Staff Selection Commission Sub Inspector Exam
Question : When a number is successively divided by 3, 4 and 7, the remainder obtained are 2, 3 and 5, respectively. What will be the remainder when 84 divides the same number?
Option 1: 71
Option 2: 30
Option 3: 48
Option 4: 53
Correct Answer: 71
Solution : Remainders corresponding to the divisor (Divisor × Quotient) + Remainder = Dividend Start from the last digits The number gives a remainder of 5 when it is divided by 7 = (7$x$ + 5) The number gives the remainder 3 when it is divided into
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 $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ = $\frac{2}{3} \div \frac{4}{30}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ = $\frac{2}{3} \div \frac{4}{30}-\frac{4}{5} \times \frac{10}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ = $5-\frac{4}{5} \times \frac{50}{24} +\frac{3}{2}$ = $5- \frac{10}{6} +\frac{3}{2}$ = $5- \frac{1}{6}$
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