Staff Selection Commission Combined Higher Secondary Level Exam
Question : Two equal circles of radius 6 cm intersect each other such that each passes through the centre of the other. The length (in cm) of the common chord is:
Option 1: $5 \sqrt{3}$
Option 2: $6 \sqrt{3}$
Option 3: $4 \sqrt{3}$
Option 4: $3 \sqrt{3}$
Correct Answer: $6 \sqrt{3}$
Solution : Let the common chord AB bisect the distance between the centre XY at O. ⇒ XO = $\frac{\text{XY}}{2}$ = $\frac{6}{2}$ = 3 cm ⇒ AX = radius = 6 (The circles pass through each other’s centre) Now, in $\triangle XAO$ right angled at O
Question : The distance of a chord JK from the centre is 7 cm. If the diameter of this circle is 50 cm, then what will be the length of this chord?
Option 1: 74 cm
Option 2: 96 cm
Option 3: 48 cm
Option 4: 24 cm
Correct Answer: 48 cm
Solution : The radius of the circle is half the diameter. The radius = $\frac{50}{2}$ = 25 cm Let the length of the chord JK = $2x$ cm The distance from the centre of the circle to the chord = 7 cm The perpendicular from the
Question :
Directions: In the following question, select the related word from the given alternatives. Dominance : Hegemony :: Independence : ?
Option 1: Sympathy
Option 2: Melancholy
Option 3: Autonomy
Option 4: Recompense
Correct Answer: Autonomy
Solution : Given: Dominance : Hegemony :: Independence : ?
Like, Hegemony is the synonym of dominance and the meaning of dominance is control or authority. Similarly, the meaning of independence is the state of being free and the synonym of independence is autonomy.
Hence, the third
Question : Comprehension:
In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each number.
Today, I want to talk to you about a very simple matter, that is, simple conversations. When we learn to speak, (1) ___ come words, then phrases, and then scripts. You would agree that the larger the bundles of words we (2) ___, the less we have to worry about combining them into sensible (3) ____. Also, the less we have to fret over syntax or (4) ___. Do you think you choose the words? Do you pre-rehearse every time you go out? (5) ____ what happens when you walk into a fast-food restaurant. My dear, how do you react in those real-life situations?
Question:
Select the most appropriate option to fill in the blank no. 3.
Option 1: executions
Option 2: traits
Option 3: expressions
Option 4: criticism
Correct Answer: expressions
Solution : The correct choice is the third option.
Expressions denote the conveyance of thoughts, feelings, or ideas through words, actions, or artistic means. It can be a verbal or non-verbal indication of emotions, opinions, or creativity.
The meanings of the other options are as follows:
Question : One litre of milk costs INR 40. Water is mixed with milk and the mixture cost becomes INR 30 per litre. Find the ratio of water and milk in the mixture.
Option 1: 2 : 5
Option 2: 1 : 3
Option 3: 1 : 2
Option 4: 2 : 3
Correct Answer: 1 : 3
Solution : Given: That one litre of milk costs INR 40. Water is mixed with milk and the mixture cost becomes INR 30 per litre. The ratio of water and milk in the mixture = 10 : 30 = 1 : 3 Hence, the correct
Question : The ratio of the angles of a triangle is 1 : 2 : 6. What is the smallest angle?
Option 1: $40^\circ$
Option 2: $45^\circ$
Option 3: $30^\circ$
Option 4: $20^\circ$
Correct Answer: $20^\circ$
Solution : Ratio of the angles of triangle = 1 : 2 : 6 Let the angles be $x, 2x$ and $6x$ and $x$ be the smallest angle. $x+2x+6x=180^\circ$ ⇒ $9x=180^\circ$ ⇒ $x = 20^\circ$ Hence, the correct answer is $20^\circ$.
Question : The line chart given below shows the production of refrigerators by 6 companies.
What is the difference between the production of refrigerators by companies E, F, and G together and the production of refrigerators by companies H, I, and J together?
Option 1: 80
Option 2: 160
Option 3: 120
Option 4: 190
Correct Answer: 120
Solution : Production of Refrigerator by company E = 500 Production of Refrigerator by company F = 470 Production of Refrigerator by company G = 460 Production of Refrigerator by company H = 440 Production of Refrigerator by the company I = 420 Production of Refrigerator by
Question : Talat Aziz is primarily a _____ singer.
Option 1: Hindustani classical
Option 2: Carnatic classical
Option 3: ghazal
Option 4: folk
Correct Answer: ghazal
Solution : The correct answer is ghazal.
Talat Aziz is primarily known as a Ghazal singer. Ghazal is a poetic and musical form of expression, often associated with themes of love, longing, and the nuances of the human heart. Talat Aziz has carved a niche for
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).
A greedy man always hankers after money.
(1) wanted
(2) greeds after
(3) runs after
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (4)
Solution : The fourth option is the correct choice.
The word "hankers" means to have a strong affection toward something and this is the best fit to the sentence.
Question : The average of 16 numbers is 35. It was found later that four numbers 18, 17, 24, and 35 were taken by mistake. What is the new average after removing these numbers?
Option 1: 38.83
Option 2: 42.33
Option 3: 46.66
Option 4: 33.33
Correct Answer: 38.83
Solution : Given that the average of 16 numbers is 35, we can calculate the sum of those 16 numbers as follows: Sum = Average × Count ⇒ Sum = 35 × 16 = 560 So, Adjusted Sum = Sum – Sum of Mistaken Numbers ⇒ Adjusted
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