Staff Selection Commission Sub Inspector Exam
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 / MIJLGH / MLJIGH (No repeated pattern found.) Second option: MIMJGLIHMI; MLJIGH / MLJIGH / MLJIGH / MLJIGH (MLJIGH is repeated in the series.) Third option: IMMJGLIIMH; ILJMGH / MLJIGH / MLJIGI / MLJHGH (No repeated pattern found.) Fourth option: IMMGJLIHIM; ILJMGH / MLGIJH / MLJIGH / ILJMGH (No repeated pattern found.) So, the sequence is MLJIGHMLJIGHMLJIGHMLJIGH. Hence, the second option is correct.
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 = OS2 + PS2 ⇒ (8+4)2 = (8-4)2 + QR2 ⇒ QR2 = 144 – 16 ⇒ QR = $8\sqrt{2}$ cm. Hence, the correct answer is $8\sqrt{2}$ cm.
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 second is different from the others as here the pairs are not even number. Hence, the second option is correct.
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 = 120 cm2 Now, The area of the triangle is covered by 3 sectors with a total angle of 180° = $\frac{180}{360}\pi$ × (4.2)2 = 27.72 cm2 ⇒ area of the triangle excluding the area covered by the sectors = 120 – 27.72 = 92.28 cm2 Hence, the correct answer is 92.28.
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 poverty line.
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 $\cos^2 \theta + \sin^2 \theta = 1$] $=\frac{\cos^2 \theta}{\sin ^2 \theta}-\frac{\sin^2 \theta}{\sin^2 \theta}$ $=\cot ^2 \theta-1$ Hence, the correct answer is $\cot ^2 \theta-1$.
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 : Identify the segment in the sentence which contains a grammatical error. If there is no error, then select the option 'No error'. Sh! Someone listens to our conversation.
Option 1: listens to
Option 2: No error
Option 3: Sh! Someone
Option 4: our conversation
Correct Answer: listens to
Solution : The error lies in the first option.
Explanation: The verb form "listens" is in the present tense, but the sentence structure with "Sh!" indicates a momentary action happening right now. To convey this, the present continuous tense "is listening" is more appropriate, indicating an ongoing action in the present moment.
Therefore, the correct sentence would be: Sh! Someone is listening to our conversation.
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. Conclusion II: Some red are not mangoes – From the Venn diagram, it is evident that some mangoes are not red but there is no negative relation of red with mangoes. Thus, the given conclusion cannot be drawn. So, this conclusion does not follow. Conclusion III: All raw are red – From the Venn diagram, it is evident that some parts of the circle representing raw lie inside the circle representing red while some lie outside. So, this conclusion does not follow.
So, no conclusion follows. Hence, the fourth option is correct.
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