In a ranking list in which only one person is holding a specific rank, Jatin's rank is 15th in a list of 40 football players. If there are only 8 players below Manoj in the list, then how many football players are there between Jatin and Manoj?
To find the number of players between Jatin and Manoj, we first need to determine Manoj's rank from the top. We are given Jatin's rank from the top and the total number of players. Once we have both Jatin's and Manoj's ranks from the top, we can calculate the number of players between them.
Total number of players: The list contains 40 football players.
Jatin's rank: Jatin's rank is 15th from the top.
Manoj's rank from the bottom: There are 8 players below Manoj. This means Manoj is the 9th person from the bottom of the list.
Manoj's rank from the top: To find Manoj's rank from the top, we use the formula:
\[ \text{Rank from top} = \text{Total players} - \text{Rank from bottom} + 1 \]\[ \text{Manoj's rank from top} = 40 - 9 + 1 = 32 \]Number of players between Jatin and Manoj: Jatin is 15th from the top, and Manoj is 32nd from the top. Since Manoj's rank is higher (further down the list) than Jatin's, we can calculate the number of players between them using the formula:
\[ \text{Players between} = \text{Manoj's rank from top} - \text{Jatin's rank from top} - 1 \]\[ \text{Players between} = 32 - 15 - 1 = 17 - 1 = 16 \]Therefore, there are 16 football players between Jatin and Manoj.
Correct Option: C) 16
The question asks for the specific name of the parliament of Denmark. This is a factual question related to the political systems of different countries, a common topic in general knowledge sections of competitive exams.
The parliament of Denmark is known as the Folketing.
Correct Option: C) Folketing is the correct answer. The Folketing is the national parliament of the Kingdom of Denmark.
We are given the ratio of two positive numbers and the product of their LCM and HCF. We need to find the sum of these numbers. We will use the property that for any two positive numbers, the product of the numbers is equal to the product of their LCM and HCF. We will represent the numbers using a common multiple based on their ratio and then solve for this multiple.
Let the two positive numbers be \(a\) and \(b\). Given that their ratio is \(7:9\), we can write them as:
\[ a = 7x \] \[ b = 9x \]where \(x\) is a common positive integer.
For any two positive numbers \(a\) and \(b\), the product of the numbers is equal to the product of their LCM and HCF.
\[ a \times b = \text{LCM}(a, b) \times \text{HCF}(a, b) \]We are given that \(\text{LCM}(a, b) \times \text{HCF}(a, b) = 25200\).
So, we have:
\[ (7x) \times (9x) = 25200 \]Simplify the equation:
\[ 63x^2 = 25200 \]Divide both sides by 63:
\[ x^2 = \frac{25200}{63} \] \[ x^2 = 400 \]Take the square root of both sides:
\[ x = \sqrt{400} \] \[ x = 20 \](Since the numbers are positive, \(x\) must be positive).
Substitute the value of \(x\) back into the expressions for \(a\) and \(b\):
\[ a = 7x = 7 \times 20 = 140 \] \[ b = 9x = 9 \times 20 = 180 \]Sum \( = a + b = 140 + 180 = 320 \)
Correct Option: A) 320
The problem involves finding an unknown number given the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers, and one of the numbers. The fundamental property relating LCM, HCF, and two numbers is that the product of the two numbers is equal to the product of their LCM and HCF.
Correct Option: D) 94
The acceleration due to gravity (\(g\)) on Earth is influenced by two primary factors: the Earth's shape (which affects the distance from the center) and its rotation (which creates a centrifugal force). We need to analyze how these factors vary across different latitudes to determine where \(g\) will be minimum.
Correct Option: A) The Equator has the largest radius from the Earth's center and experiences the maximum centrifugal force due to Earth's rotation. Both these factors contribute to the minimum value of acceleration due to gravity (\(g\)) at the Equator.
The problem states that if the total number of trees is divided into rows of 105, 210, or 420 trees, no tree is left over. This means the total number of trees must be a common multiple of 105, 210, and 420. We need to find the least such number, which is the Least Common Multiple (LCM) of these three numbers.
To find the LCM, we take the highest power of all prime factors that appear in any of the numbers.
So, the LCM is:
\[ \text{LCM}(105, 210, 420) = 2^2 \times 3 \times 5 \times 7 \]\[ = 4 \times 3 \times 5 \times 7 \]\[ = 12 \times 35 \]\[ = 420 \]The least number of trees that can be planted such that they can be arranged in rows of 105, 210, or 420 without any tree left over is 420.
B) 420 is the LCM of 105, 210, and 420. This means 420 is the smallest number of trees that satisfies the given conditions.
The question asks for India's ranking in the Global Hunger Index (GHI) for the year 2020. This requires recalling specific data related to international reports and rankings.
A) 94 is the correct answer. In the 2020 Global Hunger Index, India was ranked 94th out of 107 countries.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
. Statement:
The old leaves are replaced by new leaves.
Conclusions:
1. There can be no new leaves without old leaves.
2. Old leaves are useless.
Only conclusion 2 follows.
Neither conclusion 1 nor 2 follows.
Both conclusions 1 and 2 follow.
Only conclusion 1 follows.
This is a logical reasoning question. We need to evaluate the given conclusions based solely on the information provided in the statement, without introducing external knowledge or assumptions. The statement is: "The old leaves are replaced by new leaves."
B) Neither conclusion 1 nor 2 follows.
The question asks to identify which of the given rivers is NOT a tributary of the Brahmaputra River. To answer this, one needs to have knowledge of the major tributaries of the Brahmaputra River system.
D) Tamsa River — The Tamsa River (also known as Tons River) is a tributary of the Ganga River, not the Brahmaputra. It originates in the Kaimur Range and flows through Madhya Pradesh and Uttar Pradesh before joining the Ganga.
The Paris Agreement opened for signatures on Earth Day on ______ at the UN headquarters in New York.
22nd April 2018
22nd April 2016
22nd April 2014
22nd April 2012
The question asks for the specific date when the Paris Agreement was opened for signatures. This requires knowledge of key dates related to international environmental agreements, particularly the Paris Agreement.
B) 22nd April 2016 — The Paris Agreement was indeed opened for signatures on Earth Day, April 22, 2016, at the UN headquarters in New York. This event saw a record number of countries signing the agreement on the first day.