To find the kinetic energy of a body, we use the standard formula for kinetic energy, which relates the mass and velocity of the object. We will substitute the given values for mass and velocity into this formula and calculate the result.
The kinetic energy (\(KE\)) of a body is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]Substitute \(m = 2 \text{ kg}\) and \(v = 5 \text{ m/sec}\) into the kinetic energy formula:
\[ KE = \frac{1}{2} (2 \text{ kg}) (5 \text{ m/sec})^2 \]First, calculate the square of the velocity:
\[ (5 \text{ m/sec})^2 = 25 \text{ m}^2/\text{sec}^2 \]Now, multiply the values:
\[ KE = \frac{1}{2} \times 2 \text{ kg} \times 25 \text{ m}^2/\text{sec}^2 \]\[ KE = 1 \text{ kg} \times 25 \text{ m}^2/\text{sec}^2 \]\[ KE = 25 \text{ Joules} \]The unit for kinetic energy is Joules (J).
B) 25 joules — The calculation shows that the kinetic energy is 25 Joules.
This question tests fundamental knowledge of genetics and inheritance patterns in sexually reproducing organisms. Traits are determined by genes, which are segments of DNA. Understanding how DNA is passed from parents to offspring is key to answering this question.
B) Both maternal and paternal DNA equally. In sexual reproduction, offspring inherit half of their chromosomes from the mother and half from the father. Since genes (which determine traits) are located on chromosomes, every trait is influenced by genetic material from both parents, typically in equal measure.
The question asks to identify India's youngest Olympic medallist as of August 2024. This requires knowledge of recent Olympic events and the ages of the medallists mentioned.
Therefore, Aman Sehrawat is India's youngest Olympic medallist as of August 2024.
C) Aman Sehrawat — Aman Sehrawat won a bronze medal in wrestling at the Paris 2024 Olympics. Born on July 16, 2003, he was 21 years old at the time of his medal win, making him India's youngest Olympic medallist as of August 2024.
This problem involves a concave mirror and requires the application of the mirror formula along with the sign convention for spherical mirrors. We are given the focal length of the concave mirror and the position of the real image. We need to find the object distance.
The negative sign indicates that the object is placed in front of the mirror, which is consistent with the sign convention.
Correct Option: B) -20 cm
We are given the total salary of P and Q, and the percentage of salary each spends. We are also told that their savings are equal. We need to find P's salary. We will set up equations based on the given information and solve for P's salary.
Let P's salary be \(P\) and Q's salary be \(Q\).
From the problem statement, the sum of their salaries is ₹2,000:
\[ P + Q = 2000 \quad \text{(Equation 1)} \]P spends 95% of his salary, so P saves \(100\% - 95\% = 5\%\) of his salary.
P's savings \(= 0.05P\).
Q spends 85% of his salary, so Q saves \(100\% - 85\% = 15\%\) of his salary.
Q's savings \(= 0.15Q\).
We are given that their savings are the same:
\[ 0.05P = 0.15Q \]To simplify the equation, divide both sides by 0.05:
\[ P = \frac{0.15}{0.05}Q \]\[ P = 3Q \quad \text{(Equation 2)} \]Now, substitute Equation 2 into Equation 1:
\[ 3Q + Q = 2000 \]\[ 4Q = 2000 \]Solve for Q:
\[ Q = \frac{2000}{4} \]\[ Q = 500 \]Now that we have Q's salary, substitute it back into Equation 2 to find P's salary:
\[ P = 3Q \]\[ P = 3 \times 500 \]\[ P = 1500 \]So, P's salary is ₹1,500.
A) ₹1,500 — As calculated, P's salary is ₹1,500.
This problem involves setting up a system of linear equations based on the given information about the cost of oranges and bananas. We will define variables for the original cost of an orange and a banana, form two equations, solve them simultaneously to find the individual costs, and then calculate the final required cost.
Define variables:
Let \(x\) be the original cost of one orange (in ₹).
Let \(y\) be the original cost of one banana (in ₹).
