Staff Selection Commission Sub Inspector Exam
Question : A hemispherical bowl of internal radius 6 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 2 cm and height 4 cm. How many bottles will be needed to empty the bowl?
Option 1: 32
Option 2: 37
Option 3: 38
Option 4: 36
Correct Answer: 36
Solution : The volume of a hemisphere = $\frac{2}{3}\pi r^3$, where $r$ = radius Given that the radius of the hemisphere is 6 cm. The volume of the hemisphere = $\frac{2}{3}\pi (6)^3 = 144\pi \, \text{cm}^3$ The volume of a cylinder = $\pi r^2h$ Given that the
Question : Directions: If A denotes +, B denotes ×, C denotes −, and D denotes ÷, then what will be the value of the following equation? 80 C 16 B 4 A 96 D 4 = ?
Option 1: 37
Option 2: 54
Option 3: 120
Option 4: 40
Correct Answer: 40
Solution : Given: A denotes +, B denotes ×, C denotes −, and D denotes ÷ 80 C 16 B 4 A 96 D 4 = ?
After replacing the letters with the mathematical signs, we get: 80 – 16 × 4 + 96 ÷ 4 80
Question : Parts of the following sentence have been given as options. Select the option that contains an error. The dancers swayed dainty on the stage last night.
Option 1: last night
Option 2: on the stage
Option 3: The dancers
Option 4: swayed dainty
Correct Answer: swayed dainty
Solution : The error lies in the fourth option.
Explanation: The error lies in the phrase "swayed dainty". The word "dainty" is an adjective, and in this context, it should be used as an adverb to modify the verb "swayed".
Therefore, the correct sentence should be:
Question : A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Option 1: $\frac{1}{3}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{5}$
Option 4: $\frac{1}{7}$
Correct Answer: $\frac{1}{5}$
Solution : Given: Suppose the vessel initially contains 8 litres of liquid. In this liquid, water is 3 litres and syrup is 5 litres. So the ratio is 3 : 5. Let $x$ litres of this liquid be replaced with water. Quantity of water in $x$ litre
Question : Directions: In the question, a sentence is given with a blank to be filled in with an appropriate word. Four alternatives are suggested for each question. Choose the correct alternative out of the four alternatives.
Our life promises a lot ______pleasure and we must learn to enjoy it.
Option 1: with
Option 2: for
Option 3: of
Option 4: at
Correct Answer: of
Solution : The correct answer is the third option.
In this context, "of" is used to indicate that life holds a significant amount or abundance of pleasure, and we should learn to enjoy this abundance.
Therefore, the complete sentence is: Our life promises a lot of pleasure,
Question : If $\tan (11 \theta)=\cot (7 \theta)$, then what is the value of $\sin ^2(6 \theta)+\sec ^2(9 \theta)+\operatorname{cosec}^2(12 \theta) ?$
Option 1: $\frac{23}{6}$
Option 2: $\frac{35}{12}$
Option 3: $\frac{31}{12}$
Option 4: $\frac{43}{12}$
Correct Answer: $\frac{43}{12}$
Solution : $\tan (11 \theta)=\cot (7 \theta)$ $⇒\tan (11 \theta)=\tan (90^\circ-7 \theta)$ $⇒11 \theta=90^\circ-7 \theta$ $⇒18 \theta=90^\circ$ $⇒ \theta=5^\circ$ $\sin ^2(6 \theta)+\sec ^2(9 \theta)+\operatorname{cosec}^2(12 \theta)$ Substituting $ \theta=5^\circ$, $=\sin ^2(30 ^\circ)+\sec ^2(45 ^\circ)+\operatorname{cosec}^2(60 ^\circ)$ $=(\frac{1}{2})^2+(\sqrt2)^2+(\frac{2}{\sqrt3})^2$ $=\frac{1}{4}+2+\frac{4}{3}$ $=\frac{43}{12}$ Hence, the correct answer is $\frac{43}{12}$.
Question : Directions: Select the option that represents the correct order of the given words as they would appear in an English dictionary. 1. Interest 2. Interdisciplinary 3. Interdict 4. Interdependent 5. Intersect
Option 1: 2, 1, 4, 3, 5
Option 2: 4, 3, 2, 1, 5
Option 3: 3, 2, 4, 1,5
Option 4: 1, 2, 3, 4, 5
Correct Answer: 4, 3, 2, 1, 5
Solution : Given: 1. Interest 2. Interdisciplinary 3. Interdict 4. Interdependent 5. Intersect
Step 1: We have the first five letters I, n, t, e, r common in all the words given above, so we will start from the sixth letter. Step 2:
Question : Which type of government is based on free and fair elections where those currently in power have a fair chance of losing?
Option 1: Democratic
Option 2: Autocratic
Option 3: Monarchic
Option 4: Authoritarian
Correct Answer: Democratic
Solution : The correct answer is Democratic
Democracy is the governance of the people, by the people and for the people, according to Abraham Lincoln. Democracy is a form of government in which the people elect their leaders, who then represent them in the legislature. A democracy
Question : Directions: Find who is the shortest if; I. Sunita is taller than Anita, II. Reena is taller than Chitra but shorter than Bhanu, III. Anita is shorter than Chitra, IV. Chitra is taller than Sunita.
Option 1: Sunita
Option 2: Anita
Option 3: Reena
Option 4: Bhanu
Correct Answer: Anita
Solution : Given: I. Sunita is taller than Anita, Sunita > Anita II. Reena is taller than Chitra but shorter than Bhanu, Bhanu > Reena > Chitra III. Anita is shorter than Chitra, Anita < Chitra IV. Chitra is taller than Sunita, Chitra > Sunita
By concluding
Question : If $x + y + z = 19, x^2 + y^2 + z^2 = 133$ and $xz = y^2, x > z > 0,$ what is the value of $(x - z)$?
Option 1: 5
Option 2: 0
Option 3: –2
Option 4: –5
Correct Answer: 5
Solution : Given: $x^2 + y^2 + z^2 = 133⇒ x^2 + z^2 = 133 - y^2$ $xz = y^2$ $x + y + z = 19$ $⇒ x + z = 19 - y$ Squaring both sides, we get, $⇒ x^2 + z^2 + 2xz =
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