The problem asks how power changes when current and potential difference are tripled, while resistance remains constant. We need to use the formula for electrical power that relates current and potential difference.
Electrical power (\(P\)) in a circuit can be expressed as the product of potential difference (\(V\)) and current (\(I\)).
\[ P = V \times I \]Let the initial potential difference be \(V_1\) and the initial current be \(I_1\). The initial power will be:
\[ P_1 = V_1 \times I_1 \]According to the problem, the current is tripled, so the new current \(I_2 = 3I_1\). The potential difference is also tripled, so the new potential difference \(V_2 = 3V_1\).
Substitute the new values of potential difference and current into the power formula:
\[ P_2 = V_2 \times I_2 \]\[ P_2 = (3V_1) \times (3I_1) \]\[ P_2 = 9 \times (V_1 \times I_1) \]From step 2, we know that \(P_1 = V_1 \times I_1\). Substituting this into the equation from step 4:
\[ P_2 = 9 \times P_1 \]The new power \(P_2\) is nine times the initial power \(P_1\). Therefore, the power will increase nine fold.
D) Nine fold. As derived, when both current and potential difference are tripled, the power becomes \(3V \times 3I = 9VI\), which is nine times the original power.
To determine if a number is divisible by 8, we use a divisibility rule. A number is divisible by 8 if the number formed by its last three digits is divisible by 8. This rule simplifies the process as we only need to check a smaller part of the number.
D) 1246864 is divisible by 8 because its last three digits, 864, are divisible by 8 (\(864 \div 8 = 108\)).
What is the mode of the data given below? (Give your answer correct to 2 decimal places.)
| Age in years | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 | 75-85 |
| No. of patients | 12 | 18 | 20 | 25 | 30 | 20 | 15 |
To find the mode for grouped data, we first identify the modal class, which is the class interval with the highest frequency. Then, we use the formula for calculating the mode of grouped data.
A) 58.33 is the correct mode calculated using the formula for grouped data.
This problem involves tracking directional movements. We need to visualize Sapna's path and her orientation at each turn to determine the final direction she was facing when she reached home.
D) North — Based on the step-by-step analysis, after her final left turn, Sapna was facing North when she reached home.
To find the internal surface area of an open cuboidal tank, we need to calculate the area of its four walls and its base. Since the tank is open, it does not have a top surface. The formula for the surface area of the four walls is \(2h(l+b)\) and the area of the base is \(lb\). We will sum these two areas.
The formula for the area of the four walls of a cuboid is \(2h(l+b)\).
\[ \text{Area of walls} = 2 \times 3 \times (6 + 4) \\ \text{Area of walls} = 6 \times 10 \\ \text{Area of walls} = 60 \text{ m}^2 \]The formula for the area of the base of a cuboid is \(l \times b\).
\[ \text{Area of base} = 6 \times 4 \\ \text{Area of base} = 24 \text{ m}^2 \]Since the tank is open, the total internal surface area is the sum of the area of the four walls and the area of the base.
\[ \text{Total internal surface area} = \text{Area of walls} + \text{Area of base} \\ \text{Total internal surface area} = 60 \text{ m}^2 + 24 \text{ m}^2 \\ \text{Total internal surface area} = 84 \text{ m}^2 \]The total internal surface area of the open cuboidal tank is 84 m², which is the sum of the area of its four walls and its base.
This problem involves ratios. We are given the ratio of manganese to aluminium in an alloy and the quantity of manganese. We need to find the corresponding quantity of aluminium using the given ratio.
The ratio of manganese to aluminium is given as \(2 : 3\). This means for every 2 parts of manganese, there are 3 parts of aluminium.
\[ \frac{\text{Quantity of Manganese}}{\text{Quantity of Aluminium}} = \frac{2}{3} \]We are given that the quantity of manganese is \(24 \text{ kg}\).
