Staff Selection Commission Sub Inspector Exam
Question : If $\sin A=\frac{1}{2}$, then the value of $(\tan A+\cos A)$ is:
Option 1: $\frac{2}{3 \sqrt{3}}$
Option 2: $\frac{3}{2 \sqrt{3}}$
Option 3: $\frac{5}{2 \sqrt{3}}$
Option 4: $\frac{5}{3 \sqrt{3}}$
Correct Answer: $\frac{5}{2 \sqrt{3}}$
Solution : Given: $\sin A=\frac{1}{2}$ ⇒ $\sin A=\sin 30^\circ$ ⇒ $ A= 30^\circ$ $\therefore (\tan A+\cos A)$ = $(\tan 30^\circ+\cos 30^\circ)$ = $\frac{1}{\sqrt3}+\frac{\sqrt3}{2}$ = $\frac{2+3}{2\sqrt3}$ = $\frac{5}{2\sqrt3}$ Hence, the correct answer is $\frac{5}{2\sqrt3}$.
Question : Select the option that can be used as a one-word substitute for the given group of words. Centre of public attention
Option 1: Ambiguity
Option 2: Obscurity
Option 3: Fuzziness
Option 4: Limelight
Correct Answer: Limelight
Solution : The correct choice is the fourth option.
Explanation: The term "limelight" is commonly used as a metaphor for being the centre of public attention or scrutiny. Historically, limelight was a bright light source used in theatres to illuminate performers on stage, making them the focal
Question : Directions: In the given question, a sentence is given with a blank to be filled in with the appropriate words. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
After saying that Beverly made too many mistakes, Bob added insult to injury by saying _________.
Option 1: they were small mistakes
Option 2: she worked very slowly
Option 3: her work was excellent
Option 4: work at a remarkable pace
Correct Answer: she worked very slowly
Solution : The correct choice is the second option.
Explanation:
By saying that Beverly made too many mistakes and then adding that she worked very slowly, Bob is indeed making the situation worse for Beverly, as it implies that not only did she
Question : By the 42nd Amendment in 1976, as introduced by the ______, the chapter on the fundamental duties of citizens was incorporated into the Constitution.
Option 1: Shah Nawaz Committee
Option 2: Sachar Committee
Option 3: Swaran Singh Committee
Option 4: Balwant Rai Mehta Committee
Correct Answer: Swaran Singh Committee
Solution : The correct answer is the Swaran Singh Committee.
The Russian Constitution served as the model for the concept of fundamental duties. On the advice of the Swaran Singh Committee, they were added to Part IV-A of the Constitution by the 42nd Constitutional
Question : In the given figure, AB = 8 cm; AC = 17 cm. What is the length of AD?
Option 1: 4.68 cm
Option 2: 5.36 cm
Option 3: 3.76 cm
Option 4: 8.5 cm
Correct Answer: 3.76 cm
Solution : Given: A right-angled triangle ABC with AB = 8 cm and AC = 17 cm Applying the Pythagoras theorem to the given $\triangle$ABC ⇒ We get, AC2 = AB2 + BC2 ⇒ 172 = 82 + BC2 ⇒
Question : If $(2x - 5y)^3 - (2x+5y)^3 = y[Ax^2 + By^2]$, then what is the value of $(2A - B)$?
Option 1: 25
Option 2: 10
Option 3: 15
Option 4: 40
Correct Answer: 10
Solution : According to the question, $(2x - 5y)^3 - (2x+5y)^3 = y[Ax^2 + By^2]$ ⇒ $[2x - 5y - 2x - 5y][4x^{2} + 25y^{2} + 20 xy + 4x^{2} - 25y^{2}] = y[Ax^{2} + By^{2}]$ ⇒ $[-10y] [ 12x^{2} + 25y^{2}] = y[Ax^{2} + By^{2}]$ ⇒
Question : If $\frac{x}{y}+\frac{y}{x}=1$ and $x+y=2$, then the value of $x^3+y^3$ is:
Option 1: 1
Option 2: 3
Option 3: 0
Option 4: 2
Correct Answer: 0
Solution : $\frac{x}{y}+\frac{y}{x}=1$ and $x+y=2$ $⇒\frac{x^2+y^2}{xy}=1$ $⇒{x^2+y^2}=xy$ ___(i) $x^3+y^3=(x+y)(x^2+y^2-xy)$ From (i), $⇒x^3+y^3=0$ Hence, the correct answer is 0.
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at 1, 2 and 3 that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
Even though she was disliked by her in-laws at the beginning of her marriage, she did manage to win their hearts.
(1) win over their
(2) win over there
(3) win them over their
(4) No Improvement
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 4
Solution : The correct answer is the fourth option.
"Win their hearts" implies that she made efforts to establish a positive and loving relationship with her in-laws, and she succeeded in doing so.
Therefore, the given sentence requires no improvement.
Question : Which is the most suitable unit for expressing nuclear radius?
Option 1: Micron
Option 2: Nanometre
Option 3: Fermi
Option 4: Angstrom
Correct Answer: Fermi
Solution : The correct answer is Fermi.
The nuclear length is quantified using the unit called the "fermi" (fm), where 1 fermi is equivalent to 10-15 meters. This unit, originally named after the Italian physicist Enrico Fermi, has been replaced by the SI term "femtometer" (symbol:
Question :
The colour of the eye depends upon the pigment present in:
Option 1:
cornea
Option 2:
iris
Option 3:
rods
Option 4: cones
Correct Answer:
Solution : The correct option is the iris.
The colour of the eye depends on the amount and type of pigments present in the iris, which is the coloured part of the eye. The iris is the coloured part of the eye that surrounds the pupil.
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