Staff Selection Commission Sub Inspector Exam
Question : On a journey across Kolkata, a taxi averages 50 km/hr for 50% of the distance, 40 km/hr for 40% of it and 20 km/hr for the remaining. The average speed (in km/hr) for the whole journey is:
Option 1: 42 km/hr
Option 2: 40 km/hr
Option 3: 35 km/hr
Option 4: 45 km/hr
Correct Answer: 40 km/hr
Solution : Let us assume that the total distance travelled is 100 km. Distance travelled at $50$ km/hr = $50$% of $100$ km = $50$ km Distance travelled at $40$ km/hr = $40$% of $100$ km = $40$ km Distance travelled at $20$ km/hr = $10$%
Question : Which of the following is the maximum number of electrons that can be present in M-shell?
Option 1: 2
Option 2: 8
Option 3: 18
Option 4: 32
Correct Answer: 18
Solution : The correct answer is 18.
A precise circular path known as the shell is followed by electrons as they orbit the nucleus. The shells are either designated alphabetically with letters beginning with K (K, L, M, etc.) or according to the primary quantum numbers
Question : Directions: Three of the following four-letter clusters are alike in a certain way and one is different. Pick the odd one out.
Option 1: BSMK
Option 2: GKDT
Option 3: CQLJ
Option 4: DPNH
Correct Answer: BSMK
Solution : Let's check the options – First option: BSMK→B + S + M + K = 2 + 19 + 13 + 11 = 45 Second option: GKDT→G + K + D + T = 7 + 11 + 4 + 20 = 42 Third option:
Question : Directions: Which answer figure will complete the pattern in 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 fourth option is correct.
Question : Two equal sums were lent out at 7% and 5% simple interest respectively. The interest earned on the two loans adds up to Rs. 960 for 4 years. The total sum lent out in:
Option 1: Rs. 3500
Option 2: Rs. 2500
Option 3: Rs. 2000
Option 4: Rs. 3000
Correct Answer: Rs. 2000
Solution : If each amount lent be P, then According to the question, $\frac{\text{P×7×4}}{100}$+$\frac{\text{P×5×4}}{100}$ = 960 ⇒ $\frac{\text{48P}}{100}$ = 960 ⇒ P = Rs. 2000 Hence, the correct answer is Rs. 2000.
Question : How many numbers between 300 and 700 are divisible by 5, 6, and 8?
Option 1: 3
Option 2: 2
Option 3: 5
Option 4: 20
Correct Answer: 3
Solution : Least Common Multiple (LCM) of 5, 6, and 8 = 120 300 = 120 × 3 – 60 700 = 120 × 5 + 100 Number of numbers divisible by 5, 6, and 8 between 300 and 700 = 5 - 3 + 1 =
Question : The numerical value of $\frac{(a–b)^{2}}{(b–c)(c–a)}+\frac{(b–c)^{2}}{(c–a)(a–b)}+\frac{(c–a)^{2}}{(a–b)(b–c)}$ is: $(a\neq b\neq c)$
Option 1: $0$
Option 2: $1$
Option 3: $\frac{1}{3}$
Option 4: $3$
Correct Answer: $3$
Solution : Given: $\frac{(a–b)^{2}}{(b–c)(c–a)}+\frac{(b–c)^{2}}{(c–a)(a–b)}+\frac{(c–a)^{2}}{(a–b)(b–c)}$ Taking LCM of the given expression, we have, = $\frac{(a–b)(a–b)^{2}+(b–c)(b–c)^{2}+(c–a)(c–a)^{2}}{(a–b)(b–c)(c–a)}$ = $\frac{(a–b)^{3}+(b–c)^{3}+(c–a)^{3}}{(a–b)(b–c)(c–a)}$ We know that $x^{3}+y^{3}+z^{3}=3xyz$, if $x+y+z=0$ According to this, we have, ⇒ $(a-b)=x$, $(b-c)=y$, $(c-a)=z$ So, $x+y+z=(a-b+b-c+c-a)=0$ Now, $\frac{(a–b)^{3}+(b–c)^{3}+(c–a)^{3}}{(a–b)(b–c)(c–a)}$ = $\frac{3(a–b)(b–c)(c–a)}{(a–b)(b–c)(c–a)}$ = 3 Hence, the correct answer is $3$.
Question : P, Q, and R, when working individually, can complete a job in, respectively, 36 days, 48 days, and 144 days. P, Q, and R start working together. P leaves the job 12 days before completion and Q leaves the job 8 days before completion. R works from the beginning till the end of the job. Determine the total number of days taken to complete the job.
Option 1: 24
Option 2: 27
Option 3: 30
Option 4: 25
Correct Answer: 27
Solution : Let the total work = LCM (36, 48, and 144) = 144 According to the question, Efficiency of P = $\frac{144}{36}$ = 4 Efficiency of Q = $\frac{144}{48}$ = 3 Efficiency of R = $\frac{144}{144}$ = 1 Additional work P could have done if not
Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ is:
Option 1: $\frac{29}{6}$
Option 2: $\frac{17}{9}$
Option 3: $\frac{14}{3}$
Option 4: $\frac{49}{12}$
Correct Answer: $\frac{29}{6}$
Solution : $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ = $\frac{2}{3} \div \frac{4}{30}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ = $\frac{2}{3} \div \frac{4}{30}-\frac{4}{5} \times \frac{10}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ = $5-\frac{4}{5} \times \frac{50}{24} +\frac{3}{2}$ = $5- \frac{10}{6} +\frac{3}{2}$ = $5- \frac{1}{6}$
Question : A child below the age of __________ years cannot be employed to work in any factory under Article 24 of the Constitution of India.
Option 1: 16
Option 2: 14
Option 3: 15
Option 4: 17
Correct Answer: 14
Solution : The correct option is 14.
A child below the age of 14 years cannot be employed to work in any factory under Article 24 of the Constitution of India. Article 24 prohibits the employment of children in factories, and it is aimed at preventing
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