This problem involves calculating an unknown resistance in a series circuit. When resistors are connected in series, their total (net) resistance is the sum of individual resistances. We are given the net resistance and one of the individual resistances. We can use the formula for series resistance to find the other resistance. The information about the current flowing through them (4 amp) is extra information and not needed to solve for the resistance values.
Identify the given information:
Recall the formula for resistors in series:
When two resistors, \(R_1\) and \(R_2\), are connected in series, their net (total) resistance \(R_{\text{net}}\) is given by:
\[ R_{\text{net}} = R_1 + R_2 \]Substitute the known values into the formula:
We know \(R_{\text{net}} = 6 \, \Omega\) and \(R_1 = 2 \, \Omega\). We need to find \(R_2\).
\[ 6 \, \Omega = 2 \, \Omega + R_2 \]Solve for the unknown resistance \(R_2\):
Subtract \(2 \, \Omega\) from both sides of the equation:
\[ R_2 = 6 \, \Omega - 2 \, \Omega \] \[ R_2 = 4 \, \Omega \]A) 4 ohm. The calculated value for the other resistance is \(4 \, \Omega\).
To determine which compound can conduct electricity, we need to understand the fundamental requirements for electrical conductivity. Electrical conductivity in a substance typically requires the presence of mobile charge carriers, such as free electrons or ions.
Correct Option: C) Sodium chloride
Identify 'X' and 'Y' products respectively, in the given chemical equation.
NaOH + CH3COOH → 'X' + 'Y'
CH3COONa and H2O
NaO and CO2
Na2OH and CO2
CH3CO2H and Na(OH)2
The given chemical equation represents a reaction between a base (sodium hydroxide) and an acid (acetic acid). This is a classic acid-base neutralization reaction, which typically produces a salt and water. We need to identify the specific salt and water formed from these reactants.
A) \(\text{CH}_3\text{COONa}\) and \(\text{H}_2\text{O}\) are the products formed when sodium hydroxide reacts with acetic acid, representing the salt (sodium acetate) and water, respectively. This aligns perfectly with the principles of an acid-base neutralization reaction.
To find the gain percentage, we first need to determine the cost price (CP) and the gain amount. The problem provides the selling price (SP) and states that the gain is one-fifth of the selling price. Using these values, we can calculate the cost price and then the gain percentage.
Identify the Selling Price (SP):
The selling price of the scooter is given as ₹15,000.
\[ \text{SP} = \text{₹}15,000 \]Calculate the Gain:
The problem states that the gain is one-fifth of the selling price.
\[ \text{Gain} = \frac{1}{5} \times \text{SP} \]\[ \text{Gain} = \frac{1}{5} \times \text{₹}15,000 \]\[ \text{Gain} = \text{₹}3,000 \]Calculate the Cost Price (CP):
The relationship between selling price, cost price, and gain is:
\[ \text{SP} = \text{CP} + \text{Gain} \]Rearranging to find CP:
\[ \text{CP} = \text{SP} - \text{Gain} \]\[ \text{CP} = \text{₹}15,000 - \text{₹}3,000 \]\[ \text{CP} = \text{₹}12,000 \]Calculate the Gain Percentage:
The gain percentage is calculated with respect to the cost price:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100\% \]\[ \text{Gain Percentage} = \left( \frac{\text{₹}3,000}{\text{₹}12,000} \right) \times 100\% \]\[ \text{Gain Percentage} = \left( \frac{1}{4} \right) \times 100\% \]\[ \text{Gain Percentage} = 25\% \]Correct Option: D) 25%
The question asks to identify which of the given options is NOT a source of formal data on unemployment in India. We need to evaluate each option based on its primary function and the type of data it collects.
Correct Option: C) Reports of National Family Health Survey
The question asks for the definition of "Mango showers." This is a geographical term related to weather phenomena in India. We need to identify the correct description of these showers, including their timing and common regions.
