Staff Selection Commission Sub Inspector Exam
Question : If the hypotenuse of an isosceles right-angled triangle is 10 cm, then the other two sides (in cm) are __________.
Option 1: $10\sqrt{2}$ and $10\sqrt{2}$
Option 2: $8\sqrt{2}$ and $8\sqrt{2}$
Option 3: $6\sqrt{2}$ and $6\sqrt{2}$
Option 4: $5\sqrt{2}$ and $5\sqrt{2}$
Correct Answer: $5\sqrt{2}$ and $5\sqrt{2}$
Solution : Given: Hypotenuse of the isosceles right-angled triangle = 10 cm Let the other two equal sides be $x$ cm. Now applying the Pythagoras theorem, we get, $x^2+x^2=10^2$ ⇒ $2x^2=100$ $\therefore x=\sqrt{50}=5\sqrt{2}$ Hence, the correct answer is $5\sqrt{2}$ and $5\sqrt{2}$.
Question : Directions: In the following, two questions, given below are the two matrices each containing two classes of letters from the alphabet. The columns and rows of Matrix I are prime numbered and Matrix II are compositely numbered. Letters from these matrices can be represented first by their row number and next by their column number. e.g. P can be written as 48, 66, 84, etc. In the following questions identify one set of number pairs out of (1), (2), (3) and (4) which represented the given word.
APES
Option 1: 46, 48, 49, 44
Option 2: 96, 94, 98, 99
Option 3: 69, 64, 66, 68
Option 4: 84, 86, 89, 88
Correct Answer: 46, 48, 49, 44
Solution : Given: APES
Number representations of each letter – A→46, 68, 89, 94 P→48, 66, 84, 99 E→49, 64, 88, 96 S→44, 69, 86, 98
First option: 46, 48, 49, 44; All the letters of the word APES can be represented through this
Question : Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, whereas pipe C can empty the full tank in 40 hours. All three pipes are opened together, but pipe A is closed after 10 hours. After how many hours will the remaining part of the tank be filled?
Option 1: $12 \frac{1}{2}$
Option 2: $10$
Option 3: $20$
Option 4: $15\frac{1}{2}$
Correct Answer: $12 \frac{1}{2}$
Solution : Pipe A can fill in 1 hour = $\frac{1}{16}$ Pipe B can fill in 1 hour = $\frac{1}{24}$ Pipe C can empty in 1 hour = $\frac{1}{40}$ Together they can fill in 1 hour $=\frac{1}{16} + \frac{1}{24} – \frac{1}{40}=\frac{19}{240}$ Together they can fill in
Question : Directions: Some equations are solved based on a certain system. Find the correct answer for the unsolved equation on that basis. 5 * 6 = 35; 8 * 4 = 28; 6 * 8 = ?
Option 1: 46
Option 2: 34
Option 3: 23
Option 4: 38
Correct Answer: 46
Solution : Given: 5 * 6 = 35; 8 * 4 = 28; 6 * 8 = ?
Like, 5 * 6 = 35→5 + (6 × 5) = 5 + 30 = 35 8 * 4 = 28→8 + (4 × 5) = 8 + 20
Question : Directions: In the following question a word is followed by four other words, one of which can be formed by using the letters of the given word. Find this word. ENCOURAGEMENT
Option 1: GAME
Option 2: TEAR
Option 3: NECK
Option 4: MEAT
Correct Answer: NECK
Solution : Given: ENCOURAGEMENT
Now, let's compare all the option words with the word ENCOURAGEMENT – First option: GAME; All the letters of GAME are present in the word ENCOURAGEMENT. Second option: TEAR; All the letters of TEAR are present in the word ENCOURAGEMENT. Third option: NECK;
Question : The value of $\frac{1}{\sqrt{17+12 \sqrt{2}}}$ is closest to _____.
Option 1: 1.4
Option 2: 1.2
Option 3: 0.14
Option 4: 0.17
Correct Answer: 0.17
Solution : Given expression, $\frac{1}{\sqrt{17+12 \sqrt{2}}}$ $=\frac{1}{\sqrt{{3^2}+(2\sqrt2)^2+2\times3\times2\sqrt2}}$ $=\frac{1}{\sqrt{(3+2\sqrt2)^2}}$ $=\frac{1}{3+2\sqrt2}$ $=\frac{1}{3+2\sqrt2}\times\frac{3-2\sqrt2}{3-2\sqrt2}$ $=\frac{3-2\sqrt2}{3^2-(2\sqrt2)^2}$ [As $a^2-b^2=(a-b)(a+b)$] $=\frac{3-2\sqrt2}{9-8}$ $=3-2\sqrt2$ $=3-2\times1.414$ = 3 – 2.828 = 0.172 Hence, the correct answer is 0.17.
Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series. T, R, O, M, J, H, ?
Option 1: F
Option 2: G
Option 3: D
Option 4: E
Correct Answer: E
Solution : Given: T, R, O, M, J, H, ?
Subtract 2 and 3 alternatively to the place value of each letter, to get the next term – T – 2 = R; R – 3 = O; O – 2 = M; M – 3 =
Question : The first viceroy of India was _______.
Option 1: Lord Canning
Option 2: Lord Hardinge
Option 3: Lord Dalhousie
Option 4: Lord Elgin
Correct Answer: Lord Canning
Solution : The correct option is Lord Canning.
Lord Canning served as India's first Viceroy. Between 1858 and 1862, he was in office for four years. The doctrine of lapse was discarded once Lord Canning was appointed viceroy. In Madras, Calcutta, and Bombay, three universities
Question : Founded in 1886 by a pharmacist named John Pemberton, this product is the second most widely understood term in the world after "OK". What is its name?
Option 1: Aspirin
Option 2: ENO
Option 3: Coca-Cola
Option 4: Pepsi
Correct Answer: Coca-Cola
Solution : The correct answer is Coca-Cola.
The product "Coca-Cola" was invented in 1886 by a chemist called John Pemberton. Coca-Cola is one of the world's most well-known and recognisable brands, known for its carbonated soft drink. Coca-Cola is available in over 200 nations and territories
Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).
If you want to catch the first flight, you may leave now.
(1) must
(2) ought to
(3) could
(4) No improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct choice is the first option.
It suggests that the person has no choice but to leave now, or he will miss the flight. The modal verb "must" is used to express a compulsory action, while the other options denote a sense of
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