Write the ratios 5 : 3, 7 : 5 and 6 : 4 in descending order.
\( \frac{5}{3} \) > \( \frac{6}{4} \)> \( \frac{7}{5} \)
\( \frac{5}{3} \) > \( \frac{7}{5} \) >\( \frac{6}{4} \)
\( \frac{7}{5} \) > \( \frac{6}{4} \) > \( \frac{5}{3} \)
\( \frac{6}{4} \) >\( \frac{7}{5} \) > \( \frac{5}{3} \)
To arrange the given ratios in descending order, we need to convert them into a common format, such as decimal numbers or fractions with a common denominator. Then, we can easily compare their values.
The given ratios are \(5:3\), \(7:5\), and \(6:4\).
The fraction \(\frac{6}{4}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
\[ \frac{6}{4} = \frac{6 \div 2}{4 \div 2} = \frac{3}{2} \]Comparing the decimal values:
So, the descending order is \(1.666... > 1.5 > 1.4\).
Substituting back the original fractions:
\[ \frac{5}{3} > \frac{6}{4} > \frac{7}{5} \]A) \( \frac{5}{3} \) > \( \frac{6}{4} \)> \( \frac{7}{5} \) is the correct order as determined by comparing their decimal values.
The question asks to identify the country that held the second position in petroleum exports during 2018-19, given that Saudi Arabia was first. This requires knowledge of global energy statistics for that specific period.
Correct Option: B) Russia
Pipe A can fill a tank in 80 min and pipe B can fill the tank in 40 min. If A and B are opened together, then in how many minutes will the tank be filled?
To find the time taken to fill a tank when two pipes are opened together, we first determine the individual filling rates of each pipe. Then, we sum their rates to find the combined filling rate. Finally, we take the reciprocal of the combined rate to find the total time required to fill the tank.
Calculate the filling rate of Pipe A:
Pipe A can fill the tank in 80 minutes. So, in 1 minute, Pipe A fills \(\frac{1}{80}\) of the tank.
Calculate the filling rate of Pipe B:
Pipe B can fill the tank in 40 minutes. So, in 1 minute, Pipe B fills \(\frac{1}{40}\) of the tank.
Calculate the combined filling rate of Pipe A and Pipe B:
When both pipes are opened together, their individual rates add up. Let \(R_A\) be the rate of Pipe A and \(R_B\) be the rate of Pipe B. The combined rate \(R_{combined}\) is:
Add the fractions:
To add the fractions, find a common denominator, which is 80.
Calculate the total time to fill the tank:
The combined rate \(\frac{3}{80}\) means that \(\frac{3}{80}\) of the tank is filled in 1 minute. To find the total time \(T\) to fill the entire tank (which is 1 unit), we take the reciprocal of the combined rate.
Convert the improper fraction to a mixed number:
\[ \frac{80}{3} = 26 \frac{2}{3} \text{ minutes} \]Correct Option: B) 26 \(\frac{2}{3}\)
The calculation shows that when both pipes A and B are opened together, the tank will be filled in \(26 \frac{2}{3}\) minutes.
The question asks to identify the scholar who coined the term "Geography". This requires knowledge of the history of geography and the contributions of ancient Greek scholars.
Correct Option: D) Eratosthenes is credited with coining the term "Geography" (γεωγραφία) in the 3rd century BCE. He is often referred to as the "Father of Geography" for his systematic approach to describing the Earth, including his famous calculation of the Earth's circumference and his work on mapping the known world.
The question asks to identify an animal frequently depicted on the seals of the Harappan Civilisation. This requires knowledge of the common iconography found on Harappan seals.
Correct Option: C) Bull — The bull, particularly the humped bull, is one of the most common animals depicted on the seals of the Harappan Civilisation, suggesting its cultural or religious significance.
The question asks about a specific constitutional provision in India regarding the nomination of members to the Lok Sabha by the President, which was in effect until January 2020. This requires knowledge of Indian constitutional history and amendments.
Article 331 of the Indian Constitution originally provided for the representation of the Anglo-Indian community in the House of the People (Lok Sabha). If the President was of the opinion that the Anglo-Indian community was not adequately represented in the Lok Sabha, he could nominate not more than two members of that community to the Lok Sabha.
This provision was discontinued by the 104th Constitutional Amendment Act, 2019, which came into effect in January 2020. The amendment removed the reservation of seats for the Anglo-Indian community in the Lok Sabha and state legislative assemblies.
A) Anglo-Indian — Until January 2020, the President had the power to nominate two members from the Anglo-Indian community to the Lok Sabha if he felt they were not adequately represented. This provision was removed by the 104th Constitutional Amendment Act, 2019.
The question asks for the year in which Mahatma Gandhi led the Champaran Satyagraha. This is a factual question related to modern Indian history, specifically Mahatma Gandhi's early movements in India.
B) 1917 — The Champaran Satyagraha, Mahatma Gandhi's first major civil disobedience movement in India, occurred in 1917.
The question asks for the correct sequence of steps in the human digestive system. Understanding the fundamental processes involved in how the body processes food is key to answering this question.
B) Ingestion, Digestion, Absorption, Egestion is the correct sequence. Food is first taken in (ingestion), then broken down (digestion), nutrients are taken into the body (absorption), and finally, waste is expelled (egestion).
If \( \frac{1}{3} \) A = \( \frac{1}{4} \) B = \( \frac{1}{5} \) C, then A : B : C = ?
4 : 3 : 5
\( \frac{1}{3} \) : \( \frac{1}{4} \) : \( \frac{1}{5} \)
3 : 4 : 5
5 : 4 : 3
To find the ratio A : B : C from the given equation \[\frac{1}{3} \text{A} = \frac{1}{4} \text{B} = \frac{1}{5} \text{C}\], we can set each part of the equality to a constant, say \( k \), and then express A, B, and C in terms of \( k \). This will allow us to determine their ratio.
Given the equation:
\[ \frac{1}{3} \text{A} = \frac{1}{4} \text{B} = \frac{1}{5} \text{C} \]Let's set each part of the equality to a constant \( k \):
\[ \frac{1}{3} \text{A} = k \]\[ \frac{1}{4} \text{B} = k \]\[ \frac{1}{5} \text{C} = k \]Now, express A, B, and C in terms of \( k \):
Now, find the ratio A : B : C:
\[ \text{A} : \text{B} : \text{C} = 3k : 4k : 5k \]Since \( k \) is a common factor, we can cancel it out:
\[ \text{A} : \text{B} : \text{C} = 3 : 4 : 5 \]C) 3 : 4 : 5 — This is derived directly by setting the given fractions equal to a constant and solving for A, B, and C.
To find the L.C.M. (Least Common Multiple) of XY, YZ, and ZX, we first need to calculate the values of X, Y, and Z. Then, we will find the products XY, YZ, and ZX. Finally, we will express these products in their prime factorization form and use the rule for finding the L.C.M. of numbers expressed as products of prime factors.
Given:
\[ X = 3^2 \times 2 = 9 \times 2 = 18 \]\[ Y = 2^3 \times 3 = 8 \times 3 = 24 \]\[ Z = 3^2 \times 2^2 = 9 \times 4 = 36 \]To find the L.C.M. of numbers expressed in their prime factorization form, we take the highest power of each prime factor present in any of the numbers.
The prime factors involved are 2 and 3.
Highest power of 2:
The highest power of 2 is \(2^5\).
Highest power of 3:
The highest power of 3 is \(3^4\).
Therefore, L.C.M. (XY, YZ, ZX) = \(2^5 \times 3^4\).
C) The L.C.M. of XY, YZ, ZX is 2592, which matches our calculated value.