Let the unknown quantity of aluminium be \(x \text{ kg}\). We can set up a proportion using the given ratio and the known quantity:
\[ \frac{24 \text{ kg (Manganese)}}{x \text{ kg (Aluminium)}} = \frac{2}{3} \]To find \(x\), we can cross-multiply:
\[ 2 \times x = 24 \times 3 \] \[ 2x = 72 \]Now, divide by 2 to find \(x\):
\[ x = \frac{72}{2} \] \[ x = 36 \]So, the quantity of aluminium required is \(36 \text{ kg}\).
As calculated, \(36 \text{ kg}\) of aluminium is required to be melted with \(24 \text{ kg}\) of manganese to maintain the \(2:3\) ratio.
If the quantity of aluminium were \(12 \text{ kg}\), the ratio would be \(24:12\), which simplifies to \(2:1\). This is not the given ratio of \(2:3\).
If the quantity of aluminium were \(48 \text{ kg}\), the ratio would be \(24:48\), which simplifies to \(1:2\). This is not the given ratio of \(2:3\).
If the quantity of aluminium were \(72 \text{ kg}\), the ratio would be \(24:72\), which simplifies to \(1:3\). This is not the given ratio of \(2:3\).
To determine the net change in revenue, we need to calculate the initial revenue and the final revenue after the price reduction and sales increase. Revenue is calculated as the product of price and quantity sold. We can assume initial values for price and sale (e.g., 100 units each) to simplify calculations and then find the percentage change.
Define Initial Values: Let the initial price of the magazine be \(P = 100\) units. Let the initial sale (number of magazines sold) be \(S = 100\) units.
Calculate Initial Revenue: Initial Revenue \(= P \times S\) Initial Revenue \(= 100 \times 100 = 10000\) units.
Calculate New Price: The price was reduced by 30%. New Price \(= P - (0.30 \times P)\) New Price \(= 100 - (0.30 \times 100) = 100 - 30 = 70\) units.
Calculate New Sale: The sale increased by 70%. New Sale \(= S + (0.70 \times S)\) New Sale \(= 100 + (0.70 \times 100) = 100 + 70 = 170\) units.
Calculate New Revenue: New Revenue \(= \text{New Price} \times \text{New Sale}\) New Revenue \(= 70 \times 170 = 11900\) units.
Calculate the Change in Revenue: Change in Revenue \(= \text{New Revenue} - \text{Initial Revenue}\) Change in Revenue \(= 11900 - 10000 = 1900\) units.
Calculate the Percentage Change in Revenue: Percentage Change \[= \left( \frac{\text{Change in Revenue}}{\text{Initial Revenue}} \right) \times 100\%\] Percentage Change \(= \left( \frac{1900}{10000} \right) \times 100\%\) Percentage Change \(= 0.19 \times 100\% = 19\%\).
Since the change is positive (1900), the revenue increased by 19%.
D) increased by 19%
A) decreased by 20%: This would imply a significant drop in revenue, which is incorrect as the increase in sales was substantial enough to offset the price reduction and lead to an overall increase.
B) increased by 17%: This value is close but not the precise calculation. A small error in calculation could lead to this option.
C) decreased by 19%: This is incorrect because the revenue increased, not decreased. The sign of the change is important.
The question asks to identify the state in India that does not have a Panchayati Raj institution. This requires knowledge of the constitutional provisions regarding Panchayati Raj and the exceptions made for certain states and areas.
Correct Option: B) Meghalaya — The 73rd Constitutional Amendment Act of 1992, which established the Panchayati Raj system, does not apply to the states of Nagaland, Meghalaya, and Mizoram. These states have their own traditional local governance systems.
The problem requires simplifying an algebraic expression involving products of binomials. We can use the algebraic identity \((a-b)(a+b) = a^2 - b^2\) to simplify each term in the given expression and then combine them.
The value of the expression is 0.
Correct Option: C) 0
The question asks to identify the type of bond generally NOT found in carbon compounds. This requires understanding the fundamental bonding characteristics of carbon.
C) ionic bond — Carbon's electronegativity and its tendency to achieve a stable octet by sharing electrons make it primarily a covalent bonding element. Ionic bonds, involving the complete transfer of electrons, are generally not formed by carbon in its typical compounds.