This is a blood relation problem. We need to deduce the relationships between individuals based on the given statements. It's helpful to draw a family tree or list the relationships step-by-step to avoid confusion.
Based on these deductions, E is the paternal uncle of A.
D) Paternal uncle — As established, E is the brother of A's father, making him A's paternal uncle.
A piece of wire is bent to form a circle with a radius of 70 cm. If the same piece of wire is bent to form a square, the length of the side of the square will be ______. [Use π = \( \frac{22}{7} \)]
The problem states that a piece of wire is first bent into a circle and then into a square. The key concept here is that the length of the wire remains constant. Therefore, the circumference of the circle will be equal to the perimeter of the square. We need to calculate the circumference of the circle using the given radius and then equate it to the perimeter of the square to find the side length of the square.
Given the radius of the circle, \(r = 70 \text{ cm}\).
The formula for the circumference of a circle is \(C = 2 \pi r\).
Using the given value of \( \pi = \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 70 \text{ cm} \]\[ C = 2 \times 22 \times 10 \text{ cm} \]\[ C = 440 \text{ cm} \]Since the same piece of wire is used, the length of the wire is \(440 \text{ cm}\). When this wire is bent into a square, its length becomes the perimeter of the square.
Let the side length of the square be \(s\).
The formula for the perimeter of a square is \(P = 4s\).
Therefore,
\[ 4s = 440 \text{ cm} \]To find \(s\), divide the perimeter by 4:
\[ s = \frac{440}{4} \text{ cm} \]\[ s = 110 \text{ cm} \]Thus, the length of the side of the square will be \(110 \text{ cm}\).
Correct Option: B) 110 cm
The question asks to identify which human organ's function is mimicked by a dialyser, a machine used to clean a patient's blood. This requires knowledge of basic human physiology and the function of medical devices like dialysers.
D) kidney — A dialyser performs the vital function of filtering waste products and excess fluid from the blood, a role that is naturally carried out by the kidneys. Hence, it is often referred to as an artificial kidney.
If the selling price of an article is \( \frac{5}{4} \) of its cost price, then the profit obtained in the transaction is:
To find the profit percentage, we need to first determine the profit amount. The profit is the difference between the selling price (SP) and the cost price (CP). The problem states that the selling price is a fraction of the cost price. We can express this relationship algebraically and then calculate the profit percentage using the standard formula.
Let the Cost Price of the article be \( \text{CP} \).
According to the problem statement, the Selling Price (SP) is \( \frac{5}{4} \) of its Cost Price.
\[ \text{SP} = \frac{5}{4} \times \text{CP} \]The Profit (P) is calculated as the difference between the Selling Price and the Cost Price:
\[ \text{Profit} = \text{SP} - \text{CP} \]Substitute the expression for SP from step 2 into the profit formula:
\[ \text{Profit} = \frac{5}{4} \text{CP} - \text{CP} \]\[ \text{Profit} = \left( \frac{5}{4} - 1 \right) \text{CP} \]\[ \text{Profit} = \left( \frac{5-4}{4} \right) \text{CP} \]\[ \text{Profit} = \frac{1}{4} \text{CP} \]Now, calculate the Profit Percentage. The formula for Profit Percentage is:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100\% \]Substitute the value of Profit from step 4 into the formula:
\[ \text{Profit Percentage} = \left( \frac{\frac{1}{4} \text{CP}}{\text{CP}} \right) \times 100\% \]\[ \text{Profit Percentage} = \left( \frac{1}{4} \right) \times 100\% \]\[ \text{Profit Percentage} = 25\% \]Thus, the profit obtained in the transaction is 25%.
Correct Option: D) 25%
The question asks to identify which of the given Public Sector Undertakings (PSUs) was NOT a Navratna company as of 2021. This requires knowledge of the classification of PSUs in India, specifically the Navratna status.
Correct Option: B) Oil & Natural Gas Corporation Limited
The question asks for the headquarters of the North Atlantic Treaty Organisation (NATO). This is a factual question requiring knowledge of international organizations and their locations.
Correct Option: B) Brussels is the correct answer. The headquarters of the North Atlantic Treaty Organisation (NATO) is located in Brussels, Belgium.
We are given the percentage of students who passed and the number of students who failed. We need to find the total number of students who appeared for the examination. We can determine the percentage of students who failed and then use this percentage along with the given number of failed students to calculate the total number of students.
The total percentage of students is 100%. If 90% passed, then the percentage of students who failed is:
\[ \text{Percentage of failed students} = 100\% - \text{Percentage of passed students} \] \[ \text{Percentage of failed students} = 100\% - 90\% = 10\% \]We are given that 600 students failed. This number corresponds to 10% of the total students who appeared for the examination.
Let \(T\) be the total number of students who appeared for the examination.
\[ 10\% \text{ of } T = 600 \]To find \(T\), we can set up the equation:
\[ \frac{10}{100} \times T = 600 \]Now, solve for \(T\):
\[ T = 600 \times \frac{100}{10} \] \[ T = 600 \times 10 \] \[ T = 6000 \]So, 6000 students appeared for the examination.
C) 6000 is the correct answer. This matches our calculation that 600 students represent 10% of the total, leading to a total of 6000 students.
This is a blood relation problem. We need to deduce the relationships between the given entities based on the statements provided and then find the relationship between Pancreas and Lungs. We can use a diagram or list the relationships to solve this.
From step 5, we have established that Pancreas is the brother of Lungs.
D) Brother — As deduced, Pancreas is the maternal uncle of Kidney, and Lungs is Kidney's mother. Therefore, Pancreas is the brother of Lungs.
The question asks about the historical event that led to the termination of a major Indian independence movement. We need to identify which movement was directly affected by the Chauri Chaura incident.
Correct Option: B) The Chauri Chaura incident, a violent clash between protestors and police in February 1922, directly led Mahatma Gandhi to call off the Non-Cooperation Movement, which he had launched in 1920. Gandhi was deeply disturbed by the violence, as it went against his core principle of non-violent resistance (Satyagraha).
To find the cost price, we need to understand the relationship between selling price, cost price, and loss percentage. If an item is sold at a loss, the selling price is less than the cost price. The loss percentage is calculated on the cost price.
Let the Cost Price (CP) of the gold ring be \(P\).
The Selling Price (SP) is given as ₹17,500.
The loss percentage is 30%.
The formula for selling price when there is a loss is:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss Percentage}}{100}\right) \]Substitute the given values into the formula:
\[ 17,500 = P \times \left(1 - \frac{30}{100}\right) \]Simplify the expression:
\[ 17,500 = P \times \left(1 - 0.30\right) \] \[ 17,500 = P \times 0.70 \]Now, solve for \(P\) (Cost Price):
\[ P = \frac{17,500}{0.70} \] \[ P = \frac{17,500}{\frac{7}{10}} \] \[ P = 17,500 \times \frac{10}{7} \]Perform the division:
\[ P = 2,500 \times 10 \] \[ P = 25,000 \]So, the cost price of the gold ring is ₹25,000.
Correct Option: B) ₹25,000