Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $\left(z+\frac{1}{z}\right)=4$, then what will be the value of $\frac{1}{2}\left(z^2+\frac{1}{z^2}\right)$?
Option 1: 14
Option 2: 16
Option 3: 7
Option 4: 8
Correct Answer: 7
Solution : $(z+\frac{1}{z})=4$ Squaring both sides, we get: $(z+\frac{1}{z})^2=4^2$ ⇒ $z^2+\frac{1}{z^2}+2×z×\frac{1}{z}=16$ ⇒ $z^2+\frac{1}{z^2}=16-2$ ⇒ $z^2+\frac{1}{z^2}=14$ Thus, $\frac{1}{2}(z^2+\frac{1}{z^2})$ $=\frac{1}{2}×14 = 7$ Hence, the correct answer is 7.
Question : Choose the word that can substitute the given group of words.
A slight fault that can be forgiven
Option 1: Referral
Option 2: Libertine
Option 3: Venial
Option 4: Libel
Correct Answer: Venial
Solution : The correct choice is the third option.
Explanation:
Venial is an adjective that means a mistake that is minor and pardonable. It is the correct substitute for a slight fault that can be forgiven.
The meanings of the other options are as follows:
Question : The population of a town increased from 100000 to 250000 in 5 years. What is the approximate compounded percent increase in population per year?
Option 1: 20 percent
Option 2: 30 percent
Option 3: 10 percent
Option 4: 40 percent
Correct Answer: 20 percent
Solution : Here, the initial population was 100,000 and the final population was 250,000. So, compound interest = 250000 – 100000 = 150000 Time = 5 years Let the rate of interest be $r$. We know, $\text{Compound interest}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}-\text{Principal}$ $⇒150000=100000(1+\frac{r}{100})^5-100000$ $⇒(1+\frac{r}{100})^5=\frac{250000}{100000}$ $⇒(1+\frac{r}{100})^5=(\frac{12}{10})^5$ [$\because \sqrt[5]{250000}\approx 12$] $⇒1+\frac{r}{100}=\frac{12}{10}$ $⇒r=20\%$
Question : Directions: In the following question, select the missing number from the given series. 729, 512, 343, 216, ?
Option 1: 36
Option 2: 64
Option 3: 25
Option 4: 125
Correct Answer: 125
Solution : Given: 729, 512, 343, 216, ?
The numbers given in the series are the cubes of the natural numbers in descending order. 729 ⇒ ∛729 = 9 512 ⇒ ∛512 = 8 343 ⇒ ∛343 = 7 216 ⇒ ∛216 = 6 So, the next
Question : Which of the following is the correct representation of the number of atoms?
Option 1: (given mass/molar mass) × Avogadro number
Option 2: (Avogadro number/given mass) × molar mass
Option 3: (molar mass/given mass) × Avogadro number
Option 4: (given mass/Avogadro number) × molar mass
Correct Answer: (given mass/molar mass) × Avogadro number
Solution : The correct answer is (given mass/molar mass) × Avogadro number.
The correct representation of the number of atoms is:
(given mass/molar mass) × Avogadro number. The value of Avogadro's number is approximately 6.022×1023 particles per mole.
This formula
Question : The table given below shows the production of bikes by a company during the second half of 2021.
In which month was the production of all types of bikes the lowest?
Option 1: September
Option 2: December
Option 3: November
Option 4: October
Correct Answer: November
Solution : Production of bikes in July = 58 + 89 + 54 + 72 = 273 Production of bikes in August = 38 + 46 + 64 + 53 = 201 Production of bikes in September = 56 + 45 + 76 + 65 = 242
Question : On which of the following two dates does the equinox fall?
Option 1: 23 September and 22 December
Option 2: 21 March and 23 September
Option 3: 21 March and 21 June
Option 4: 21 June and 23 September
Correct Answer: 21 March and 23 September
Solution : The correct answer is 21 March and 23 September.
The Sun is directly above Earth's equator during the equinoxes, two periods each year when neither pole faces the Sun. The equinoxes typically occur around March 21 and September 23. On March
Question : Doordarshan was started by the Indian Government in which year?
Option 1: 1939
Option 2: 1949
Option 3: 1959
Option 4: 1969
Correct Answer: 1959
Solution : The correct option is 1959.
Doordarshan was started by the Indian government on September 15, 1959. It is one of the biggest broadcasting organisations in India in terms of studio and transmitter infrastructure. Doordarshan broadcasts on digital terrestrial transmitters as well, offering television, radio,
Question : Directions: In the following question, three statements are given followed by two conclusions I, II, III and IV. You have to consider the statements to be true, even if it is seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follow from the given statements. Statements: A. Rabindranath Tagore wrote many poems. B. Every poet has aesthetic knowledge. C. Aesthetic is a part of the axiological study. Conclusions: I. Rabindranath Tagore did a different axiological study. II. He followed the base of logic and ethics.
Option 1: Only conclusion I follows
Option 2: Both conclusions I and II follow
Option 3: Only conclusion II follows
Option 4: None of these
Correct Answer: Both conclusions I and II follow
Solution : According to the given statements – Conclusion I: Rabindranath Tagore did a different axiological study. According to the given statements, Rabindranath Tagore was a poet and every poet has aesthetic knowledge. And, aesthetics is a part of axiological study. So,
Question : Simplify the given expression. $\frac{0.24 \times 0.24 \times 0.24-0.008}{0.24 \times 0.24+0.048+0.04}$
Option 1: 0.04
Option 2: 0.02
Option 3: 0.01
Option 4: 0.03
Correct Answer: 0.04
Solution : $\frac{0.24\times 0.24\times 0.24-0.008}{0.24\times 0.24 + 0.048+0.04}$ = $\frac{0.24^3-0.2^3}{0.24\times 0.24 + 0.048+0.04}$ Using identity: $(a^3-b^3)=(a-b)(a^2+b^2+ab)$ = $\frac{(0.24-0.2)(0.24^2+0.24\times 0.2+0.2^2)}{0.24\times 0.24 + 0.048+0.04}$ = 0.24 – 0.2 = 0.04 Hence, the correct answer is 0.04.
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