Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $x^2+y^2=427$ and $xy=202$, then find the value of $\frac{x+y}{x-y}$.
Option 1: $\sqrt{\frac{835}{23}}$
Option 2: $\sqrt{\frac{830}{29}}$
Option 3: $\sqrt{\frac{831}{23}}$
Option 4: $\sqrt{\frac{830}{23}}$
Correct Answer: $\sqrt{\frac{831}{23}}$
Solution : Given: $x^2+y^2=427$ and $xy=202$. Now, $(x+y)^2=x^2+y^2+2xy$ ⇒ $(x+y)^2=427+2×202$ ⇒ $(x+y)=\sqrt{831}$ ---------------------------------------(1) Also, $(x-y)^2=x^2+y^2-2xy$ ⇒ $(x-y)^2=427-2×202$ ⇒ $(x-y)= \sqrt{23}$ ------------------------------------(2) So, $\frac{x+y}{x-y}$ $= \frac{\sqrt{831}}{\sqrt{23}}$ $= \sqrt{\frac{831}{23}}$. Hence, the correct answer is $\sqrt{\frac{831}{23}}$.
Question : Directions: What will come in the place of '?' in the following equation, if '+' and '–' are interchanged with '÷' and '×', respectively? 88 + 8 – 17 × 16 ÷ 40 = ?
Option 1: 203
Option 2: 197
Option 3: 200
Option 4: 211
Correct Answer: 211
Solution : Given: 88 + 8 – 17 × 16 ÷ 40 = ?
After interchanging the signs as per instructions, the new equation will be –
= 88 ÷ 8 × 17 – 16 + 40 = 11 × 17 – 16 + 40 = 187
Question : Directions: If A stands for ÷, B stands for ×, C stands for +, and D stands for –, what will come in place of the question mark (?) in the following equation? 3 B 26 C 15 D 36 A 3 = ?
Option 1: 82
Option 2: 80
Option 3: 81
Option 4: 83
Correct Answer: 81
Solution : Given: A stands for ÷, B stands for ×, C stands for +, and D stands for – 3 B 26 C 15 D 36 A 3 = ?
After interchanging the alphabet into the signs the equation becomes – = 3 × 26 +
Question : Select the most appropriate option that expresses the given sentence in active voice. The letter was written by the author and mailed to the publisher.
Option 1: The letter was written and mailed to the publisher by the author.
Option 2: The author wrote the letter and mailed it to the publisher.
Option 3: The publisher received the letter written by the author.
Option 4: The letter was being written by the author and mailed to the publisher.
Correct Answer: The author wrote the letter and mailed it to the publisher.
Solution : The correct choice is the second option.
Active voice is a sentence construction where the subject performs the action stated by the verb. In an active voice sentence, the subject is the doer of the
Question : The simple interest on a sum of money in 6 years at the rate of 15% per annum is INR 1,440 less than the simple interest accrued on the same sum in 9 years at 18% per annum. What is the sum of money (in INR)?
Option 1: 1800
Option 2: 2000
Option 3: 2700
Option 4: 2400
Correct Answer: 2000
Solution : Let the principal be $P$. Simple interest1st $=\frac{\text{Principal × Rate × Time}}{100}$$=\frac{P\times 15\times 6}{100}=\frac{90P}{100}$ And, Simple interest2nd $=\frac{P\times 18\times 9}{100}=\frac{162P}{100}$ According to the question, Simple interest1st = Simple interest2nd – 1440 ⇒ $\frac{90P}{100}=\frac{162P}{100}-1440$ ⇒ $\frac{162P-90P}{100}=1440$ ⇒ $72P=144000$ ⇒ $P=\frac{144000}{72}$ = INR
Question : In two alloys, the ratio of Aluminium to Zinc is 5 : 6 and 3 : 5. If 242 kg of the first alloy and 144 kg of the second alloy are mixed, then the ratio of Aluminium and Zinc in the new alloy will be:
Option 1: 76 : 117
Option 2: 82 : 111
Option 3: 93 : 100
Option 4: 68 : 125
Correct Answer: 82 : 111
Solution : Given: The ratio of Aluminium to Zinc in two alloys is $5: 6$ and $3: 5$. 242 kg of the first alloy to be taken. Aluminium in the first alloy = $\frac{5}{5+6}×242=110$ kg Zinc in the first alloy = $\frac{6}{5+6}×242=132$ kg 144 kg
Question : Gaan-Ngai is a five-day festival primarily celebrated in which part of India?
Option 1: Northern
Option 2: Northeastern
Option 3: Western
Option 4: Southern
Correct Answer: Northeastern
Solution : The correct option is Northeastern.
Gann-Ngai is a regional public holiday in the state of Manipur in northeastern India. In the Western calendar, it occurs in either December or January.
Question : Direction: Which set of letters when sequentially placed at the gaps in the given letter series shall complete it? cc_b_c_ba_ab
Option 1: ccac
Option 2: cbaa
Option 3: aabb
Option 4: cdab
Correct Answer: ccac
Solution : Given: cc_b_c_ba_ab
To fill the series we have to divide the series – cc_b / _c_b / a_ab Let's check each option – First option: ccac; cccb / ccab / acab Second option: cbaa; cccb /
Question : Which of these is not one of the reasons why the public sector played a dominant role in establishing the Industrial sector in India post-independence?
Option 1: Poor savings capacity of the public
Option 2: To avoid the generation of private profit
Option 3: Absence of a large enough market for output
Option 4: Lack of adequate capital with private industrialists
Correct Answer: To avoid the generation of private profit
Solution : The correct answer is To avoid the generation of private profit.
India is a socialist country. Post-independence, it was tough for our leaders because capitalists and communists were in full swing. But India chooses its way differently from
Question : Chlorophyll containing autotrophic thallophytes is called as :
Option 1: algae
Option 2: lichens
Option 3: fungi
Option 4: bryophytes
Correct Answer: algae
Solution : The correct option is algae.
Autotrophic thallophytes with chlorophyll are frequently referred to as "algae." Algae are photosynthetic organisms that range in size from single-celled microalgae to multicellular seaweeds. They may be found in a variety of aquatic settings, including freshwater and marine areas, and
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