Staff Selection Commission Sub Inspector Exam
Question : The value of $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}-\sec 35^{\circ} \cdot \sin 55^{\circ}}{\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}}$ is equal to:
Option 1: $\frac{1}{8}$
Option 2: $-\frac{1}{4}$
Option 3: $\frac{1}{4}$
Option 4: $-\frac{1}{8}$
Correct Answer: $-\frac{1}{8}$
Solution : Given: $\frac{\sin ^2 30^{\circ}+\cos ^2 60^{\circ}-\sec 35^{\circ} \cdot \sin 55^{\circ}}{\sec 60^{\circ}+\operatorname{cosec} 30^{\circ}}$ = $\frac{(\frac{1}{2})^2+(\frac{1}{2})^2 - \sec 35^{\circ} \cdot \sin (90-35)^{\circ}}{2+2}$ = $\frac{(\frac{1}{4})+(\frac{1}{4}) - \sec 35^{\circ} \cdot \cos 35^{\circ}}{2+2}$ = $\frac{(\frac{2}{4}) - (\frac{1}{ \cos 35^{\circ}}) \cdot \cos 35^{\circ}}{4}$ = $\frac{(\frac{2}{4}) - 1}{4}$ = $-\frac{1}{8}$ Hence, the
Question : Directions: If 1 / 4 / 3 = 254 and 3 / 6 / 8 = 479, then 5 / 2 / 7 = ?
Option 1: 416
Option 2: 461
Option 3: 368
Option 4: 638
Correct Answer: 638
Solution : Given: 1 / 4 / 3 = 254; 3 / 6 / 8 = 479
1 / 4 / 3→1 + 1 = 2; 4 + 1 = 5; 3 + 1 = 4→254 3 / 6 / 8→3 + 1 = 4; 6 +
Question : Directions: If + means ×, × means –, – means ÷ and ÷ means +, then what will come in place of the (?) in the following equation? 250 – 10 + 10 × 5 ÷ 2 = ?
Option 1: 247
Option 2: 167
Option 3: 320
Option 4: 234
Correct Answer: 247
Solution : Given: 250 – 10 + 10 × 5 ÷ 2 = ?
After interchanging the given mathematical signs, we get – ⇒ 250 ÷ 10 × 10 – 5 + 2 ⇒ 25 × 10 – 5 + 2 ⇒ 250 – 5 + 2
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 =
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