The question asks to identify the specific payment made by an employer to an employee at the time of retirement for services rendered. We need to distinguish between different types of employee benefits and identify the one that fits this description.
Correct Option: D) Gratuity is a lump sum payment made by an employer to an employee at the time of retirement (or resignation/termination) as a token of gratitude for the services rendered over a period of time, usually five years or more. This directly aligns with the question's description.
The question asks for the approximate percentage of tiger deaths due to poaching and electrocution between 2012 and 2018, according to the National Tiger Conservation Authority (NTCA). To answer this, we need to recall or refer to the relevant statistics provided by NTCA for that specific period.
C) 31% is the correct answer. According to NTCA data for the period 2012-2018, tiger deaths due to poaching and electrocution collectively accounted for approximately 31% of the total tiger mortalities.
The question asks to identify the community governed by Sharia law. This requires knowledge of religious legal systems and their associated communities.
Sharia law is derived from the Quran and the Sunnah (the teachings and practices of Prophet Muhammad) and is applied in various forms in many Muslim-majority countries and communities worldwide.
A) Muslim — Sharia is the religious law forming part of the Islamic tradition. It is derived from the religious precepts of Islam, particularly the Quran and the Hadith, and governs the lives of Muslims.
If \(\frac{9^m\times3^5\times27^3}{3\times81^4}\) = 3⁹, then the value of m is:
To find the value of \(m\), we need to simplify the given equation by expressing all terms as powers of the same base, which is 3. Then, we can use the laws of exponents to solve for \(m\).
Correct Option: C) 6
This problem can be solved by using the principle of inclusion-exclusion for sets or by systematically listing the number of people in each distinct category based on their preferences. Since there are no people who like all three places, and no one likes both Agra and Dubai, the problem simplifies significantly. We will sum up the number of people in each unique preference group.
People who like only Goa: The problem states that 8 persons like only Goa.
\(N(\text{only Goa}) = 8\)
People who like only Dubai: The problem states that 9 persons like only Dubai.
\(N(\text{only Dubai}) = 9\)
People who like only Agra: The problem states that only one person likes only Agra.
\(N(\text{only Agra}) = 1\)
People who like both Goa and Agra: 10 persons like both Goa and Agra. Since there is no one who likes all three, these 10 people like only Goa and Agra.
\(N(\text{Goa and Agra only}) = 10\)
People who like both Dubai and Goa: 2 persons like both Dubai and Goa. Since there is no one who likes all three, these 2 people like only Dubai and Goa.
\(N(\text{Dubai and Goa only}) = 2\)
People who like both Agra and Dubai: The problem states there is no such person who likes both Agra and Dubai.
\(N(\text{Agra and Dubai only}) = 0\)
People who like all three: The problem states there is no one in the group who likes all three.
\(N(\text{Goa and Dubai and Agra}) = 0\)
Calculate the total number of persons: Sum up the number of people in all distinct categories.
\( \text{Total Persons} = N(\text{only Goa}) + N(\text{only Dubai}) + N(\text{only Agra}) + N(\text{Goa and Agra only}) + N(\text{Dubai and Goa only}) + N(\text{Agra and Dubai only}) + N(\text{Goa and Dubai and Agra}) \)
\( \text{Total Persons} = 8 + 9 + 1 + 10 + 2 + 0 + 0 \)
\( \text{Total Persons} = 30 \)
B) 30
This problem involves relative speed. When two objects move in the same direction, their relative speed is the difference between their individual speeds. We need to convert units to be consistent (km/h to m/s or vice versa) and then use the formula: \(\text{Distance} = \text{Relative Speed} \times \text{Time}\).
It's usually easier to work with meters and seconds first, then convert back to km/h if needed. Convert the bus speed from km/h to m/s:
\[ S_B = 45 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}} = 45 \times \frac{5}{18} \text{ m/s} \]\[ S_B = \frac{225}{18} = 12.5 \text{ m/s} \]Let the speed of the truck be \(S_T\) (in m/s). Since the bus overtakes the truck, the bus is faster than the truck. When moving in the same direction, the relative speed (\(S_R\)) is the difference between their speeds:
\[ S_R = S_B - S_T \]The distance the bus covers relative to the truck is the initial distance between them (150 m).
\[ D = S_R \times T \]\[ 150 \text{ m} = (S_B - S_T) \times 30 \text{ s} \]We know \(S_R = S_B - S_T\), so \(S_T = S_B - S_R\).
\[ S_T = 12.5 \text{ m/s} - 5 \text{ m/s} = 7.5 \text{ m/s} \]Correct Option: B) 27 km/h
The problem can be solved by first setting up an equation based on the given information to find the unknown number. Once the number is found, we can calculate 20% of that number.
Let the number be \(x\).
"Half of a number" can be written as \(\frac{1}{2}x\).
"One-fourth of half of a number" can be written as \[\frac{1}{4} \times \left(\frac{1}{2}x\right)\].
We are given that this expression equals 25. So, the equation is:
\[ \frac{1}{4} \times \frac{1}{2}x = 25 \]Simplify the left side of the equation:
\[ \frac{1}{8}x = 25 \]Multiply both sides by 8 to find \(x\):
\[ x = 25 \times 8 \]\[ x = 200 \]So, the number is 200.
Now, we need to find 20% of 200.
\[ 20\% \text{ of } 200 = \frac{20}{100} \times 200 \]\[ = 20 \times 2 \]\[ = 40 \]Correct Option: D) 40
The question asks for the year when Babur defeated Ibrahim Lodhi. This is a direct historical fact related to the establishment of the Mughal Empire in India. Recalling the key battles and their dates is essential for answering such questions.
Correct Option: A) 1526
The problem asks us to identify the odd one out from a given set of four numbers. This type of question typically involves finding a common property or pattern shared by three of the numbers, while the fourth number does not share that property. We need to test for common number properties like primality, divisibility, or digit sums.
Correct Option: B) 123 is the odd one out because it is a composite number, while the other three numbers (131, 83, 79) are prime numbers.
The question asks to identify the acid commonly used as a constituent in eyewash solutions. This requires knowledge of common chemical applications, specifically those related to medical or pharmaceutical uses where mild and safe substances are preferred.
Correct Option: B) Boric acid is a very weak acid with mild antiseptic and antifungal properties. Dilute solutions of boric acid (often 1-2%) are commonly used as eyewash solutions to cleanse and soothe irritated eyes, or to remove foreign particles, because they are gentle and have a pH that is well-tolerated by the ocular surface.