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Staff Selection Commission Sub Inspector Exam

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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: $\frac{5}{3 \sqrt{3}}$

Team Careers360 17th Jan, 2024

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 $\frac{5}{2\sqrt3}$.

123 Views

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

Team Careers360 19th Jan, 2024

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

9 Views

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

Team Careers360 20th Jan, 2024

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

52 Views

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

Team Careers360 24th Jan, 2024

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

11 Views

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

Team Careers360 20th Jan, 2024

Correct Answer: 10


Solution : According to the question,
$(2x - 5y)^3 - (2x+5y)^3 = y[Ax^2 + By^2]$
⇒ $[2x - 5y - 2x - 5y][4x^{2} + 25y^{2} + 20 xy + 4x^{2} - 25y^{2}] = y[Ax^{2} + By^{2}]$
⇒ $[-10y] [ 12x^{2} + 25y^{2}] =  y[Ax^{2} + By^{2}]$

11 Views

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

Team Careers360 24th Jan, 2024

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.

16 Views

Question : Which is the most suitable unit for expressing nuclear radius?

Option 1: Micron

Option 2: Nanometre

Option 3: Fermi

Option 4: Angstrom

Team Careers360 19th Jan, 2024

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:

24 Views

Question :

The colour of the eye depends upon the pigment present in:

Option 1:

cornea

Option 2:

iris

Option 3:

rods

 

Option 4: cones

Team Careers360 17th Jan, 2024

Correct Answer:

iris


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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