UPSC CISF-AC-EXE

1. Consider the following sum : @37 + 46@ + 5@3 = 1@@@@ In the above sum,

Consider the following sum :
@37 + 46@ + 5@3 = 1@@@@
In the above sum, @ stands for which one among the following?

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For all digits
For even digits only
For odd digits only
For no digits
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In the given sum, ‘@’ stands for any digit from 0 to 9, which means for all digits.
Let the sum be represented by the equation:
$(100 \times @ + 30 + 7) + (100 \times 4 + 60 + @) + (100 \times 5 + 10 \times @ + 3) = (1000 \times 1 + 100 \times @ + 10 \times @ + @)$
Simplifying the left side:
$100@ + 37 + 460 + @ + 500 + 10@ + 3 = (100@ + @ + 10@) + (37 + 460 + 500 + 3) = 111@ + 1000$
Simplifying the right side:
$1000 + 100@ + 10@ + @ = 1000 + 111@$
The equation becomes $111@ + 1000 = 111@ + 1000$.
This equation is an identity, which means it holds true for any value of @. Since @ represents a single digit in a number, it must be one of the digits from 0 to 9. Therefore, @ can be any digit. The structure of the column-wise addition also confirms this: in each column (units, tens, hundreds), the sum is $(10 + @)$, resulting in the units digit @ and a carry-over of 1 to the next column. The final carry-over of 1 becomes the thousands digit of the total sum, which is also 1, matching the format 1@@@@. This structure works regardless of the specific digit @, as long as it’s 0-9.

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2. If $\frac{625}{0.625} = \frac{62.5}{x}$, then the value of x is

If $\frac{625}{0.625} = \frac{62.5}{x}$, then the value of x is

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0.0625
0.00625
6.25
0.000625
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The value of x is 0.0625.
The given equation is $\frac{625}{0.625} = \frac{62.5}{x}$.
First, evaluate the left side of the equation:
$\frac{625}{0.625} = \frac{625}{\frac{625}{1000}} = 625 \times \frac{1000}{625} = 1000$.
Now substitute the value back into the equation:
$1000 = \frac{62.5}{x}$
To solve for x, multiply both sides by x and divide by 1000:
$x = \frac{62.5}{1000}$
Dividing $62.5$ by $1000$ means moving the decimal point three places to the left:
$x = 0.0625$.

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3. What is the value of the following sum? $\frac{1}{(\sqrt{2}+\sqrt{1})}

What is the value of the following sum?
$\frac{1}{(\sqrt{2}+\sqrt{1})} + \frac{1}{(\sqrt{3}+\sqrt{2})} + \frac{1}{(\sqrt{4}+\sqrt{3})} + … + \frac{1}{(\sqrt{100}+\sqrt{99})}$

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9
8
7
6
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The value of the given sum is 9.
The given sum is $\sum_{k=1}^{99} \frac{1}{\sqrt{k+1}+\sqrt{k}}$. We can rationalize each term by multiplying the numerator and denominator by the conjugate of the denominator:
$\frac{1}{\sqrt{k+1}+\sqrt{k}} \times \frac{\sqrt{k+1}-\sqrt{k}}{\sqrt{k+1}-\sqrt{k}} = \frac{\sqrt{k+1}-\sqrt{k}}{(\sqrt{k+1})^2 – (\sqrt{k})^2} = \frac{\sqrt{k+1}-\sqrt{k}}{(k+1) – k} = \sqrt{k+1}-\sqrt{k}$.
The sum becomes a telescoping series:
$(\sqrt{2}-\sqrt{1}) + (\sqrt{3}-\sqrt{2}) + (\sqrt{4}-\sqrt{3}) + \dots + (\sqrt{100}-\sqrt{99})$
The intermediate terms cancel out: $(-\sqrt{1} + \sqrt{2}) + (-\sqrt{2} + \sqrt{3}) + (-\sqrt{3} + \sqrt{4}) + \dots + (-\sqrt{99} + \sqrt{100})$.
The sum simplifies to $\sqrt{100} – \sqrt{1}$.
$\sqrt{100} = 10$ and $\sqrt{1} = 1$.
The sum is $10 – 1 = 9$.

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4. A company calculates its profit or loss quarterly. The company makes 2

A company calculates its profit or loss quarterly. The company makes 25% profit, 20% loss and 20% loss in three consecutive quarters. What minimum profit or loss should the company make in fourth quarter to have no loss overall?

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20% profit
20% loss
25% profit
25% loss
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To have no loss overall, the company should make a minimum profit of 25% in the fourth quarter.
Let the initial capital be $C$.
Quarter 1: Profit of 25%. Capital becomes $C \times (1 + 0.25) = 1.25C$.
Quarter 2: Loss of 20%. Capital becomes $1.25C \times (1 – 0.20) = 1.25C \times 0.80 = C$.
Quarter 3: Loss of 20%. Capital becomes $C \times (1 – 0.20) = C \times 0.80 = 0.8C$.
After three quarters, the capital is $0.8C$.
To have no loss overall after four quarters, the final capital must be at least the initial capital, $C$. Let the profit percentage in the fourth quarter be $p$ (as a decimal). The capital after the fourth quarter will be $0.8C \times (1+p)$.
We need $0.8C \times (1+p) \ge C$.
Dividing by $0.8C$ (assuming $C>0$): $1+p \ge \frac{C}{0.8C} = \frac{1}{0.8} = \frac{1}{4/5} = 1.25$.
$p \ge 1.25 – 1 = 0.25$.
So, the minimum profit percentage in the fourth quarter must be $0.25 \times 100\% = 25\%$.

