Staff Selection Commission Sub Inspector Exam
Question : If $\cos A=\frac{1}{2}, 0 \leq A \leq 90^{\circ}$, then what is the value of sin (180 - A)?
Option 1: $\frac{1}{2}$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\frac{1}{\sqrt{3}}$
Option 4: $1$
Correct Answer: $\frac{\sqrt{3}}{2}$
Solution : According to the question sin2A + cos2A = 1 ⇒ sin$^{2} A + \frac{1}{2}^{2}$ = 1 ⇒ sin$^{2} A + \frac{1}{4}$ = 1 ⇒ sin$^{2} A = 1 - \frac{1}{4}$ = $\frac{3}{4}$ ⇒ Sin A = $\frac{\sqrt{3}}{2}$ Now, ⇒ sin(180 −
Question : Select the most appropriate meaning of the given idiom. Spill the beans
Option 1: To make anything visible
Option 2: To reveal secret information
Option 3: To ruin someone’s plan
Option 4: To talk randomly
Correct Answer: To reveal secret information
Solution : The correct choice is the second option.
Explanation: The idiom spill the beans means to disclose a secret or reveal confidential information unintentionally or prematurely. It is often used when someone reveals information that was supposed to be kept confidential or
Question : If $a, b, c$ are all non-zero and $a+b+c=0$, then find the value of $\frac{a^2}{b c}+\frac{b^2}{c a}+\frac{c^2}{ab}$.
Option 1: $3$
Option 2: $4$
Option 3: $1$
Option 4: $\frac{1}{2}$
Correct Answer: $3$
Solution : Given: $a+b+c=0$ According to the question, $a^3+b^3+c^3=3abc$ Dividing both sides by $abc$, we get $\frac{a^3}{abc}+\frac{b^3}{abc}+\frac{c^3}{abc}=\frac{3abc}{abc}$ ⇒ $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}=3$ Hence, the correct answer is 3.
Question : If $\cos A=\frac{15}{17}, 0 \leq A \leq 90^{\circ}$, then the value of $\cot(90° - A)$ is:
Option 1: $\frac{8}{15}$
Option 2: $\frac{2 \sqrt{2}}{15}$
Option 3: $\frac{\sqrt{2}}{15}$
Option 4: $\frac{7}{15}$
Correct Answer: $\frac{8}{15}$
Solution : Given: $\cos A=\frac{15}{17}$ $\sec A=\frac{1}{\cos A}=\frac{17}{15}$ $\cot(90^\circ - A)=\tan A=\sqrt{\sec^2 A-1}$ $=\sqrt{(\frac{17}{15}^2)-1}$ $=\sqrt{\frac{289}{225}-1}$ $=\sqrt{\frac{289-225}{225}}$ $=\sqrt{\frac{64}{225}}$ $=\frac{8}{15}$ Hence, the correct answer is $\frac{8}{15}$.
Question : A and B together can complete a piece of work in 18 days, B and C in 24 days, and A and C in 36 days. In how many days, will all of them together complete the work?
Option 1: 16 days
Option 2: 15 days
Option 3: 12 days
Option 4: 10 days
Correct Answer: 16 days
Solution : 1 day work of A and B = $\frac{1}{18}$ ---------(1) 1 day work of B and C = $\frac{1}{24}$ ---------(2) 1 day work of A and C = $\frac{1}{36}$ ---------(3) Adding equations (1), (2) and (3), we get: ⇒ 2 × (A + B
Question : Directions: In each of the following, questions, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices, given below. The columns and rows of Matrix (I) are numbered from 0 to 4 and that of Matrix (II) are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g. M can be represented by 01, 23, etc, and E can be represented by 58, 88 etc. Similarly, you have to identify the set for the word given in each question. LANE
Option 1: 11, 66, 33, 96
Option 2: 11, 67, 32, 97
Option 3: 31, 87, 32, 97
Option 4: 31, 66, 33, 97
Correct Answer: 31, 87, 32, 97
Solution : Given: LANE
Number representations of each letter – L→11, 31 A→66, 87, 99 N→32 E→58, 79, 88, 97
First option: 11, 66, 33, 96; N and E cannot be represented as 33 and 96 respectively. Second option: 11, 67, 32, 97; A
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at line MN as shown.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection. Here, according to the information provided, the mirror is placed on the right side of the figure (on Line MN). So, the left side of the reflected image will appear
Question : Directions: A graph showing the price of rice in India during the years 2000 to 2003 is given below. Study the graph carefully and answer the questions.
The maximum difference in price between any two years was in the month of:
Option 1: January
Option 2: November
Option 3: March
Option 4: December
Correct Answer: December
Solution : From the given table in question, Difference = 23 – 5 = 18 So, the maximum difference in price between any two years was in the month of December. Hence, the answer is December.
Question : If a car covers 75.5 km in 3.5 litres of petrol, how much distance (in km) will it cover in 28 litres of petrol?
Option 1: 603
Option 2: 602
Option 3: 604
Option 4: 600
Correct Answer: 604
Solution : Here, 3.5 litres of petrol covers 75.5 km. $\therefore$ 1litre of petrol covers = $\frac{75.5}{3.5}$ km So, 28 litres of petrol = $\frac{75.5}{3.5} \times 28$ = 604 Hence, the correct answer is 604 km.
Question : The seven years of war in the 18th century was fought between Britain and ________.
Option 1: Spain
Option 2: France
Option 3: Germany
Option 4: Portugal
Correct Answer: France
Solution : The correct answer is France.
The Seven Years' War, initiated in 1756, primarily centred around North American land disputes between France and Great Britain, particularly near Pittsburgh, Pennsylvania. This conflict, also known as the French and Indian War, expanded globally, involving Europe, Africa and
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