Which of the following teams was the winner of the 17th Edition of Indian Premier League in 2024?
Kolkata Knight Riders
Mumbai Indians
Delhi Capitals
Gujarat Titans
The question asks to identify the winner of the 17th edition of the Indian Premier League (IPL) in 2024. This requires knowledge of recent major sporting event outcomes, specifically the IPL.
Correct Option: A) Kolkata Knight Riders
Kolkata Knight Riders (KKR) won the 17th edition of the Indian Premier League in 2024, defeating Sunrisers Hyderabad in the final match.
This problem involves decoding a mathematical expression where letters represent arithmetic operations. We need to substitute the given symbols with their corresponding operations and then solve the expression following the order of operations (BODMAS/PEMDAS).
The original equation is: \(121 \text{ C } 21 \text{ D } 11 \text{ A } 11 \text{ B } 121 = ?\)
Substituting the operations, we get:
\[ 121 + 21 - 11 \div 11 \times 121 = ? \]BODMAS/PEMDAS stands for Brackets/Parentheses, Orders/Exponents, Division, Multiplication, Addition, Subtraction. We perform operations in this specific order.
C) 21 — After substituting the operations and applying the BODMAS/PEMDAS rule, the final value of the expression is 21.
The problem requires us to evaluate a given mathematical expression after interchanging certain arithmetic operators. We need to first apply the given interchange rules to the operators in the expression and then solve the modified expression following the order of operations (BODMAS/PEMDAS).
The original expression is: \(8 \times 2 + 3 - 2 \div 6 = ?\)
The rules are:
Applying these rules to the original expression:
The modified expression becomes: \(8 \div 2 - 3 + 2 \times 6\)
The order of operations is:
Let's evaluate the modified expression: \(8 \div 2 - 3 + 2 \times 6\)
Step 3.1: Perform Division.
\[ 8 \div 2 = 4 \]The expression becomes: \(4 - 3 + 2 \times 6\)
Step 3.2: Perform Multiplication.
\[ 2 \times 6 = 12 \]The expression becomes: \(4 - 3 + 12\)
Step 3.3: Perform Subtraction and Addition from left to right.
First, subtraction:
\[ 4 - 3 = 1 \]The expression becomes: \(1 + 12\)
Finally, addition:
\[ 1 + 12 = 13 \]Correct Option: D) 13
After interchanging the operators and performing the calculations according to the order of operations, the final value of the expression is 13.
If the perimeters of two similar triangles ABC and DEF are 75 cm and 40 cm respectively, and if BC is 15 cm, then the length of \(\overline{EF}\) is:
When two triangles are similar, the ratio of their corresponding sides is equal to the ratio of their perimeters. We will use this property to find the length of the unknown side.
Given that triangle ABC is similar to triangle DEF (denoted as \(\triangle ABC \sim \triangle DEF\)).
The perimeter of \(\triangle ABC\) is 75 cm.
The perimeter of \(\triangle DEF\) is 40 cm.
The length of side BC in \(\triangle ABC\) is 15 cm.
For similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides. Therefore:
\[ \frac{\text{Perimeter of } \triangle ABC}{\text{Perimeter of } \triangle DEF} = \frac{BC}{EF} \]Substitute the given values into the formula:
\[ \frac{75}{40} = \frac{15}{EF} \]Now, solve for EF:
\[ 75 \times EF = 40 \times 15 \] \[ 75 \times EF = 600 \] \[ EF = \frac{600}{75} \] \[ EF = 8 \text{ cm} \]Correct Option: D) 8 cm
Which of the following formulas is used to calculate the volume by volume percentage of a solution?
=\(\frac{\text{Mass of solute}}{\text{Volume of solution}}\times100\)
=\(\frac{\text{Mass of solute}}{\text{Mass of solution}}\times100\)
=\(\frac{\text{Volume of solute}}{\text{Volume of solution}}\times100\)
=\(\frac{\text{Volume of solution}}{\text{Mass of solute}}\times100\)
The question asks for the formula to calculate the volume by volume percentage of a solution. This is a common way to express the concentration of a solution, especially when both the solute and solvent are liquids.
C) =\[\frac{\text{Volume of solute}}{\text{Volume of solution}}\times100\] This formula correctly represents the volume by volume percentage, which is the ratio of the volume of the solute to the total volume of the solution, expressed as a percentage.
