Staff Selection Commission Sub Inspector Exam
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:
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
Question : Direction: The table given below shows the statistics of the top 10 scores in IPL 2016. A few entries are missing in the table. Here INN, AVG and SR stand for innings played, batting average, and batting strike rate respectively. Based on the table answer the following question. (Strike rate = $\frac{\text{Runs}}{\text{balls faced}}\times $100) and AVG = $\frac{\text {Runs}}{\text {INN – NOT OUT}}$
How many runs were scored by hitting sixes taking all the players together?
Option 1: 780
Option 2: 880
Option 3: 786
Option 4: 886
Correct Answer: 786
Solution : As per the given table: Runs scored by sixes = (28 + 32 + 23 + 9 + 5 + 4 + 12 + 6 + 12) × 6 = 131 × 6 = 786 Hence, the correct answer is 786.
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
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
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
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 =
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
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
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
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
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%
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
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: $1-\cot ^2 \theta$
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 $\cos^2 \theta + \sin^2 \theta = 1$] $=\frac{\cos^2 \theta}{\sin ^2 \theta}-\frac{\sin^2 \theta}{\sin^2 \theta}$ $=\cot ^2 \theta-1$
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
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.
Question : Directions: In the following question below, some statements are followed by some conclusions. Taking the given statements to be true, even if they seem to be at variance from commonly known facts, read all the conclusions and then decide which of the given conclusions logically follows from the given statements. Statements: I. Some mangoes are not red. II. All reds are raw. III. Some raw are mangoes. Conclusions: I. Some mangoes are not raw. II. Some red are not mangoes. III. All raw are red.
Option 1: Only conclusion I follows
Option 2: Only conclusions II and III follow
Option 3: Only conclusions I and III follow
Option 4: No conclusion follows
Correct Answer: No conclusion follows
Solution : The possible Venn diagram, according to the given statements is as follows–
Let's analyse the conclusions – Conclusion I: Some mangoes are not raw – There is no direct or definite negative relation between mango and raw. So, this conclusion does not follow.
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