Staff Selection Commission Combined Higher Secondary Level Exam
Question : How many solid spheres are made if a metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each?
Option 1: 105
Option 2: 101
Option 3: 108
Option 4: 103
Correct Answer: 108
Solution : Given: A metallic cone of radius 12 cm and height 24 cm is melted into spheres of radius 2 cm each We know, The volume of a cone = $\ \frac {1}{3}\pi r^2h$, where $r$ and $h$ are the radius and height of the cone
Question : 51% of a whole number is 714. What is 25% of that number?
Option 1: 350
Option 2: 450
Option 3: 550
Option 4: 250
Correct Answer: 350
Solution : Let the number be $x$. According to the question, $x × \frac{51}{100} = 714$ ⇒ $x = 1400$ Now, 25% of that number is $1400 × \frac{25}{100} = 350$ Hence, the correct answer is 350.
Question : The six-digit number $\mathrm{N = 4a6b9c}$ is divisible by $99$, then the maximum sum of the digits of $\mathrm{N}$ is:
Option 1: 18
Option 2: 36
Option 3: 45
Option 4: 27
Correct Answer: 27
Solution : We have, the six-digit number $\mathrm{N = 4a6b9c}$ is divisible by $99$. Divisibility rule for $9$, A number is divisible by $9$ if the sum of digits is divisible by $9$. As $\mathrm{N = 4a6b9c}$ is divisible by $9$. The sum of the digits $=\mathrm{(4+a+6+b+9+c)}$
Question : Choose the option that is the correct passive form of the sentence.
Daniel and Mary invited us to their wedding.
Option 1: We have been invited to Daniel and Mary's wedding.
Option 2: We were invited to Daniel and Mary's wedding.
Option 3: We are invited to Daniel and Mary's wedding.
Option 4: We had been invited to Daniel and Mary's wedding.
Correct Answer: We were invited to Daniel and Mary's wedding.
Solution : The correct choice is the second option.
Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in
Question : A is three times as good a worker as B and therefore, able to finish a piece of work in 60 days less than B. The time (in days) in which they can do it working together is:
Option 1: 22 days
Option 2: $22\frac{1}{2}$ days
Option 3: 23 days
Option 4: $23\frac{1}{4}$ days
Correct Answer: $22\frac{1}{2}$ days
Solution : Given: A : B = 3 : 1 A takes = $x$ days and B takes = $x$ + 60 days If the difference of time is 2 days, B takes 3 days. If the difference in time is 60 days, B takes =
Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No Error".
In India, (1) / there are (2) / many poors. (3) / No Error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (3)
Solution : The error lies in the third part of the sentence.
"Poors" is not grammatically correct, it should be replaced with "poor people". Here, it refers to a group of people who have little or no money. So, the correct sentence is, "In India, there are
Question : Directions: Select the triad in which the numbers are related in the same way as the numbers of the following triads. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. – operations on 13 such as adding/subtracting/multiplying etc. 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 15–14–13 17–21–25
Option 1: 19–22–25
Option 2: 34–12–28
Option 3: 38–28–10
Option 4: 23–42–46
Correct Answer: 19–22–25
Solution : Given: (15–14–13); (17–21–25)
Divide the sum of the first and the third numbers by 2 to obtain the second number. (15–14–13)→15 + 13 = 28; 28 ÷ 2 = 14 (17–21–25)→17 + 25 = 42; 42 ÷ 2 = 21
Let's check each option –
Question : If $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$, then the positive value of $\cot \theta+\cos \theta$ is:
Option 1: $\frac{3 \sqrt{3}}{2}$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\frac{2}{3 \sqrt{3}}$
Option 4: $\frac{2}{\sqrt{3}}$
Correct Answer: $\frac{3 \sqrt{3}}{2}$
Solution : Given: $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$...................(equation 1) We know that $\sec^2\theta-\tan^2\theta=1$ $⇒(\sec\theta-\tan\theta)(\sec\theta+\tan\theta)=1$ Putting the value, we get $⇒(\sec\theta-\tan\theta)(\frac{1}{\sqrt3})=1$ $⇒(\sec\theta-\tan\theta)=\sqrt3$............(equation 2) From equations 1 and 2, we get: $⇒2\sec\theta=\sqrt3+\frac{1}{\sqrt3}$ $⇒2\sec\theta=\frac{4}{\sqrt3}$ $⇒\sec\theta=\frac{2}{\sqrt3}$ We know that, $\sec\theta=\frac{h}{b}=\frac{2}{\sqrt3}$ So, $p=\sqrt{ h^2-b^2}$ $⇒p=\sqrt{2^2-\sqrt3^2}=1$ $\therefore \cot\theta+\cos\theta=\frac{b}{p}+\frac{b}{h}=\frac{\sqrt3}{1}+\frac{\sqrt3}{2}=\frac{3\sqrt3}{2}$ Hence, the correct answer is $\frac{3\sqrt3}{2}$.
Question : Simplify the given expression $\frac{4\left[(17)^3-(7)^3\right]}{(17)^2+(7)^2+119}$
Option 1: 40
Option 2: 50
Option 3: 60
Option 4: 30
Correct Answer: 40
Solution : Given, $\frac{4\left[(17)^3-(7)^3\right]}{(17)^2+(7)^2+119}$ = $\frac{4(17-7)((17)^2+(7)^2+(17)(7))}{(17)^2+(7)^2+(17)(7)}$ = $4×10$ = $40$ Hence, the correct answer is 40.
Question : Comprehension: In the following passage, some of the words have been deleted. Read the passage carefully and select the correct answer for the given blank out of the four alternatives.
Fresh pineapple, chilled watermelon, and an icy cold soft drink on a hot summer's day. What do these things have in (1)_____? They all taste so good because of the sweetness the sugar in them provides. When you think of sugar, you probably picture the white (2)_____ you put in cookies, that your parents put in their coffee, or that you (3)_____ on your cereal. Actually, this is just one kind of sugar, called sucrose, which is (4)______ from sugar cane or sugar beets. Technically, sugar is a carbohydrate that occurs (5)_____ in every fruit and vegetable.
Select the most appropriate option to fill in the blank number (3).
Option 1: raise
Option 2: sprinkle
Option 3: send
Option 4: place
Correct Answer: sprinkle
Solution : The correct answer is the second option.
The word sprinkle means to scatter or distribute something in small drops or particles over a surface. It involves adding sugar in such a way that it is evenly distributed or dispersed across the cereal, enhancing its sweetness.
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