Staff Selection Commission Combined Higher Secondary Level Exam
Question : Direction: The following pie chart shows the percentage distribution of the expenditure incurred in publishing a book. Read the pie chart and answer the question.
The central angle of the sector corresponding to the expenditure incurred on royalty is?
Option 1: 15°
Option 2: 48°
Option 3: 54°
Option 4: 24°
Correct Answer: 54°
Solution : The total value of the pie chart is 360°. So, the angle of expenditure on royalty $=\frac{15}{100}×360°=54°$ Hence, the correct answer is 54°.
Question : The perpendicular drawn from the vertices, to the opposite sides of a triangle, meet at the point whose name is:
Option 1: incentre
Option 2: circumcentre
Option 3: centroid
Option 4: orthocentre
Correct Answer: orthocentre
Solution : AD is perpendicular to BC. BE is perpendicular to AC. CF is perpendicular to AB. They meet at a point called the orthocentre. Hence, the correct answer is 'orthocentre'.
Question : Directions: In the following question, find the odd number from the given alternatives.
Option 1: 8
Option 2: 64
Option 3: 125
Option 4: 343
Correct Answer: 64
Solution : Let's check the options – First option: 8; 8 = 23 (2 is a prime number.) Second option: 64; 64 = 43 (4 is not a prime number.) Third option: 125; 125 = 53 (5 is a prime number.) Fourth option: 343;
Question : In $\triangle ABC$, the internal bisectors of $\angle B$ and $\angle C$ meet at point $O$. If $\angle A = 80^\circ$, then $\angle BOC$ is equal to:
Option 1: $100^\circ$
Option 2: $120^\circ$
Option 3: $130^\circ$
Option 4: $140^\circ$
Correct Answer: $130^\circ$
Solution : Given: $\angle A = 80^\circ$ To find: $\angle BOC$ We know that, Angle formed by internal bisectors of base angles = $90^\circ+\frac{1}{2}\angle A$ ⇒ $\angle BOC$ = $90^\circ+\frac{1}{2}\angle A$ = $90^\circ+\frac{1}{2}×80^\circ$ = $90^\circ+40^\circ$ = $130^\circ$ Hence, the correct answer is $130^\circ$.
Question : Sudesh is the owner of a multipurpose shop. For a specific month, his profits are detailed below.
To estimate the expected profit for the next month, he assigns the weights of 6, 5, and 8 to the different categories in the same order. What will be the weighted average of his profits?
Option 1: INR 25,265.18 (nearly)
Option 2: INR 24,863.16 (nearly)
Option 3: INR 25,163.16 (nearly)
Option 4: INR 25,263.16 (nearly)
Correct Answer: INR 25,263.16 (nearly)
Solution : By using the table: Total weights = 6 + 5 + 8 = 19 Profit earned on groceries in weight = 6 × 50000 = 300000 Profit earned on cosmetics in weight = 5 × 20000 = 100000 Profit earned on ladies' dresses
Question : Select the most appropriate option that can be used as a one-word substitute for the underlined segment in the following sentence. As I walked through the old town, I couldn’t help but feel a sentimental longing for the simpler times of my childhood.
Option 1: affection
Option 2: homesickness
Option 3: inertia
Option 4: nostalgia
Correct Answer: nostalgia
Solution : The fourth option is the correct answer.
Nostalgia is the term that represents the sentimental longing for the past, especially for a period or place with happy memories. It perfectly captures the feeling described in the sentence.
The meanings of other options are as follows:
Question : Which state appointed Robin Uthappa as brand ambassador for the Brain Health Initiative in 2022?
Option 1: Tamil Nadu
Option 2: West Bengal
Option 3: Odisha
Option 4: Karnataka
Correct Answer: Karnataka
Solution : The correct option is Karnataka
The Karnataka Brain Health Initiative (Ka-BHI) was introduced in January by the Karnataka State Government in collaboration with NIMHANS and Niti Ayog. The Karnataka-Brain Health Initiative has named Indian cricketer Robin Uthappa as its brand ambassador (Ka-BHI).
Question : Who among the following Indian music composers won the Oscar Award in the year 2023?
Option 1: Mani Sharma
Option 2: A. R. Rahman
Option 3: Devi Sri Prasad
Option 4: M. M. Keeravani
Correct Answer: M. M. Keeravani
Solution : The correct option is M. M. Keeravani.
M. M. Keeravani is an Indian music composer who won the Best Original Song Award at the 95th Academy Awards in 2023, along with lyricist-singer Chandrabose, for the song "Naatu Naatu" from the movie RRR.
Question : Find the length of the arc if the angle at the centre of the circle of radius 7 units is 60°.
Option 1: $4$ units
Option 2: $\frac{11}{4}$ units
Option 3: $\frac{22}{3}$ units
Option 4: $21$ units
Correct Answer: $\frac{22}{3}$ units
Solution : Given: The radius of the circle: 7 units The angle at the centre is 60°. Length of arc = $\frac{θ}{360°} × 2πr$, here $r$ is the radius and $\theta$ is the angle at centre. ⇒ Length of the arc = $\frac{60°}{360°} × 2 ×
Question : If $\frac{xy}{x+y}=a$, $\frac{xz}{x+z}=b$ and $\frac{yz}{y+z}=c$, where $a,b,c$ are all non-zero numbers, $x$ equals to:
Option 1: $\frac{2abc}{ab+bc–ac}$
Option 2: $\frac{2abc}{ab+ac–bc}$
Option 3: $\frac{2abc}{ac+bc–ab}$
Option 4: $\frac{2abc}{ab+bc+ac}$
Correct Answer: $\frac{2abc}{ac+bc–ab}$
Solution : Given: $\frac{xy}{x+y}=a$, $\frac{xz}{x+z}=b$ and $\frac{yz}{y+z}=c$, where $a,b,c$ are all non-zero numbers. We can write $\frac{xy}{x+y}=\frac{1}{\frac{1}{x}+\frac{1}{y}}$ ⇒ $\frac{1}{a}=\frac{1}{x}+\frac{1}{y}$ -------------------------------(1) Similarly, we can write, $\frac{xz}{x+z}=\frac{1}{\frac{1}{x}+\frac{1}{z}}$ ⇒ $\frac{1}{b}=\frac{1}{x}+\frac{1}{z}$ --------------------------------(2) Similarly, $\frac{1}{c}=\frac{1}{y}+\frac{1}{z}$ ----------------------(3) Adding equation (1) and equation (2), ⇒ $\frac{1}{a}+\frac{1}{b}=\frac{2}{x}+\frac{1}{y}+\frac{1}{z}$ ⇒ $\frac{1}{a}+\frac{1}{b}=\frac{2}{x}+\frac{1}{c}$ ⇒ $\frac{1}{a}+\frac{1}{b}–\frac{1}{c}=\frac{2}{x}$ ⇒ $\frac{(bc+ac–ab)}{abc}=\frac{2}{x}$ $\therefore x=\frac{2abc}{(bc+ac–ab)}$
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