Staff Selection Commission Sub Inspector Exam
Question : Solve for $\theta: \cos ^2 \theta-\sin ^2 \theta=\frac{1}{2}, 0<\theta<90^{\circ}$.
Option 1: 45o
Option 2: 60o
Option 3: 30o
Option 4: 40o
Correct Answer: 30o
Solution : Given, cos2θ − sin2θ = $\frac{1}{2}$ ⇒ cos2θ = $\frac{1}{2}$ + sin2θ since, cos2θ + sin2θ = 1 ⇒ 1 − sin2θ = $\frac{1}{2}$ + sin2θ ⇒ sin
Question : A money bill under Article 111 of the Constitution of India, presented to the President for assent, has to be endorsed by a Certificate of the ____________ signed by him/her that it is a money bill.
Option 1: Speaker of the Lok Sabha
Option 2: Secretary General of the Rajya Sabha
Option 3: Deputy Chairman of the Rajya Sabha
Option 4: Secretary General of the Lok Sabha
Correct Answer: Speaker of the Lok Sabha
Solution : The correct answer is Speaker of the Lok Sabha.
The Speaker of the Lok Sabha or the presiding officer of the Lok Sabha decides whether the bill is a money bill or not. He is the final authority who determines the
Question : Two inlet pipes can fill a cistern in 10 and 12 hours respectively and an outlet pipe can empty 80 gallons of water per hour. All three pipes working together can fill the empty cistern in 20 hours. What is the capacity (in gallons) of the tank?
Option 1: 360
Option 2: 300
Option 3: 600
Option 4: 900
Correct Answer: 600
Solution : Let the time taken by the outlet pipe to empty the tank be $x$ hour. One hour's work of pipe A = $\frac{1}{10}$ One hour's work of pipe B = $\frac{1}{12}$ One hour's work of pipe C = $-\frac{1}{x}$ When all pipes work together, the
Question : $16 \sec ^2 A-16 \tan ^2 A=$_________.
Option 1: 9
Option 2: 0
Option 3: 16
Option 4: 1
Correct Answer: 16
Solution : Given expression, $16 \sec ^2 A-16 \tan ^2 A$ $= 16(\sec^2A-\tan^2A)$ $= 16 × (1)$ $= 16$ Hence, the correct answer is 16.
Question : Two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. Then the distance between their centres is:
Option 1: 10 cm
Option 2: 8 cm
Option 3: 13.3 cm
Option 4: 15 cm
Correct Answer: 13.3 cm
Solution : Let O and P be the centre of two circles with radii 10 cm and 8 cm. OA = 10 cm, PA = 8 cm, and AB = 12 cm Then AC = $\frac{1}{2}$ × 12 = 6 cm In $\triangle OCA$, $OA^2=OC^2+AC^2$ ⇒
Question : Which of the following is also termed as main memory of a computer?
Option 1: RAM
Option 2: ROM
Option 3: Hard disk
Option 4: Compact disk
Correct Answer: RAM
Solution : The correct answer is RAM.
The primary memory of a computer, also referred to as main memory or Random-Access Memory (RAM), serves as a temporary data repository. It acts as a quick-access storage bank where the computer stores data required for immediate retrieval. RAM
Question : Refer to the following table. Read the table and answer the question. Food grain Production in a country in 1999. (in lakh tons)
What was the proportion of rice production to wheat production in the country?
Option 1: 411 : 422
Option 2: 473 : 411
Option 3: 418 : 422
Option 4: 322 : 311
Correct Answer: 473 : 411
Solution : Total production of Rice = 55 + 58 + 69 + 51 + 47 + 78 + 67 + 48 = 473 Total production of Wheat = 113 + 96 + 42 +47 + 32 + 25 + 18 + 38 = 411
Question : Directions: In the given figure, how many keys are duplicates but not steel?
Option 1: 16
Option 2: 18
Option 3: 0
Option 4: 34
Correct Answer: 0
Solution : According to the question, there is no common region that represents keys that are duplicate but not steel is the region common to both keys and duplicate, but uncommon to the steel region.
From the Venn diagram, such a region does not exist.
Therefore, the
Question : The two parallel sides of a trapezium are 17 cm and 15 cm, respectively. If the height of the trapezium is 6 cm, then its area (in m2) is:
Option 1: 9.6
Option 2: 960
Option 3: 0.96
Option 4: 0.0096
Correct Answer: 0.0096
Solution : The area of a trapezium = $\frac{1}{2}$ × sum of lengths of parallel sides × height Substituting the given values, The area of the trapezium = $\frac{1}{2}$ × (17 + 15) × 6 = 96 cm2 We know that, 1 m2 = 10,000
Question : Determine the LCM of two numbers if their HCF is 12 and their ratio is 13 : 15.
Option 1: 1780
Option 2: 2450
Option 3: 1890
Option 4: 2340
Correct Answer: 2340
Solution : HCF of two numbers = 12 Ratio of two numbers = 13 : 15 Let $13x$ and $15x$ be the two numbers. HCF of $13x$ and $15x = x$ $\therefore x =12$ LCM of $13x$ and $15x = 13×15×x = 13×15×12 = 2340$ Hence, the
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