Staff Selection Commission Sub Inspector Exam
Question : The subatomic particle that does not have any electric charge is a/an_______.
Option 1: Electron
Option 2: Proton
Option 3: Neutron
Option 4: All options are correct
Correct Answer: Neutron
Solution : The correct option is a Neutron
Neutrons are subatomic particles located in an atom's nucleus that have no electrical charge but contribute to the atom's mass along with protons. Neutrons increase the total mass of an atom but do not affect the atom's chemical behaviour.
Question : Directions: In the following question, you have to identify the correct response from the given premises stated according to the following symbols. If + stands for multiplication, – stands for division, × stands for addition, and ÷ stands for subtraction, then which one of the following equations is correct?
Option 1: 12 × 5 + 4 – 5 ÷ 4 = 20
Option 2: 12 ÷ 5 + 4 – 5 × 4 = 18
Option 3: 12 + 5 – 4 × 5 ÷ 4 = 16
Option 4: 12 ÷ 5 – 4 × 5 + 4 = 22
Correct Answer: 12 + 5 – 4 × 5 ÷ 4 = 16
Solution : Given: + stands for multiplication, – stands for division, × stands for addition, and ÷ stands for subtraction.
Replace the mathematical signs and solve the equations. Let's check the given options – First option: 12
Question : Select the most appropriate meaning of the given idiom. Spill the beans
Option 1: Sound familiar
Option 2: Fail to make an impact
Option 3: To be very expensive
Option 4: Give away a secret
Correct Answer: Give away a secret
Solution : The correct choice is the fourth option.
Explanation: The idiom "spill the beans" means to give away a secret or disclose information that was meant to be kept confidential. It's often used when someone unintentionally reveals something that was supposed to be
Question : Train ‘A’ requires 15 seconds to cross train ‘B’ of length 300 m moving in the opposite direction at a speed of 36 km/hr. Further, train ‘A’ requires 30 seconds to cross a 500 m long stationary train ‘C’. Find the length (in m) of train ‘A’.
Option 1: 200
Option 2: 300
Option 3: 250
Option 4: 275
Correct Answer: 200
Solution : Speed = $\frac{\text{Distance}}{\text{time}}$ Train ‘A’ requires 15 seconds to cross train ‘B’ of length 300 m. Speed of train B = 36 km/hr = $36 \times \frac{5}{18}$ = 10 m/s Distance covered by train B in 15 sec = $10\times 15$ = 150 m Let
Question : If $x + \frac{1}{x} = \sqrt{3}$, then the value of $x^{18} + x^{12} + x^{6} + 1$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
Correct Answer: 0
Solution : $x^{18}+x^{12}+x^{6}+1$ = $x^{6}(x^{12}+1)+1(x^{12}+1)$ = $(x^{6}+1)(x^{12}+1)$ --------------------------(i) $x+\frac{1}{x} = \sqrt{3}$ Squaring both sides, we get, ⇒ $(x+\frac{1}{x})^2 = (\sqrt{3})^2$ ⇒ $(x)^2+(\frac{1}{x})^2+2×x×\frac{1}{x} = 3$ ⇒ $(x)^2+(\frac{1}{x})^2 = 3-2 = 1$ Cubing both sides, we get, $((x)^2+(\frac{1}{x})^2)^3 = 1^3$ ⇒ $(x)^6+(\frac{1}{x})^6+3×((x)^2+(\frac{1}{x})^2) = 1^3$ ⇒ $(x)^6+(\frac{1}{x})^6 = 1 -
Question : The monthly salary of a person is INR 50,000. He spends 40% of his salary on household expenses, 25% on rent, and 15% on transportation, and saves the remaining amount. What is his yearly savings?
Option 1: INR 1,00,000
Option 2: INR 1,10,000
Option 3: INR 1,20,000
Option 4: INR 90,000
Correct Answer: INR 1,20,000
Solution : The monthly salary of a person = INR 50,000 Household expenses = 40% of INR 50000 Rent = 25% of INR 50000 Transportation = 15% of INR 50000 Monthly savings = (100 – 40 – 25 – 15)% of INR 50000 = 20% of
Question : Directions: In the following question, some parts of the sentence have errors, and some are correct. Find out which part of the sentence has an error. The number of that part is the answer. If a sentence is error-free, your answer is "No Error".
This is John's book on the table.
(1) No Error
(2) John's book
(3) on the table.
(4) This is
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 2
Solution : The error is in option two.
The correct sentence should be "John's book is on the table"
The subject "this" is redundant in this sentence. The remaining sentence is complete and conveys the intended meaning. The phrase "on the table" is a prepositional phrase
Question : Sujatha sold 75% of her goods at a profit of 24% and the remaining at a loss of 40%. What is her gain or loss percentage on the whole transaction?
Option 1: 8% gain
Option 2: 10% gain
Option 3: 7.5% loss
Option 4: 9% loss
Correct Answer: 8% gain
Solution : Let the total goods be 100 and their value is 100. So, total cost price = 100 × 100 = 10000 Sujatha sold 75% of her goods at a profit of 24%. So, the selling price = 75 × (100 + 24) = 75
Question : Directions: Select the option in which the numbers share the same relationship as that shared by the given pair of numbers. 84 : 72
Option 1: 77 : 64
Option 2: 64 : 56
Option 3: 68 : 54
Option 4: 76 : 62
Correct Answer: 68 : 54
Solution : Given: 84 : 72
Subtract the sum of the digits of the first number from the first number to obtain the second number in the given set of numbers – 84 : 72→84 – (8 + 4) = 84 – 12 = 72
Question : If $a+b+c=m$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0$, then the average of $a^{2}, b^{2},$ and $c^{2}$ is:
Option 1: $m^{2}$
Option 2: $\frac{m^{2}}{3}$
Option 3: $\frac{m^{2}}{9}$
Option 4: $\frac{m^{2}}{27}$
Correct Answer: $\frac{m^{2}}{3}$
Solution : Given: $a+b+c=m$ Squaring both sides, we get, ⇒ $(a+b+c)^{2}=m^{2}$ ⇒ $a^{2}+b^{2}+c^{2}+2(ab+bc+ca)=m^{2}$ ------(1) [Using $(a+b+c)^{2} = a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$ ] $\because\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0$ ⇒ $\frac{bc+ac+ab}{abc}=0$ ⇒ $bc+ac+ab=0$ Putting the value of $bc+ac+ab=0$ in equation (1), we have, ⇒ $a^{2}+b^{2}+c^{2}+2(0)=m^{2}$ ⇒ $a^{2}+b^{2}+c^{2}=m^{2}$ Dividing by 3, both sides to find the average,
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