Staff Selection Commission Combined Higher Secondary Level Exam
Question : If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm2. The radius of the sphere initially was: (use $\pi =\frac{22}{7}$)
Option 1: 4 cm
Option 2: 5 cm
Option 3: 3 cm
Option 4: 6 cm
Correct Answer: 6 cm
Solution : Let the initial radius be $r$ Area before increment $= 4\pi r^2$ Given: After increasing the radius by 2 cm, the area is increased by = 352 cm$^2$ According to the question, $4\pi r^2 + 352 = 4\pi (r+2)^2$ ⇒ $4\pi r^2 + 352
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".
I met the gentleman (1) / today morning on my way (2) / to the market. (3) / No error (4)
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The error lies in the first part of the sentence.
The article "the" should replace "a" to make the sentence grammatically accurate, as the person is not specified.
Therefore, the correct sentence is: "I met a gentleman today morning on my way to the market."
Question : Directions: How many are both buttons and bottles?
Option 1: 3
Option 2: 7
Option 3: 5
Option 4: 2
Correct Answer: 7
Solution : In the diagram, the shaded part represents the region of both buttons and bottles.
Therefore, the number is→5 + 2 = 7
So, from the above, 7 are both buttons and bottles. Hence, the second option is correct.
Question : Select the most appropriate synonym of the given word. Tranquil
Option 1: Anxious
Option 2: Dilemma
Option 3: Fierce
Option 4: Peaceful
Correct Answer: Peaceful
Solution : The most appropriate synonym for the word "tranquil" is the fourth option.
"Tranquil" means calm, serene, and free from disturbance. "Peaceful" conveys a similar meaning, as it also suggests a lack of disturbance, noise, or agitation.
The meanings of the other options are as follows:
Question : Manoj sold an article at a marked price of Rs. 13,000. Had he offered a discount of 10% on the marked price he would have earned a profit of 30%. What is the cost price?
Option 1: Rs. 10,000
Option 2: Rs. 9,900
Option 3: Rs. 9,000
Option 4: Rs. 11,000
Correct Answer: Rs. 9,000
Solution : Given: Marked price = Rs. 13,000 Discount = 10% Selling price = Marked price – Discount = $13000-\frac{10}{100}\times13000$ = $13000-1300$ = $11700$ Profit = 30% Cost price = $\frac{100}{100+\text{Profit}\%}$ × Selling price = $\frac{100}{130}$ × 11700 = 9000 Hence, the correct answer is Rs.
Question : If $a^{2}+b^{2}+c^{2}-ab-bc-ca=0$, then $a:b:c$ is:
Option 1: $1:1:2$
Option 2: $1:1:1$
Option 3: $1:2:1$
Option 4: $2:1:1$
Correct Answer: $1:1:1$
Solution : Given: $a^{2}+b^{2}+c^{2}-ab-bc-ca=0$ $a^{2}+b^{2}+c^{2}-ab-bc-ca=\frac{1}{2}[(a-b)^2 + (b-c)^2+(c-a)^2] =0$ So, $a=b=c$ So, $a:b:c=1:1:1$ Hence, the correct answer is $1:1:1$.
Question : Direction: In a certain code, if AUDITORIUM is written as MUIROTIDUA, how will MISFORTUNE be written in that code?
Option 1: ENUTROFSIM
Option 2: ENUTROMISF
Option 3: TUNEROFSIM
Option 4: TUNEMISFOR
Correct Answer: ENUTROFSIM
Solution : Given:
AUDITORIUM is written as MUIROTIDUA
Here, the order of each letter is reversed to get the corresponding codes.
Similarly, MISFORTUNE will be coded as ENUTROFSIM.
Hence, the first option is correct.
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).
The mother with her children were expected.
(1) Was
(2) Will
(3) Have
(4) No Improvement
Solution : The sentence can be improved using the first option.
As per the subject-verb agreement rules, when two nouns are connected by with, the verb must agree with the first subject. Hence, were should be replaced with was as the correct helping verb.
Therefore, the
Question : Directions: Which conclusion is true for the given statements? Statements: (i) Roy studies History and Political Science. (ii) Roy studies at Oxford University. Conclusions: 1. Roy does not study History. 2. Roy does not study Political Science. 3. Roy studies History and Political Science at Oxford University. 4. Roy studies Social Science.
Option 1: Only 1 is correct
Option 2: Only 3 is correct
Option 3: Both 1 and 2 are correct
Option 4: Both 3 and 4 are correct
Correct Answer: Only 3 is correct
Solution : Let's analyse the given conclusions – Conclusion 1: Roy does not study History – According to the given statements, Roy studies History and Political Science. Thus, this conclusion does not follow. Conclusion 2: Roy does not study Political Science – According to
Question : The table given below shows the production of refrigerators by 6 companies.
What is the average production of refrigerators by all six companies?
Option 1: 132.44
Option 2: 113.33
Option 3: 93.33
Option 4: 156.44
Correct Answer: 113.33
Solution : Total production = 200 + 140 + 120 + 80 + 40 + 100 = 680 Total companies = 6 Average $=\frac{\text{Total production}}{\text{Total number of companies}} = \frac{680}{6}= 113.33$ Hence, the correct answer is 113.33.
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