Staff Selection Commission Sub Inspector Exam
Question : Directions: In the following question observe the series and figure out the pattern used to form it. What will be the 3rd term of the series? 1, 5, ?, 22, 35
Option 1: 11
Option 2: 14
Option 3: 10
Option 4: 12
Correct Answer: 12
Solution : Given: 1, 5, ?, 22, 35
The difference between each consecutive term is increasing by 3 – 1 + 4 = 5 5 + (4 + 3) = 5 + 7 = 12 12 + (7 + 3) = 12 + 10 = 22 22
Question : A sum amounts to INR 7,562 in 4 years and to INR 8,469.44 in 5 years, at a certain rate per cent per annum when the interest is compounded yearly. If INR 10,000 at the same rate of interest is borrowed for two years, then what will be the compound interest (in INR)?
Option 1: 2,544
Option 2: 1,736
Option 3: 2,764
Option 4: 1,965
Correct Answer: 2,544
Solution : Let P be the principal. We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$ $\text{P}(1 +\frac{r}{100})^4$ = 7562 -----------------(1) $\text{P}(1 +\frac{r}{100})^5$ = 8469.44 -------------(2) Dividing (2) by (1) we get, $(1 +\frac{r}{100}) = \frac{846944}{756200}$ $⇒\frac{r}{100} = 1.12 - 1$ $\therefore r = 12$ Compound Interest $=10,000 × [(1 + \frac{12}{100})^2
Question : As observed from the top of a lighthouse, 45 m high above the sea level, the angle of depression of a ship, sailing directly towards it, changes from 30° to 45°. The distance travelled by ship during the period of observation is: (Your answer should be correct to one decimal place.)
Option 1: 32.9 m
Option 2: 33.4 m
Option 3: 36.9 m
Option 4: 24.8 m
Correct Answer: 32.9 m
Solution : Given, AB = 45 m In $\triangle$ABC $\tan$ 45° = $\frac{\text{AB}}{\text{BC}}$ ⇒ 1 = $\frac{45}{\text{BC}}$ ⇒ BC = 45 m In $\triangle$ABD $\tan 30° = \frac{\text{AB}}{\text{BD}}$ ⇒ $\frac{1}{\sqrt{3}} = \frac{45}{\text{BD}}$ ⇒ BD = $45\sqrt{3}$ Also, BD = CD + BC ⇒ $45\sqrt{3}$ = CD
Question : $\frac{\sqrt{24}+\sqrt{216}}{\sqrt{96}}$ is equal to:
Option 1: 1
Option 2: 6
Option 3: 8
Option 4: 2
Correct Answer: 2
Solution : Given: $\frac{\sqrt{24}+\sqrt{216}}{\sqrt{96}}$ = $\frac{2\sqrt{6}+6\sqrt{6}}{4\sqrt{6}}$ = $\frac{8\sqrt{6}}{4\sqrt{6}}$ = $2$ Hence, the correct answer is 2.
Question : If a 4-digit number x58y is exactly divisible by 9, then the least value of (x + y) is:
Option 1: 4
Option 2: 5
Option 3: 3
Correct Answer: 5
Solution : A number is divisible by 9 if the sum of its digits is divisible by 9. Given a 4-digit number x58y, the sum of its digits is x + 5 + 8 + y = (x + y) + 13. For the number to be
Question : Directions: Select the figure from among the given options that can replace the question mark (?) in the following series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : In the given series, the small circle alternates shaded and unshaded and moves clockwise from one corner to another. Also, the figure at the centre of the box is moving 45° anticlockwise. Thus, the answer figure is –
Therefore, the series becomes –
Hence, the fourth
Question : One calorie of heat energy is equivalent to approximately ____________ joules of mechanical energy.
Option 1: 0.24
Option 2: 0.48
Option 3: 2.4
Option 4: 4.2
Correct Answer: 4.2
Solution : The correct option is 4.2.
One calorie of heat energy is equivalent to approximately 4.2 joules of mechanical energy. The calorie is a unit of energy commonly used in the field of thermodynamics and represents the amount of heat required to raise the temperature
Question : What is the simplified value of $(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x-\frac{1}{x})(x^{16}+\frac{1}{x^{16}})(x+\frac{1}{x})(x^{4}+\frac{1}{x^{4}})?$
Option 1: $(x^{64}+\frac{1}{x^{64}})$
Option 2: $\frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$
Option 3: $\frac{(x^{64}-\frac{1}{x^{64}})}{(x+\frac{1}{x})}$
Option 4: $\frac{(x^{32}-\frac{1}{x^{32}})}{(x+\frac{1}{x})}$
Correct Answer: $\frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$
Solution : Given: $(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x-\frac{1}{x})(x^{16}+\frac{1}{x^{16}})(x+\frac{1}{x})(x^{4}+\frac{1}{x^{4}})$ $=(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^2-\frac{1}{x^2})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})$ Multiplying it by $\frac{(x^2+\frac{1}{x^2})}{(x^2+\frac{1}{x^2})}$, we get, $= \frac{(x^2+\frac{1}{x^2})}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^2-\frac{1}{x^2})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})$ $= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})(x^{4}-\frac{1}{x^{4}})$ $= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^{16}+\frac{1}{x^{16}})(x^{8}-\frac{1}{x^{8}})$ $= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{16}+\frac{1}{x^{16}})(x^{16}-\frac{1}{x^{16}})$ $= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{32}-\frac{1}{x^{32}})$ $= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{64}-\frac{1}{x^{64}})$ $= \frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$ Hence, the correct answer is $\frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$.
Question : A and B started a business investing amounts of INR 92,500 and INR 1,12,500, respectively. If B's share in the profit earned by them is INR 9,000, what is the profit (in INR) earned by A?
Option 1: 9,000
Option 2: 10,000
Option 3: 7,400
Option 4: 11,240
Correct Answer: 7,400
Solution : Amount invested by A = INR 92,500 Amount invested by B = INR 1,12,500 B's share in profit = INR 9,000 Let the profit earned by A be INR $x$. According to the question, $(\frac{92500}{112500}) = (\frac{x}{9000})$ ⇒ $x = \frac{(92500 × 9000)}{112500}$ ⇒ $x
Question : Select the INCORRECTLY spelt word.
Option 1: Assembly
Option 2: Disipline
Option 3: Group
Option 4: Leader
Correct Answer: Disipline
Solution : The correct choice is the second option.
The misspelt word among the options provided is "disipline", which should be spelt as discipline. The reason for the incorrect spelling is that it does not contain the letter "c", and it refers to a code
The Question containing Inaapropriate or Abusive Words
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