To find the velocity of the body, we will use the formula for kinetic energy, which relates kinetic energy to mass and velocity. We are given the mass and kinetic energy, so we can rearrange the formula to solve for velocity.
The kinetic energy (\(KE\)) of a body is given by the formula:
\[ KE = \frac{1}{2}mv^2 \]where \(m\) is the mass of the body and \(v\) is its velocity.
To find \(v\), take the square root of both sides:
\[ v = \sqrt{100} \] \[ v = 10 \text{ m/s} \]Since velocity is a speed in this context (magnitude), we take the positive root.
Correct Option: A) 10 m/s
The problem describes a scenario where a man sells a certain number of mangoes (320) for the cost price of a larger number of mangoes (400). We need to calculate the gain percentage. The key is to understand that the selling price of 320 mangoes is equal to the cost price of 400 mangoes. We can assume a unit cost price for a single mango to simplify calculations.
B) 25% is the calculated gain percentage.
The question asks to identify the biological process that ensures the stability of species populations. We need to consider how each given option contributes to or affects population numbers over time.
Correct Option: A) Reproduction is the process by which organisms produce offspring. This continuous generation of new individuals is essential to replace those that die, thereby maintaining the population size and ensuring the stability and survival of the species over time.
The value of (0.04)-1.5 is:
To find the value of \((0.04)^{-1.5}\), we need to convert the decimal to a fraction, express the exponent in a fractional form, and then apply the rules of exponents. Specifically, we will use the rules \((a/b)^{-n} = (b/a)^n\) and \((a^m)^n = a^{mn}\).
Convert the decimal to a fraction:
The number \(0.04\) can be written as a fraction:
\[ 0.04 = \frac{4}{100} = \frac{1}{25} \]Convert the decimal exponent to a fraction:
The exponent \(-1.5\) can be written as a fraction:
\[ -1.5 = -\frac{15}{10} = -\frac{3}{2} \]Substitute these values into the expression:
Now the expression becomes:
\[ \left(\frac{1}{25}\right)^{-\frac{3}{2}} \]Apply the negative exponent rule:
Recall that \(a^{-n} = \frac{1}{a^n}\) or \((a/b)^{-n} = (b/a)^n\). Applying this rule:
\[ \left(\frac{1}{25}\right)^{-\frac{3}{2}} = \left(\frac{25}{1}\right)^{\frac{3}{2}} = (25)^{\frac{3}{2}} \]Evaluate the expression:
The exponent \(\frac{3}{2}\) means taking the square root first, and then cubing the result (or vice versa). It can be written as \((25^{1/2})^3\) or \((25^3)^{1/2}\).
It's easier to take the square root first:
\[ (25)^{\frac{3}{2}} = (\sqrt{25})^3 \]\[ \sqrt{25} = 5 \]\[ (5)^3 = 5 \times 5 \times 5 = 125 \]D) The calculated value of \((0.04)^{-1.5}\) is \(125\).
This question tests the fundamental understanding of displacement in physics. Displacement is a vector quantity that represents the shortest distance between an object's initial and final positions. To have zero displacement, the object must end up at the same point where it started.
A) When the initial and final position of the object is the same. This statement directly aligns with the definition of zero displacement. If an object starts at point A and returns to point A, its displacement is zero, regardless of the path taken or the distance covered.
The question asks to identify the program that organized youth exchange visits across states in 2024, focusing on the '5 Ps': Paryatan (Tourism), Parampara (Traditions), Pragati (Development), Paraspar Sampark (People-to-people connect), and Prodyogiki (Technology). This requires knowledge of recent government initiatives related to youth engagement and cultural exchange.
B) Yuva Sangam is the correct answer. The Yuva Sangam program, an initiative of the Ministry of Education under the 'Ek Bharat Shreshtha Bharat' umbrella, specifically organizes youth exchange visits across states. Its objective is to provide an immersive experience of diverse cultures, traditions, and developmental aspects of India to the youth, aligning perfectly with the '5 Ps': Paryatan (Tourism), Parampara (Traditions), Pragati (Development), Paraspar Sampark (People-to-people connect), and Prodyogiki (Technology).
The question asks for the specific date when India and the USA signed their first-ever Cultural Property Agreement (CPA). This is a factual question requiring knowledge of recent international agreements between the two countries. We need to identify the correct date from the given options.
India and the USA signed their first-ever Cultural Property Agreement (CPA) on 26 July 2024. This agreement aims to prevent the illegal trafficking of cultural artifacts and promote their legitimate exchange for cultural, educational, and scientific purposes. This was a significant step in strengthening cultural ties and cooperation between the two nations.
The problem asks for the sum of the third largest and the largest even numbers from a sequence of five consecutive even numbers whose sum is given. We will first find the average of these numbers, which will be the middle number. Then, we can determine all five numbers and calculate the required sum.
Correct Option: C) 1492
When 0.292929...... is converted into a fraction, then the result is:
\( \frac{1}{5} \)
\( \frac{29}{99} \)
\( \frac{2}{9} \)
\( \frac{29}{100} \)
To convert a repeating decimal into a fraction, we can use an algebraic method. We assign the repeating decimal to a variable, multiply it by a power of 10 to shift the repeating part, and then subtract the original equation to eliminate the repeating digits.
Let the given repeating decimal be \(x\):
\[ x = 0.292929... \quad \text{(Equation 1)} \]Identify the number of repeating digits. In this case, the digits '29' are repeating, so there are two repeating digits.
Multiply Equation 1 by \(10^2 = 100\) (since there are two repeating digits) to shift the decimal point:
\[ 100x = 29.292929... \quad \text{(Equation 2)} \]Subtract Equation 1 from Equation 2:
\[ 100x - x = 29.292929... - 0.292929... \] \[ 99x = 29 \]Solve for \(x\):
\[ x = \frac{29}{99} \]Thus, 0.292929...... converted into a fraction is \( \frac{29}{99} \).
B) \( \frac{29}{99} \) is the correct conversion of the repeating decimal 0.292929... into a fraction.
A) \( \frac{1}{5} \) — This fraction is equal to 0.2. It does not represent 0.292929... .
C) \( \frac{2}{9} \) — This fraction is equal to 0.2222... . It does not represent 0.292929... .
D) \( \frac{29}{100} \) — This fraction is equal to 0.29. This is a terminating decimal, not a repeating decimal like 0.292929... .
The volume of a cylinder is 5500 m³. Find its diameter of base if the height of the cylinder is 70 m. [Use π = \( \frac{22}{7} \)]
To find the diameter of the base of the cylinder, we will use the formula for the volume of a cylinder, which is \(V = \pi r^2 h\). We are given the volume (\(V\)) and the height (\(h\)), and we need to find the radius (\(r\)) first. Once we have the radius, we can easily calculate the diameter using the relation \(D = 2r\).
The volume \(V\) of a cylinder is given by:
\[ V = \pi r^2 h \]We have \(5500 = \frac{22}{7} \times r^2 \times 70\).
First, simplify the right side of the equation:
\[ 5500 = 22 \times r^2 \times \frac{70}{7} \]\[ 5500 = 22 \times r^2 \times 10 \]\[ 5500 = 220 r^2 \]Divide both sides by 220:
\[ r^2 = \frac{5500}{220} \]\[ r^2 = \frac{550}{22} \]\[ r^2 = 25 \]Take the square root of both sides:
\[ r = \sqrt{25} \]\[ r = 5 \text{ m} \]The diameter is twice the radius:
\[ D = 2r \]\[ D = 2 \times 5 \]\[ D = 10 \text{ m} \]Correct Option: C) 10 m