Staff Selection Commission Sub Inspector Exam
Question : Simplify. $\cos \left(36^{\circ}-\mathrm{A}\right) \cos \left(36^{\circ}+\mathrm{A}\right)+\cos \left(54^{\circ}-\mathrm{A}\right) \cos \left(54^{\circ}+\mathrm{A}\right)$
Option 1: $\cos A$
Option 2: $\sin 2A$
Option 3: $\cos 2A$
Option 4: $\sin A$
Correct Answer: $\cos 2A$
Solution :
Given: $\cos(36^{\circ}-A) \cos (36^{\circ}+A)+\cos (54^{\circ}-A) \cos (54^{\circ}+A)$ = $\sin[90^{\circ} - (36^{\circ} - A)]\sin[90^{\circ} - (36^{\circ} + A)] + \cos (54^\circ - A) \cos (54^\circ + A)$ = $\sin(54^\circ + A)\sin(54^\circ - A) + \cos (54^\circ - A)\cos (54^\circ + A)$ = $\cos(54^{\circ} + A
Question : Directions: If LOVE is coded as 27, then how is COME coded as?
Option 1: 38
Option 2: 18
Option 3: 28
Option 4: 8
Correct Answer: 18
Solution : Given: LOVE is coded as 27.
Add the place value of the letters of the LOVE and divide it by 2 to get the codes – L→12; O→15; V→22; E→5 (12 + 15 + 22 + 5) ÷ 2 = 27 So, LOVE is coded
Question : Which of the following statements is correct regarding fuse wire?
Option 1: It has a low melting point and low conductivity.
Option 2: It has a high melting point and low conductivity.
Option 3: It has a low melting point and high conductivity.
Option 4: It has a high melting point and high conductivity.
Correct Answer: It has a low melting point and high conductivity.
Solution : The correct answer is that it has a low melting point and high conductivity.
The material used to make fuse wire has a high conductivity and a low melting point. It will prevent excessive power from
Question : The numbers of students who passed with different honours from a college from 2015 to 2018 are depicted in the given table. Study the table and answer the following question.
How many students passed Mathematics, Physics, Chemistry, Zoology, and Botany from the year 2015 to 2018?
Option 1: 112
Option 2: 97
Option 3: 100
Option 4: 99
Correct Answer: 112
Solution : From the table, The number of Mathematics students from 2015-2018 = 38 The number of Physics students from 2015-2018 = 26 The number of Chemistry students from 2015-2018 = 20 The number of Zoology students from 2015-2018 = 18 The number of Botany students from
Question : The next number of the sequences 3, 7, 15, 31, 63, ? is:
Option 1: 95
Option 2: 111
Option 3: 123
Option 4: 127
Correct Answer: 127
Solution : Given: The sequences 3, 7, 15, 31, 63,? Here, 3 + (22) = 7 7 + (23) = 15 15 + (24) = 31 31 + (25) = 63 63 + (26) = 127 Hence,
Question : If $\left (\sqrt{5} \right)^{7}\div \left (\sqrt{5} \right)^{5}=5^{p},$ then the value of $p$ is:
Option 1: $5$
Option 2: $2$
Option 3: $\frac{3}{2}$
Option 4: $1$
Correct Answer: $1$
Solution : Given: $\frac{(\sqrt{5})^7}{(\sqrt{5})^5} = 5^p$ $⇒(\sqrt{5})^{7 - 5} = 5^p$ $⇒(\sqrt{5})^2 = 5^p$ $⇒5^{\frac{1}{2}×2} = 5^{p}$ $⇒5^1=5^p$ Comparing both sides, we get, $\therefore p=1$ Hence, the correct answer is $1$.
Question : El Nino occurs over:
Option 1: Atlantic Ocean
Option 2: Indian Ocean
Option 3: Pacific Ocean
Option 4: Mediterranean Sea
Correct Answer: Pacific Ocean
Solution : The correct answer is the Pacific Ocean.
El Nino is a climate phenomenon characterised by unusually warm surface waters in the eastern tropical Pacific Ocean. When the eastern tropical Pacific's coastal waters warm (El Nino), the air pressure above the ocean falls. Increased
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (7, 12, 25) (6, 9, 21)
Option 1: (9, 13, 24)
Option 2: (5, 8, 19)
Option 3: (8, 14, 24)
Option 4: (4, 11, 20)
Correct Answer: (5, 8, 19)
Solution : Given: (7, 12, 25); (6, 9, 21)
The logic here is – (The first number + The second number + 6) = The third number (7, 12, 25)→7 + 12 + 6 = 19 + 6 = 25 (6, 9, 21)→6 + 9
Question : Select the most appropriate option to substitute the underlined segment in the given sentence. Any sort of unfair conduct is not tolerated in international sports tournaments as it can completely ruin an athlete’s career.
Option 1: straw in the eye
Option 2: hand in the mud
Option 3: foul play
Option 4: red handed
Correct Answer: foul play
Solution : The correct choice is the third option.
Foul play is a term commonly used to describe dishonest or unsportsmanlike behaviour, especially when it comes to breaking the rules of a game or competition. It is well-established in the context of sports ethics, making it
Question : Directions: Select the letter cluster that can replace the question mark (?) in the given letter cluster series. UKS, ZPX, EUC, JZH, ?
Option 1: ODN
Option 2: OEM
Option 3: PEM
Option 4: ODM
Correct Answer: OEM
Solution : Given: UKS, ZPX, EUC, JZH, ?
Add 5 to each letter of the previous term to obtain the next term in the series – UKS→U + 5 = Z; K + 5 = P; S + 5 = X ZPX→Z +
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