Form the first equation:
Arpita buys 9 oranges and 8 bananas for ₹276.
\[ 9x + 8y = 276 \quad \text{(Equation 1)} \]Calculate new cost of an orange:
The cost of an orange is decreased by 10%.
New cost of one orange \( = x - 0.10x = 0.90x \).
The cost of a banana remains the same, i.e., \(y\).
Form the second equation:
The cost of 5 oranges and 10 bananas is ₹210 with the new orange price.
\[ 5(0.90x) + 10y = 210 \]\[ 4.5x + 10y = 210 \quad \text{(Equation 2)} \]Solve the system of equations:
We have:
Equation 1: \( 9x + 8y = 276 \)
Equation 2: \( 4.5x + 10y = 210 \)
Multiply Equation 2 by 2 to make the coefficient of \(x\) similar to Equation 1:
\( 2 \times (4.5x + 10y) = 2 \times 210 \)
\[ 9x + 20y = 420 \quad \text{(Equation 3)} \]Subtract Equation 1 from Equation 3:
\( (9x + 20y) - (9x + 8y) = 420 - 276 \)
\( 12y = 144 \)
\( y = \frac{144}{12} \)
\( y = 12 \)
So, the original cost of one banana is ₹12.
Substitute \(y\) into Equation 1 to find \(x\):
\( 9x + 8(12) = 276 \)
\( 9x + 96 = 276 \)
\( 9x = 276 - 96 \)
\( 9x = 180 \)
\( x = \frac{180}{9} \)
\( x = 20 \)
So, the original cost of one orange is ₹20.
Calculate the original cost of 3 oranges and 4 bananas:
Required cost \( = 3x + 4y \)
\( = 3(20) + 4(12) \)
\( = 60 + 48 \)
\( = 108 \)
The original cost of 3 oranges and 4 bananas is ₹108.
Correct Option: A) ₹108
The question asks for the specific date of demise of Justice M. Fathima Beevi, the first female Supreme Court Judge of India. This is a factual question requiring knowledge of current affairs or significant historical legal figures.
Correct Option: B) 23 November 2023
The problem asks us to identify the letter-cluster that does not fit a certain pattern among four given options. This is a common type of odd-one-out question based on logical reasoning and alphabetical order. We need to find a hidden rule or relationship between the letters in each cluster and then identify the cluster that violates this rule.
Let's apply this to each option:
Now, let's examine the differences for each cluster:
It is clear that options B, C, and D follow the same pattern: the second letter is 5 positions before the first letter, and the third letter is 4 positions after the second letter. Option A, however, follows a different pattern.
A) VRU — This cluster has a difference of +4 between the first and second letters, and -3 between the second and third letters (V(22) - R(18) = 4; R(18) - U(21) = -3). This pattern \((+4, -3)\) is different from the pattern \((+5, -4)\) observed in the other three options.
When a solid object is melted and recast into another shape, the volume of the material remains constant. Therefore, the volume of the metal ball will be equal to the volume of the cylinder formed.
Since the material is melted and recast, the volume remains constant:
\[ V_{\text{ball}} = V_{\text{cylinder}} \]\[ \frac{4}{3} \pi R_{\text{ball}}^3 = \pi R_{\text{cylinder}}^2 h \]We have \(R_{\text{ball}} = 3 \text{ cm}\) and \(R_{\text{cylinder}} = 3 \text{ cm}\).
\[ \frac{4}{3} \pi (3)^3 = \pi (3)^2 h \]\[ \frac{4}{3} \pi (27) = \pi (9) h \]Cancel \(\pi\) from both sides:
\[ \frac{4}{3} (27) = 9 h \]\[ 4 \times 9 = 9 h \]\[ 36 = 9 h \]Correct Option: B) The height of the cylinder would be 4 cm.
The question asks for the correct definition of pollination. We need to evaluate each option based on the biological process of plant reproduction.
D) Pollination is transfer of pollen grains from stamen to stigma. This is the precise definition of pollination. It is the process by which pollen is transferred from the anther (part of the stamen) to the stigma (part of the pistil) of a flower, enabling fertilization and reproduction.