Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $a + 5b = 13$ and $ab = 9$, then find the value of $a^2 + 25b^2$.
Option 1: 69
Option 2: 79
Option 3: 49
Option 4: 59
Correct Answer: 79
Solution : Given: $ab = 9$ $a + 5b = 13$ $⇒(a + 5b)^2 = 13^2$ $⇒a^2 + 25b^2 + 10ab = 169$ $⇒a^2 + 25b^2 +10×9 = 169$ $⇒a^2 + 25b^2 = 169-90=79$ Hence, the correct answer is 79.
Question : Directions: In the following question a series is given, with one number missing. Choose the correct alternative from the given ones that will complete the series. 30, 62, 189, 760, (?)
Option 1: 3306
Option 2: 1157
Option 3: 2185
Option 4: 3805
Correct Answer: 3805
Solution : Given: 30, 62, 189, 760, (?)
Multiply and add consecutive numbers to the previous number to get the next number – 30 × 2 + 2 = 60 + 2 = 62 62 × 3 + 3 = 186 + 3 = 189 189 ×
Question : Directions: In the following question, select the one which is different from the other three alternatives.
Option 1: 725
Option 2: 840
Option 3: 632
Option 4: 475
Correct Answer: 632
Solution : Let's check the options – First option: 725; 725 is divisible by 5. Second option: 840; 840 is divisible by 5. Third option: 632; 632 is not divisible by 5. Fourth option: 475; 475 is divisible by 5.
So, the third option is different from
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".
Shakespeare has written (1) / many plays (2) / as well as some poetries. (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.
"Poetries" should be replaced with "poetry" as it is also the plural form.
"Poetry" is a term used to describe a whole set of "poems". This is the correct usage and conveys the intended meaning
Question : If $(a-b)=9$, and $(a^3-b^3)$ = 4401, find the value of $ab$.
Option 1: 190
Option 2: 112
Option 3: 162
Option 4: 136
Correct Answer: 136
Solution : Given: $(a-b)=9$ and $\left(a^3-b^3\right)=4401$ Taking, $(a-b)=9$ Cubing both sides, we get, $⇒a^3-b^3-3ab(a-b)=729$ $⇒4401-3ab(9)=729$ $⇒27ab=4401-729$ $⇒ab=\frac{3672}{27}=136$ Hence, the correct answer is 136.
Question : Directions: Find which word cannot be made from the letters used in the word INCREASINGLY.
Option 1: SINGLE
Option 2: ARISE
Option 3: UGLY
Option 4: CRANE
Correct Answer: UGLY
Solution : Given: INCREASINGLY
Now, let's compare all the option words with the word INCREASINGLY – First option: SINGLE; All the letters of SINGLE are present in the word INCREASINGLY. Second option: ARISE; All the letters of ARISE are present in the word INCREASINGLY. Third option:
Question : Directions: In the following question, some parts of the sentence may have 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 told the teacher (1) / that the homework set for the day (2) / was much too heavy for us to complete. (3) / No Error (4)
Correct Answer: (4)
Solution : There is no error in this sentence.
It may seem that there's an error in the third part of the sentence, but it is correct. ''Much too'' is followed by an adjective (heavy is an adjective), and ''too much'' is followed by a noun.
Question : Find the fourth proportion to 0.24, 0.6, and 20.
Option 1: 50
Option 2: 24
Option 3: 54
Option 4: 48
Correct Answer: 50
Solution : Assuming the fourth proportion is $x$. $0.24:0.6: : 20:x$ ⇒ $\frac{0.24}{0.6}$ = $\frac{20}{x}$ ⇒ $x$ = $\frac{20×0.6}{0.24}$ ⇒ $x$ = 50 Hence, the correct answer is 50.
Question : $2\ \text{cosec}^{2}\: 23°\cot^{2}67°-\sin^{2}23°-\sin^{2}67°-\cot^{2}67°$ is equal to:
Option 1: $1$
Option 2: $\sec^{2}23°$
Option 3: $\tan^{2}23°$
Option 4: $0$
Correct Answer: $\sec^{2}23°$
Solution : $2\ \text{cosec}^{2}\: 23°\cot^{2}67°-\sin^{2}23°-\sin^{2}67°-\cot^{2}67°$ $=2\: \frac{1}{\sin^{2}\: 23°}\tan^{2}23°-\sin^{2}23°-\cos^{2}23°-\tan^{2}23°$ $=2\: \frac{1}{\cos^{2}23°}-(\sin^{2}23°+\cos^{2}23°)-\frac{\sin^{2}23°}{\cos^{2}23°}$ $=2\: \frac{1}{\cos^{2}23°}-1-\frac{\sin^{2}23°}{\cos^{2}23°}$ $=\frac{2-\cos^2 23° - \sin^223°}{\cos^2 23°}$ $=\frac{2-1}{\cos^2 23°}$ $=\sec^2 23°$ Hence, the correct answer is $\sec^2 23°$.
Question : Select the most appropriate ANTONYM of the given word. Pernicious
Option 1: Malicious
Option 2: Wicked
Option 3: Injurious
Option 4: Compassionate
Correct Answer: Compassionate
Solution : The correct antonym is the fourth option: Compassionate.
Explanation for each option:
Malicious - This word is a synonym of "pernicious" and does not provide an appropriate antonym. Both words have a similar meaning of causing harm or being harmful.
Wicked - This word is
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