Staff Selection Commission Sub Inspector Exam
Question : If $0\leq \theta\leq \frac{\pi}{2}$ and $\sec^{2}\theta+\tan^{2}\theta=7$, then $\theta$ is:
Option 1: $\frac{5\pi}{12}$
Option 2: $\frac{\pi}{3}$
Option 3: $\frac{\pi}{5}$
Option 4: $\frac{\pi}{6}$
Correct Answer: $\frac{\pi}{3}$
Solution : Given: $\sec^{2}\theta+\tan^{2}\theta=7$ -------------(1) We know that $\sec^{2}\theta-\tan^{2}\theta=1$ ------------(2) Adding equations (1) and (2), we have, ⇒ $2\sec^{2}\theta=8$ ⇒ $\sec^{2}\theta=4$ ⇒ $\sec\theta=2$ ⇒ $\sec\theta=\sec60°$ ⇒ $\theta=60°=\frac{\pi}{3}$ Hence, the correct answer is $\frac{\pi}{3}$.
Question : Which of the following options best describes the meaning of Nritta in the Kuchipudi dance form?
Option 1: Abstract Narrative Dancing
Option 2: Non-Narrative and Abstract Dancing
Option 3: Interpretative Dancing
Option 4: Narrative Dancing
Correct Answer: Non-Narrative and Abstract Dancing
Solution : The correct option is Non-Narrative and Abstract Dancing.
Nritta in the Kuchipudi dance form refers to the pure, abstract, and rhythmic elements of dance. It involves intricate footwork, body movements, and hand gestures performed in a structured and rhythmic manner. Nritta does
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the given sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 - operations on 13 such as adding/subtracting/multiplying, etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (3, 11, 92) (4, 8, 264)
Option 1: (2, 32, 50)
Option 2: (7, 13, 2401)
Option 3: (5, 35, 660)
Option 4: (6, 12, 676)
Correct Answer: (5, 35, 660)
Solution : Given: (3, 11, 92); (4, 8, 264)
The pattern is as follows – (3, 11, 92)→(3)4 + 11 = 81 + 11 = 92 (4, 8, 264)→(4)4 + 8 = 256 + 8 = 264
Let's check the options – First
Question : Directions: Select the option that represents the letters that when sequentially placed from left to right in the blanks will complete the letter series. _st_ _lbz_tmm_ _zs_ _mlb
Option 1: zmlslbmt
Option 2: zmmslbtm
Option 3: zmmsbltm
Option 4: zmmslbmt
Correct Answer: zmmslbtm
Solution : Given: _st_ _lbz_tmm_ _zs_ _mlb
To fill the series, we have to divide the series – _st_ _lb / z_tmm_ _ / zs_ _mlb Let's check each option – First option: zmlslbmt; zstmllb / zstmmlb / zsmtmlb
Question : AB is a common tangent to both the circles in the given figure. Find the distance (correct to two decimal places) between the centres of the two circles.
Option 1: 18.98 units
Option 2: 23.58 units
Option 3: 26.59 units
Option 4: 21.62 units
Correct Answer: 23.58 units
Solution : Given, The radius of the smaller circle = 5 units Let the radius of the larger circle be $x$ units. Common tangent(AB) to both circles of length = 20 units We know that two triangles are said to be similar if they have the
Question : Satish bought 35 notebooks for Rs. 700 and sold 28 of them for Rs. 600. Find his gain percentage.
Option 1: $7 \frac{1}{7} \%$
Option 2: $9 \frac{1}{7} \%$
Option 3: $6 \frac{1}{7} \%$
Option 4: $8 \frac{1}{7} \%$
Correct Answer: $7 \frac{1}{7} \%$
Solution : First, the cost price (CP) per notebook = $\frac{700}{35}$ = Rs. 20 Then, the selling price (SP) per notebook = $\frac{600}{28}$ = Rs. 21.43 The gain is the difference between the SP and CP = 21.43 – 20 = Rs. 1.43 per notebook
Question : If a change in all input leads to a proportionate change in output, it is a case of:
Option 1: constant returns to the scale
Option 2: diminishing returns to the scale
Option 3: increasing returns to the scale
Option 4: variable returns to the scale
Correct Answer: constant returns to the scale
Solution : The correct option is constant returns to the scale.
Returns to scale describe the long-term relationship between a rise in output and the corresponding increases in inputs. When adding more inputs causes an equivalent rise in output, it is called
Question : Which of the following Indian players scored maximum goals in hockey at the Tokyo Olympics – 2020?
Option 1: Rupinder Pal Singh
Option 2: Gurjant Singh
Option 3: Simranjeet Singh
Option 4: Harmanpreet Singh
Correct Answer: Harmanpreet Singh
Solution : The correct answer is Harmanpreet Singh.
In hockey, Harmanpreet Singh scored the most goals in the 2020 Tokyo Olympics. Indian hockey player Harmanpreet Singh captains the team in addition to playing defence for the national team. He competed for India in hockey and
Question : Direction: The following pie chart shows the expenditure of five companies P, Q, R, S and T in the year 2016. Total expenditure = 48 crores
What is the total expenditure (in crores) of company Q, R, and T together?
Option 1: 19.2
Option 2: 28.8
Option 3: 24.3
Option 4: 31.4
Correct Answer: 28.8
Solution : Total expenditure = 48 crores Expenditure of the companies Q, R, and T together = (22 + 18 + 20)% of total expenditure Expenditure of the companies Q, R, and T together = 60% of 48 = 28.8 crores Hence, the correct answer is 28.8.
Question : Select the most appropriate idiom or phrase to complete the given sentence. I like her because she never likes to make _________.
Option 1: a slap on the wrist
Option 2: a drop in the bucket
Option 3: a bed of roses
Option 4: a quick buck
Correct Answer: a quick buck
Solution : The fourth option is correct.
A quick buck: This idiom means to make money quickly and easily, often implying a short-term or opportunistic approach to earning money without considering long-term consequences or ethics.
Therefore, the complete sentence would be: I like her because
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