{5}{24}$
Option 1: $1$
Option 2: $2$
Option 3: $\frac{1}{24}$
Option 4: $\frac{1}{12}$
Correct Answer: $1$
Solution : $7 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}-\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)-\frac{5}{24}$ $= \frac{22}{3} \div \frac{5}{2}\times \frac{8}{5}-\left(\frac{3}{8}+\frac{1}{7} \times \frac{7}{4}\right)-\frac{5}{24}$ $= \frac{22}{3} \div 4-\left(\frac{3}{8}+\frac{1}{4} \right)-\frac{5}{24}$ $= \frac{22}{12}-\left(\frac{5}{8} \right)-\frac{5}{24}$ $= \frac{44-15-5}{24}$ $= \frac{24}{24}$ $=1$ Hence, the correct answer is $1$.
Question : After allowing a 10% discount, a dealer wishes to sell a machine for Rs. 2,700. At what price must the machine be marked?
Option 1: Rs. 270
Option 2: Rs. 3,000
Option 3: Rs. 2,970
Option 4: Rs. 2,430
Correct Answer: Rs. 3,000
Solution : Discount = 10% of marked price Selling price = Rs. 2,700 $\therefore$ Marked Price = $\frac{2700×100}{90}$ = Rs. 3,000 Hence, the correct answer is Rs. 3,000.
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