What is the perimeter of a sector of a circle (in cm) if the radius of the circle is 10.5 cm and the angle subtended at the centre of the circle is 60°? (Use π = \( \frac{22}{7} \))
To find the perimeter of a sector of a circle, we need to calculate the length of its arc and add it to the lengths of the two radii that form the sector. The formula for the arc length of a sector is given by \(L = \frac{\theta}{360^{\circ}} \times 2\pi r\), where \(\theta\) is the angle subtended at the centre and \(r\) is the radius. The perimeter of the sector will then be \(L + 2r\).
Correct Option: A) 32
The average price of three items of furniture is Rs 16,875. If their prices are in the ratio 3:5:7, the price of the cheapest item (in Rs) is
To find the price of the cheapest item, we first need to determine the total price of the three items using their average price. Then, we can use the given ratio of their prices to find the individual prices and identify the cheapest one.
Given the average price of three items is Rs 16,875.
\[ \text{Total price} = \text{Average price} \times \text{Number of items} \]\[ \text{Total price} = 16,875 \times 3 \]\[ \text{Total price} = 50,625 \text{ Rs} \]The prices are in the ratio 3:5:7. Let the prices of the three items be \(3x\), \(5x\), and \(7x\) respectively.
The sum of the individual prices must equal the total price.
\[ 3x + 5x + 7x = 50,625 \]\[ 15x = 50,625 \]\[ x = \frac{50,625}{15} \]\[ x = 3,375 \]The cheapest item corresponds to the smallest ratio part, which is \(3x\).
\[ \text{Price of cheapest item} = 3x \]\[ \text{Price of cheapest item} = 3 \times 3,375 \]\[ \text{Price of cheapest item} = 10,125 \text{ Rs} \]C) 10,125 is the price of the cheapest item, calculated as \(3 \times 3,375 = 10,125\).
The question asks about the phenomenon that occurs when light interacts with the surfaces of a prism, specifically when it exits. This involves understanding the basic principles of light propagation through different media.
A) Light is refracted. This is correct because refraction is the bending of light as it passes from one medium to another, which happens both when light enters and exits a prism.
To solve this problem, we will first assume B's salary to be a convenient value, typically 100. Then, we will calculate A's salary based on the given percentage increase. Finally, we will determine the percentage by which B's salary is less than A's salary using the formula for percentage decrease.
Assume B's salary: Let B's salary be \( \$100 \).
Calculate A's salary: Given that A's salary is 37% more than that of B.
\[ \text{A's salary} = \text{B's salary} + 37\% \text{ of B's salary} \] \[ \text{A's salary} = 100 + \left(\frac{37}{100} \times 100\right) \] \[ \text{A's salary} = 100 + 37 = \$137 \]Calculate the difference in salaries: Difference \( = \text{A's salary} - \text{B's salary} = 137 - 100 = \$37 \).
Calculate the percentage by which B's salary is less than A's salary: To find how much percent B's salary is less than A's salary, we use A's salary as the base for comparison.
\[ \text{Percentage less} = \left(\frac{\text{Difference}}{\text{A's salary}} \times 100\right)\% \] \[ \text{Percentage less} = \left(\frac{37}{137} \times 100\right)\% \] \[ \text{Percentage less} \approx (0.27007299 \times 100)\% \] \[ \text{Percentage less} \approx 27.007299\% \]Round to two decimal places: Rounding 27.007299% to two decimal places gives 27.01%.
Correct Option: D) 27.01%
To identify what is being reduced in a redox reaction, we need to determine the oxidation states of each element on both sides of the equation. Reduction is defined as a decrease in oxidation state.
Correct Option: D) Manganese (Mn)
The question asks to identify the Indian athlete who won a gold medal at the Paris Paralympics 2024. This requires knowledge of recent sports achievements, specifically related to the Paralympic Games.
B) Navdeep Singh — Navdeep Singh created history by winning India's first-ever gold medal at the Paris Paralympics 2024. He achieved this feat in the men's javelin throw F41 event with a throw of 43.58 meters, setting a new Paralympic record.
The question asks for the best description of a combination reaction. We need to recall the definitions of different types of chemical reactions and identify which one matches the description of a combination reaction.
Correct Option: C) Two elements combine to form a compound. This statement accurately describes a fundamental characteristic of a combination reaction, where simpler substances (often elements) unite to form a more complex compound.
To find the value of angle B in a quadrilateral, we use the property that the sum of all interior angles of a quadrilateral is 360°. Given the ratio of the angles, we can represent each angle as a multiple of a common factor and then solve for that factor.
Let the four angles of the quadrilateral be \(\angle A\), \(\angle B\), \(\angle C\), and \(\angle D\).
The given ratio of the angles is \(\angle A : \angle B : \angle C : \angle D :: 2 : 3 : 5 : 8\).
Let the common multiple be \(x\). Then the angles can be expressed as:
\[ \angle A = 2x \]\[ \angle B = 3x \]\[ \angle C = 5x \]\[ \angle D = 8x \]The sum of the interior angles of a quadrilateral is 360°.
\[ \angle A + \angle B + \angle C + \angle D = 360^\circ \]Substitute the expressions for the angles into the sum equation:
\[ 2x + 3x + 5x + 8x = 360^\circ \]Combine the terms:
\[ (2 + 3 + 5 + 8)x = 360^\circ \]\[ 18x = 360^\circ \]Solve for \(x\):
\[ x = \frac{360^\circ}{18} \]\[ x = 20^\circ \]Now, calculate the value of \(\angle B\):
\[ \angle B = 3x \]\[ \angle B = 3 \times 20^\circ \]\[ \angle B = 60^\circ \]Correct Option: A) 60° is the correct value for angle B, calculated using the given ratio and the property of quadrilaterals.
Find the simple interest (in closest integral ₹) on ₹3,000 at 8% per annum rate of interest for the period from 25 February 2024 to 26 April 2024
To find the median of a given set of data, we first need to arrange the data in ascending or descending order. Once ordered, the median is the middle value if the number of data points is odd. If the number of data points is even, the median is the average of the two middle values.
14, 14, 29, 40, 48, 50, 51, 73, 76, 78, 89
Position of median \[= \frac{11+1}{2} = \frac{12}{2} = 6^{\text{th}}\] term.
14, 14, 29, 40, 48, 50, 51, 73, 76, 78, 89
Thus, the median of the given data is 50.
Correct Option: D) 50