Staff Selection Commission Sub Inspector Exam
Question : If the volume of a sphere is 38808 cm³, then its surface area is:
Option 1: 5554 cm²
Option 2: 5574 cm²
Option 3: 5564 cm²
Option 4: 5544 cm²
Correct Answer: 5544 cm²
Solution : Volume of sphere (radius = $r$) = 38808 cm$^3$ Volume of sphere = $\frac{4}{3}\pi r^3$ Surface Area of sphere = $4\pi r^2$ Calculation: ⇒ $\frac{4}{3}\pi r^3$ = 38808 ⇒ $\frac{4}{3}\times\frac{22}{7}\times r^3$ = 38808 ⇒ $r^3$ = $\frac{38808\times21}{88}$ ⇒ $r^3$ = 9261 ⇒ $r$ =
Question : The value of $\frac{1}{\sqrt{7-4 \sqrt{3}}}$ is closest to:
Option 1: 1.2
Option 2: 4.1
Option 3: 4.2
Option 4: 3.7
Correct Answer: 3.7
Solution : $\frac{1}{\sqrt{7-4 \sqrt{3}}}$ $=\frac{1}{\sqrt{2^2+(\sqrt3)^2-2\times2\sqrt{3}}}$ $=\frac{1}{\sqrt{(2-\sqrt3)^2}}$ $=\frac{1}{(2-\sqrt3)}\times\frac{2+\sqrt3}{2+\sqrt3}$ $=\frac{2+\sqrt3}{4-3}$ $=2+\sqrt3$ = 2 + 1.732 = 3.732 Hence, the correct answer is 3.7.
Question : Directions: In the given 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.
The three brothers formed a little _______ within a family.
Option 1: clique
Option 2: camp
Option 3: coterie
Option 4: band
Correct Answer: coterie
Solution : The correct choice is the third option.
Explanation:
It means a small, exclusive group of people with shared interests or tastes. They do things together but do not like to include others. It is a suitable choice for the sentence implying that they established
Question : In which year did Ambedkar start a temple entry movement?
Option 1: 1931
Option 2: 1927
Option 3: 1925
Option 4: 1938
Correct Answer: 1927
Solution : The correct option is 1927.
B. R. Ambedkar initiated the temple entry movement in 1927. Advocating for social equality, he led the Mahad Satyagraha, where Dalits asserted their right to access public water tanks and temples. This movement marked a crucial step in challenging caste-based
Question : Directions: Select the missing number in the pattern from the given responses.
Option 1: 97
Option 2: 88
Option 3: 91
Option 4: 106
Correct Answer: 97
Solution : Given:
The pattern is running horizontally along the rows. Each alternate row follows the same pattern. Row 1: (1)3 + (3)3 = 1 + 27 = 28 Row 2: (3)2
Question : Directions: In the following question, two statements are given followed by three conclusions I, II, and III. You have to consider the two statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements Statements: I. All men are hardworking. II. No advocate is hardworking. III. Some beautiful are men. Conclusions: I. Some beautiful are hardworking. II. Some advocates are not beautiful. III. Some beautiful are not advocates.
Option 1: Only conclusion III follows
Option 2: Only conclusion I and III follow
Option 3: Only conclusions II and III follow
Option 4: Only conclusions I and II follow
Correct Answer: Only conclusion I and III follow
Solution : The possible Venn diagram for the given statement according to the question –
Let's analyse the conclusions – Conclusion (I): Some beautiful are hardworking – From the Venn diagram, we can see that the circles representing beautiful and hardworking intersect
Question : Directions: The number of letters repeated in the given word is indicated in front of each alternative. Identify the correct alternative. MEASUREMENTS
Option 1: M2E2A2S2U1R1N1T1
Option 2: M2E3A1S1U2R1N2T1
Option 3: M2E2A1S2U1R1N1T1
Option 4: M2E3A1S2U1R1N1T1
Correct Answer: M2E3A1S2U1R1N1T1
Solution : Given: MEASUREMENTS
The number of times a specific letter is repeated is shown below – M→2; E→3; A→1; S→2; U→1; R→1; N→1; T→1
So, MEASUREMENTS can be formed with the
Question : A person bought an article at a 30% discount on its marked price. The person then sold it at 30% profit for INR 427.70. What was the marked price of the article?
Option 1: INR 470
Option 2: INR 450
Option 3: INR 500
Option 4: INR 480
Correct Answer: INR 470
Solution : Let the marked price of the article be $x$ Cost price of the article at 30% discount = $x × \frac{70}{100}$ Selling price at 30% profit = $\frac{130}{100}\times$ cost price According to the question, $x × \frac{70}{100} × \frac{130}{100} = 427.70$ ⇒ $x =
Question : The value of $\frac{5-2 \div 4 \times[5-(3-4)]+5 \times 4 \div 2 \text { of } 4}{4+4 \div 8 \text { of } 2 \times(8-5) \times 2 \div 3-8 \div 2 \text { of } 8}$ is:
Option 1: $\frac{9}{8}$
Option 2: $\frac{9}{4}$
Option 3: $\frac{15}{32}$
Option 4: $\frac{89}{4}$
Correct Answer: $\frac{9}{8}$
Solution : Given: $\frac{5-2 \div 4 \times[5-(3-4)]+5 \times 4 \div 2 \text { of } 4}{4+4 \div 8 \text { of } 2 \times(8-5) \times 2 \div 3-8 \div 2 \text { of } 8}$ = $\frac{5-\frac{2}{4} \times6+5 \times 4 \div 8}{4+4 \div 16 \times3 \times 2
Question : A ladder leaning against a wall makes an angle $\theta$ with the horizontal ground such that $\cos \theta=\frac{5}{13}$. If the height of the top of the ladder from the wall is 18 m, then what is the distance (in m) of the foot of the ladder from the wall?
Option 1: 18
Option 2: 7.5
Option 3: 13
Option 4: 19.5
Correct Answer: 7.5
Solution : Let's the distance of the foot of the ladder as $x$, and the height of the top of the ladder is 18 m Length of the ladder = $L$ (Hypotenuse) $h$ = 18 cm and cos θ = $\frac{5}{13}$ Now, ⇒ cos θ = $\frac{5}{13}$
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