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Staff Selection Commission Sub Inspector Exam

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Question : Directions: Select the correct mirror image of the given combination when the mirror is held at the right side.

Option 1:

Option 2:

Option 3:

Option 4:

Team Careers360 27th Jan, 2024

Correct Answer:


Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection.
Here, according to the information provided, the mirror is placed on the right side of the figure. So, the left side of the reflected image will appear as the right

14 Views

Question : Directions: Select the option that represents the letters that when placed from left to right in the blanks below will complete the letter series.
_LJ_GH_L_I_HM_J_G_ _LJ_GH

Option 1: MMIJGILHMI

Option 2: MIMJGLIHMI

Option 3: IMMJGLIIMH

Option 4: IMMGJLIHIM

Team Careers360 27th Jan, 2024

Correct Answer: MIMJGLIHMI


Solution : Given:
_LJ_GH_L_I_HM_J_G_ _LJ_GH

To fill the series, we have to divide the series – _LJ_GH / _L_I_H / M_J_G_ / _LJ_GH
Let's check the given options –
First option: MMIJGILHMI; MLJMGH / ILJIGH / MIJ

396 Views

Question : Two circles with their centres at O and P and radii 8 cm and 4 cm respectively touch each other externally. The length of their common tangent is:

Option 1: 8.5 cm

Option 2: $\frac{8}{\sqrt{2}}$ cm

Option 3: $8\sqrt{2}$ cm

Option 4: 8 cm

Team Careers360 27th Jan, 2024

Correct Answer: $8\sqrt{2}$ cm


Solution :
Given, OQ = 8 cm and PR = 4 cm
Construction: Draw a perpendicular from P to OQ.
Since QR is a tangent, $\angle$ OQR = $\angle$ PRQ = 90$^\circ$
So, PSQR forms a rectangle.
Applying Pythagoras theorem in $\triangle$ POS,
PO2 =

10 Views

Question : Directions: Four pairs of numbers have been given, out of which three are alike in some manner, while one is different. Choose out the odd one.

Option 1: 42, 72

Option 2: 56, 63

Option 3: 20, 42

Option 4: 132, 182

Team Careers360 26th Jan, 2024

Correct Answer: 56, 63


Solution : Let's check each option –

First option: 42, 72; Both are even numbers.
Second option: 56, 63; Consists of one even and one odd number.
Third option: 20, 42; Both are even numbers.
Fourth option: 132, 182; Both are even numbers.

So, the option

22 Views

Question : The sides of a triangle are 24 cm, 26 cm, and 10 cm. At each of its vertices, circles of radius 4.2 cm are drawn. What is the area ( in cm2) of the triangle, excluding the portion covered by the sectors of the circles? $\left(\pi=\frac{22}{7}\right)$

Option 1: 120

Option 2: 105.86

Option 3: 92.28

Option 4: 27.72

Team Careers360 26th Jan, 2024

Correct Answer: 92.28


Solution : According to the question,
Side of triangles = 24 cm, 26 cm, and 10 cm.
Since $(26)^{2} = (24)^{2} + (10)^{2}$, then the triangle is right angles triangle.
So, the area of triangle = $\frac{1}{2}$ × base × height = $\frac{1}{2}$ × 24 × 10

10 Views

Question : What is the percentage of people below the poverty line estimated in rural areas of India in 2011–12?

Option 1: 25.7%

Option 2: 13.7%

Option 3: 35.9%

Option 4: 21.9%

Team Careers360 26th Jan, 2024

Correct Answer: 25.7%


Solution : The correct answer is 25.7%.

According to a news release from the Commission, the estimated percentage of people living below the poverty line in 2011–12 was 25.7% in rural areas, 13.7% in urban areas, and 21.9% nationwide. However, each state will have a different

20 Views

Question : Simplify $\frac{\cos ^4 \theta-\sin ^4 \theta}{\sin ^2 \theta}$.

Option 1: $1-\tan ^2 \theta$

Option 2: $\tan ^2 \theta-1$

Option 3: $\cot ^2 \theta-1$

Option 4: $1-\cot ^2 \theta$

Team Careers360 27th Jan, 2024

Correct Answer: $\cot ^2 \theta-1$


Solution : $\frac{\cos ^4 \theta-\sin ^4 \theta}{\sin ^2 \theta}$
$= \frac{(\cos^2 \theta - \sin^2 \theta)(\cos^2 \theta + \sin^2 \theta)}{\sin ^2 \theta}$
$=\frac{\cos^2 \theta - \sin^2 \theta}{\sin ^2 \theta}$ [As $\cos^2 \theta + \sin^2 \theta = 1$]
$=\frac{\cos^2 \theta}{\sin ^2 \theta}-\frac{\sin^2 \theta}{\sin^2 \theta}$
$=\cot ^2 \theta-1$

16 Views

Question : The value of $[(0.87)^2+(0.13)^2+(0.87)×(0.26)]^{2013}$ is:

Option 1: 0

Option 2: 2013

Option 3: 1

Option 4: –1

Team Careers360 26th Jan, 2024

Correct Answer: 1


Solution : Given:
$[(0.87)^2+(0.13)^2+(0.87)×(0.26)]^{2013}$
= $[(0.87)^2+(0.13)^2+(0.87)×2×(0.13)]^{2013}$
= $(0.87+0.13)^{2\times  2013}$
= $(1)^{2\times 2013}$
= $1$
Hence, the correct answer is 1.

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