Correct Option: B) pre-monsoon showers which are common in the states of Karnataka and Kerala
Six boxes M, N, O, P, Q and R are kept one above the other but not necessarily in the same order. Only 2 boxes are kept below M. Only one box is kept above Q. O is kept at any of the positions above R but not at the topmost position. R is not kept at the bottom most position. N is kept at any of positions below Q. Where is box P kept?
2nd from the bottom
3rd from the top
At the topmost position
3rd from the bottom
This is a linear arrangement puzzle where six boxes are stacked one above the other. We need to deduce the exact position of each box based on the given clues and then identify the position of box P.
Total boxes: There are 6 boxes. Let's number the positions from bottom to top as 1 to 6.
Clue 1: Only 2 boxes are kept below M.
This means M is at the 3rd position from the bottom (Position 3).
Position 6: Position 5: Position 4: Position 3: M Position 2: Position 1:
Clue 2: Only one box is kept above Q.
This means Q is at the 5th position from the bottom (Position 5).
Position 6: Position 5: Q Position 4: Position 3: M Position 2: Position 1:
Clue 3: R is not kept at the bottommost position.
This means R is not at Position 1.
Clue 4: N is kept at any of positions below Q.
Q is at Position 5. So, N can be at Position 1, 2, 3, or 4. Since M is at Position 3, N can be at Position 1, 2, or 4. We will use this later.
Clue 5: O is kept at any of the positions above R but not at the topmost position.
The topmost position is Position 6. So, O is not at Position 6. Also, O is above R.
Combining clues for R and O:
R is not at Position 1. O is not at Position 6. O is above R.
Let's consider the remaining empty slots: Positions 1, 2, 4, 6.
From Clue 4, N is below Q (Position 5), so N can be at 1, 2, or 4.
If N is at Position 4, then R cannot be at Position 4 (as O is above R). This would leave R at Position 1 or 2. But R cannot be at Position 1. So R must be at Position 2. If R is at Position 2, O must be above R and not at Position 6. The only position above R (Position 2) and below Q (Position 5) is Position 4. So O is at Position 4.
Position 6: Position 5: Q Position 4: O Position 3: M Position 2: R Position 1:
Placing N: N must be below Q. The only remaining position below Q is Position 1.
Position 6: Position 5: Q Position 4: O Position 3: M Position 2: R Position 1: N
Placing P: The only box left is P, and the only position left is Position 6.
Position 6: P Position 5: Q Position 4: O Position 3: M Position 2: R Position 1: N
Final check:
- Only 2 boxes below M (R, N) - Correct.
- Only 1 box above Q (P) - Correct.
- O is above R (O at 4, R at 2) and not topmost - Correct.
- R is not at bottommost - Correct.
- N is below Q (N at 1, Q at 5) - Correct.
Box P is at the topmost position.
C) At the topmost position — As determined in the step-by-step solution, P is at Position 6, which is the topmost position.
The question asks to identify the country that won the Thomas Cup for the first time in 2022. This requires knowledge of recent major sporting event outcomes, specifically in badminton.
Correct Option: A) India
P, Q, R, S and T live on five different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 5. P lives immediately below T and immediately above S. P lives on an odd numbered floor. If R is not on the lowermost floor, where does T live?
This is a logical reasoning problem involving arrangement. We need to deduce the floor on which T lives by using the given clues about the relative positions of P, Q, R, S, and T on a five-story building.
Correct Option: D) 4 th floor
Match the cities in column-A with the rivers in column-B.
| Column-A (City) | Column-B (River) |
| a. Ahmedabad | 1. Godavari |
| b. Kolkata | 2. Brahmaputra |
| c. Guwahati | 3. Sabarmati |
| d. Nasik | 4. Hooghly |
a-4, b-3, c-1, d-2
a-3, b-4, c-2, d-1
a-4, b-3, c-2, d-1
a-1, b-2, c-3, d-4
To answer this question, we need to match each city with the river it is located on. This requires knowledge of Indian geography, specifically the major cities and the rivers flowing through them.
Combining these matches, we get: a-3, b-4, c-2, d-1.
Correct Option: B) a-3, b-4, c-2, d-1