Staff Selection Commission Sub Inspector Exam
Question : The value of the expression $\cos ^2 45^{\circ}+\cos ^2 135^{\circ}+\cos ^2 225^{\circ}+\cos ^2 315^{\circ}$ is:
Option 1: $2$
Option 2: $\frac{1}{2}$
Option 3: $\frac{3}{2}$
Option 4: $1$
Correct Answer: $2$
Solution : Here, we have : $\cos^245^\circ = (\frac{1}{\sqrt{2}})^2 = \frac{1}{2}$ $\cos^2135^\circ = \cos^2(90^\circ + 45^\circ ) = -\sin^245^\circ = (-\frac{1}{\sqrt{2}})^2 = \frac{1}{2}$ $\cos^2225^\circ = \cos^2(180^\circ + 45^\circ ) = -\cos^245^\circ = (-\frac{1}{\sqrt{2}})^2 = \frac{1}{2}$ $\cos^2315^\circ = \cos^2(360^\circ -45^\circ ) = \cos^245^\circ = (\frac{1}{\sqrt{2}})^2 = \frac{1}{2}$ $\cos^245^\circ
Question : Coulomb/second is a unit of which of the following?
Option 1: Capacitance
Option 2: Resistance
Option 3: Electric current
Option 4: Magnetism
Correct Answer: Electric current
Solution : The correct option is Electric current.
A coulomb/second is a unit of electric current measured in amperes (A). One coulomb per second represents the flow of one ampere of electric charge per second. This unit is crucial in quantifying the rate of electric charge
Question : A can do a piece of work in 10 days. B can do it in 15 days. With the assistance of C, they completed the work in 5 days. How many days C alone can do it?
Option 1: 20
Option 2: 25
Option 3: 30
Option 4: 35
Correct Answer: 30
Solution : Time taken by A alone to do the work = 10 days Part of work done by A in a day = $\frac{1}{10}$ Time taken by B alone to do the work = 15 days Part of work done by A in a day =
Question : India joined the United Nations after ratifying the UN Charter in___________.
Option 1: December 1945
Option 2: May 1946
Option 3: October 1945
Option 4: February 1946
Correct Answer: October 1945
Solution : The correct option is October 1945.
India joined the United Nations (UN) on October 30, 1945, after ratifying the UN Charter. India became a member of the United Nations shortly after gaining independence from British rule. The country played an active role in
Question : What is the literacy rate in India as per Census 2011?
Option 1: 74.04%
Option 2: 76.04%
Option 3: 78.04%
Option 4: 72.04%
Correct Answer: 74.04%
Solution : The correct option is 74.04%.
As per the Census of India 2011, the literacy rate in the country was reported to be 74.04%. The literacy rate is an indicator of the percentage of the population aged 7 and above who can read and write
Question : If 86y5 is exactly divisible by 3, then the least value of y is:
Option 1: 3
Option 2: 0
Option 3: 1
Option 4: 2
Correct Answer: 2
Solution : The divisibility rule of 3 states that a number is divisible by 3 if the sum of its digits is also divisible by 3. For the number 86y5 to be divisible by 3, the sum of its digits (8 + 6 + y + 5)
Question : Select the correct spelling for the INCORRECTLY spelt word in the given sentence. The Eustachian tube and vestubular complex in the middle and inner ear, respectively, have an important role to play.
Option 1: vestibular
Option 2: midle
Option 3: respictevely
Option 4: importent
Correct Answer: vestibular
Solution : The correct answer to this question is the first option.
Explanation:
Vestibular: This term refers to the vestibular system, which is responsible for the sense of balance and spatial orientation. The correct spelling is with an "i" after "v", not "u".
Context: The correct spelling
Question : The simplified value of $\sqrt{900} + \sqrt{0.09} - \sqrt{0.000009}$ is:
Option 1: $30.27$
Option 2: $30.297$
Option 3: $30.097$
Option 4: $30.197$
Correct Answer: $30.297$
Solution : $\sqrt{900} + \sqrt{0.09} - \sqrt{0.000009}$ $ = \sqrt{900} + \sqrt{\frac{9}{100}} - \sqrt{\frac{9}{1000000}}$ $ = 30 + 0.3 - 0.003$ $ = 30.297$ Hence, the correct answer is $30.297$.
Question : Select the most appropriate ANTONYM of the underlined word in the given sentence.
The court absolved the defendant of all charges due to a lack of evidence.
Option 1: accused
Option 2: condemned
Option 3: attacked
Option 4: criticised
Correct Answer: accused
Solution : The correct choice is the first option.
Absolve means to officially remove guilt or responsibility for something wrong that someone has done or might have done. Accuse means to charge someone with an offence or crime, which makes it the correct antonym of absolve.
Question : The SI unit of luminous emittance is:
Option 1: Lux
Option 2: Candela
Option 3: Lumen
Option 4: Lumen second
Correct Answer: Lux
Solution : The correct option is Lux.
A surface's visible light emission per unit area is measured by luminous emittance. The lux, denoted by the symbol lx, is the SI unit of light emittance. It is equal to 1 lx = 1 lm/m² or one lumen
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