This problem involves projectile motion under gravity. When a ball is thrown vertically upwards, its initial kinetic energy is converted into potential energy as it rises, and its velocity decreases due to gravity. At the maximum height, its final velocity becomes zero. We can use the third equation of motion to relate the initial velocity, final velocity, acceleration due to gravity, and the height achieved.
The third equation of motion relates initial velocity (\(u\)), final velocity (\(v\)), acceleration (\(a\)), and displacement (\(h\)):
\[ v^2 = u^2 + 2ah \]Here, \(v = 0\), \(a = -g = -10 \text{ m/s}^2\), and \(h = 20 \text{ m}\).
\[ 0^2 = u^2 + 2(-10)(20) \]Correct Option: A) 20 m/s is the initial velocity of the ball.
The question asks to identify the political party of HD Kumaraswamy, who won the Mandya parliamentary seat in the 2024 general elections and became the Minister of Heavy Industries. This is a factual question related to current political affairs in India.
Correct Option: B) Janata Dal (S)
To find the majority by which the winner won, we first need to calculate the total number of valid votes. Then, we determine the number of votes each candidate received based on the percentage of valid votes. Finally, the difference between their votes will give us the winning majority.
Given that 20% of the total votes were invalid, we calculate the number of invalid votes from the total number of votes.
\[ \text{Total votes} = 7500 \] \[ \text{Invalid votes} = 20\% \text{ of } 7500 = \frac{20}{100} \times 7500 = 20 \times 75 = 1500 \]The number of valid votes is the total votes minus the invalid votes.
\[ \text{Valid votes} = \text{Total votes} - \text{Invalid votes} \] \[ \text{Valid votes} = 7500 - 1500 = 6000 \]The winner received 55% of the total valid votes.
\[ \text{Winner's votes} = 55\% \text{ of } 6000 = \frac{55}{100} \times 6000 = 55 \times 60 = 3300 \]Since there are only two candidates, the loser received the remaining percentage of valid votes, which is \(100\% - 55\% = 45\%\).
\[ \text{Loser's votes} = 45\% \text{ of } 6000 = \frac{45}{100} \times 6000 = 45 \times 60 = 2700 \]The majority is the difference between the winner's votes and the loser's votes.
\[ \text{Majority} = \text{Winner's votes} - \text{Loser's votes} \] \[ \text{Majority} = 3300 - 2700 = 600 \]Correct Option: C) 600
The question asks to identify the cup-shaped part of the nephron that is associated with a capillary cluster in the kidney. This requires knowledge of the basic structure and function of a nephron, the functional unit of the kidney.
B) Bowman's capsule is the cup-shaped structure that encloses the glomerulus, which is a network of capillaries. This is where the first step of blood filtration in the kidney takes place.
This problem involves calculating the total number of valid votes based on the percentage of votes secured by one candidate and the majority by which they won. We will set up an equation where the difference in vote percentages corresponds to the majority votes, and then solve for the total number of valid votes.
Let the total number of valid votes be \(V\).
The winning candidate secured 70% of the valid votes. So, the votes for the winning candidate are \(0.70V\).
Since there are only two candidates, the losing candidate secured the remaining percentage of valid votes. Percentage of votes for the losing candidate \( = 100\% - 70\% = 30\%\).
So, the votes for the losing candidate are \(0.30V\).
The winning candidate won by a majority of 172 votes. This means the difference between the votes of the winning candidate and the losing candidate is 172.
\[ 0.70V - 0.30V = 172 \]Simplify the equation:
\[ 0.40V = 172 \]Solve for \(V\):
\[ V = \frac{172}{0.40} \]\[ V = \frac{172}{\frac{40}{100}} \]\[ V = \frac{172 \times 100}{40} \]\[ V = \frac{17200}{40} \]\[ V = 430 \]Therefore, the total number of valid votes was 430.
C) 430 is the correct answer. This is derived by calculating that 40% of the total valid votes (the difference between 70% and 30%) equals 172, leading to a total of 430 votes.
A) 570 — This value is incorrect. If the total votes were 570, then 40% of 570 would be \(0.40 \times 570 = 228\), which is not 172.
B) 560 — This value is incorrect. If the total votes were 560, then 40% of 560 would be \(0.40 \times 560 = 224\), which is not 172.
D) 480 — This value is incorrect. If the total votes were 480, then 40% of 480 would be \(0.40 \times 480 = 192\), which is not 172.