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5. Which one of the following languages is not included in the Eighth S

Which one of the following languages is not included in the Eighth Schedule of the Constitution of India?

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Bodo
Maithili
Santhali
Ladakhi
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Ladakhi is not included in the Eighth Schedule of the Constitution of India.
The Eighth Schedule lists the languages recognized by the Constitution of India. As of 2004, there are 22 languages in the Eighth Schedule.
The 22 languages are Assamese, Bengali, Bodo, Dogri, Gujarati, Hindi, Kannada, Kashmiri, Konkani, Maithili, Malayalam, Manipuri, Marathi, Nepali, Odia, Punjabi, Sanskrit, Santhali, Sindhi, Tamil, Telugu, and Urdu. Bodo, Maithili, and Santhali were added by the 92nd Amendment Act of 2003. Ladakhi is a language spoken in the Ladakh region but is not among the scheduled languages.

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6. Which one among the following is not correct as per Article 14 of th

Which one among the following is not correct as per Article 14 of the Constitution of India?

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Equality before law is guaranteed to citizens of India only.
It secures for any person equal protection of laws within the territory of India.
The State shall not deny to any person equality before law within the territory of India.
The State shall not deny to non-citizens equality before law within the territory of India.
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The statement that is not correct as per Article 14 of the Constitution of India is A) Equality before law is guaranteed to citizens of India only.
Article 14 guarantees equality before the law and equal protection of the laws to ‘any person’ within the territory of India. The term ‘person’ includes not only citizens but also non-citizens (foreigners) and legal entities like corporations and companies.
Article 14 is a fundamental right that prohibits discrimination. ‘Equality before law’ is a negative concept implying the absence of any special privilege for any person and the equal subjection of all persons to the ordinary law of the land. ‘Equal protection of laws’ is a positive concept requiring the State to treat persons alike in similar circumstances, allowing for reasonable classification but forbidding class legislation. Options B, C, and D correctly reflect that Article 14 applies to ‘any person’ and guarantees both equality before law and equal protection of laws within India’s territory, including to non-citizens.

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7. Which one of the following provisions of the Universal Declaration of

Which one of the following provisions of the Universal Declaration of Human Rights states, “Everyone has the right to life, liberty and security of person”?

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Article 1
Article 2
Article 3
Article 4
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Article 3 of the Universal Declaration of Human Rights (UDHR) states, “Everyone has the right to life, liberty and security of person”.
The Universal Declaration of Human Rights, adopted by the United Nations General Assembly in 1948, is a foundational document outlining fundamental human rights that should be universally protected.
Article 1 of the UDHR states that “All human beings are born free and equal in dignity and rights”. Article 2 deals with equality and non-discrimination. Article 4 prohibits slavery and servitude. The right to life, liberty, and security of person is a fundamental right recognized globally and is elaborated upon in subsequent international human rights treaties.

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8. Which one of the following States of India does not have a Legislati

Which one of the following States of India does not have a Legislative Council?

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Bihar
West Bengal
Uttar Pradesh
Karnataka
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Among the given states, West Bengal does not have a Legislative Council as of the current status.
Article 169 of the Constitution of India provides for the creation or abolition of Legislative Councils in states. A state Legislative Council can be created if the State Legislative Assembly passes a resolution to that effect by a special majority, and if Parliament subsequently passes a law for the same.
As of late 2023 / early 2024, the states having Legislative Councils are Andhra Pradesh, Telangana, Uttar Pradesh, Bihar, Maharashtra, and Karnataka. West Bengal previously had a Legislative Council which was abolished in 1969. The State Legislative Assembly passed a resolution in 2021 to revive the Legislative Council, but this requires Parliament’s approval, which has not yet been granted.

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9. Which one among the following legal maxims means ‘we command’?

Which one among the following legal maxims means ‘we command’?

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Habeas corpus
Mandamus
Audi alteram partem
Non bis in idem
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Among the given legal maxims, ‘Mandamus’ means ‘we command’.
Mandamus is a writ issued by a superior court to a lower court, tribunal, public authority, or corporation, commanding it to perform a public duty that it is legally bound to perform. It is one of the five prerogative writs in the Indian Constitution.
A) Habeas corpus means ‘You may have the body’, a writ used to bring a person before a court to determine if detention is lawful.
C) Audi alteram partem means ‘hear the other side’, a principle of natural justice.
D) Non bis in idem means ‘not twice in the same thing’ or ‘double jeopardy’, a principle preventing a person from being tried twice for the same offense.

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10. In which year was a Cabinet resolution passed to replace the Planning

In which year was a Cabinet resolution passed to replace the Planning Commission with NITI Aayog?

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2014
2015
2016
2018
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The Cabinet resolution to replace the Planning Commission with the National Institution for Transforming India (NITI) Aayog was passed on January 1, 2015.
The Planning Commission was a non-constitutional and non-statutory body established in March 1950 through a Cabinet resolution. NITI Aayog, its successor, was also established by a Cabinet resolution.
The proposal to replace the Planning Commission was first announced by Prime Minister Narendra Modi on Independence Day, August 15, 2014. The formal resolution establishing NITI Aayog came into effect on January 1, 2015.

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