Consider two circuits, A and B, each of which has six resistors, and each resistor in the circuits has resistance RA and RB, respectively. In each circuit, the resistors are arranged in such a way that the net resistance of each circuit is minimum. Now, a 20 V battery with negligible internal resistance is connected across each circuit separately, and the currents drawn by circuits A and B are 6 A and 8 A, respectively. Then RA and RB will be:
RA=15 Ω and RB=20 Ω
RA=20 Ω and RB=15 Ω
RA=30 Ω and RB=15 Ω
RA=15 Ω and RB=30 Ω
To find the resistance of each resistor in circuits A and B, we first need to determine the equivalent resistance of each circuit. The problem states that the resistors are arranged to achieve minimum net resistance. This occurs when all resistors are connected in parallel. We will use Ohm's Law to relate voltage, current, and equivalent resistance, and then use the formula for parallel resistors to find the individual resistance values.
Determine the arrangement for minimum net resistance: For a given set of resistors, the minimum net resistance is achieved when all resistors are connected in parallel. Since each circuit has six resistors, and each resistor in circuit A has resistance \(R_A\), and in circuit B has resistance \(R_B\), we can calculate the equivalent resistance for parallel connection.
Calculate equivalent resistance for circuit A (\(R_{eq,A}\)): When six resistors of resistance \(R_A\) are connected in parallel, the equivalent resistance is given by:
\[ \frac{1}{R_{eq,A}} = \frac{1}{R_A} + \frac{1}{R_A} + \frac{1}{R_A} + \frac{1}{R_A} + \frac{1}{R_A} + \frac{1}{R_A} = \frac{6}{R_A} \] \[ R_{eq,A} = \frac{R_A}{6} \]Calculate equivalent resistance for circuit B (\(R_{eq,B}\)): Similarly, for six resistors of resistance \(R_B\) connected in parallel:
\[ \frac{1}{R_{eq,B}} = \frac{6}{R_B} \] \[ R_{eq,B} = \frac{R_B}{6} \]Apply Ohm's Law for circuit A: Given voltage \(V = 20 \text{ V}\) and current \(I_A = 6 \text{ A}\). According to Ohm's Law, \(V = I_A \cdot R_{eq,A}\).
\[ 20 \text{ V} = 6 \text{ A} \cdot R_{eq,A} \] \[ R_{eq,A} = \frac{20}{6} = \frac{10}{3} \, \Omega \]Find \(R_A\): Using the relation from step 2:
\[ \frac{R_A}{6} = \frac{10}{3} \] \[ R_A = 6 \cdot \frac{10}{3} = 2 \cdot 10 = 20 \, \Omega \]Apply Ohm's Law for circuit B: Given voltage \(V = 20 \text{ V}\) and current \(I_B = 8 \text{ A}\). According to Ohm's Law, \(V = I_B \cdot R_{eq,B}\).
\[ 20 \text{ V} = 8 \text{ A} \cdot R_{eq,B} \] \[ R_{eq,B} = \frac{20}{8} = \frac{5}{2} \, \Omega \]Find \(R_B\): Using the relation from step 3:
\[ \frac{R_B}{6} = \frac{5}{2} \] \[ R_B = 6 \cdot \frac{5}{2} = 3 \cdot 5 = 15 \, \Omega \]Therefore, \(R_A = 20 \, \Omega\) and \(R_B = 15 \, \Omega\).
Correct Option: B) R A =20 Ω and R B =15 Ω
This is a question based on Syllogism. We need to analyze the given statements and derive conclusions using Venn diagrams or logical deduction. We will draw Venn diagrams for each statement and then check if the conclusions logically follow from these diagrams.
This means that the set of 'jugs' is entirely contained within the set of 'cans'.
Diagram:
This means that the set of 'cans' is entirely contained within the set of 'engines'.
Combining with the previous diagram:
Current hierarchy: Jugs \(\subset\) Cans \(\subset\) Engines.
This means there is an overlap between the set of 'jugs' and the set of 'stoves'.
Combining with the previous diagram:
Since Jugs are inside Cans, and Cans are inside Engines, any 'jug' that is a 'stove' must also be a 'can' and an 'engine'.
From the combined diagram, we know that some 'jugs' are 'stoves'. Since all 'jugs' are 'cans' and all 'cans' are 'engines', it implies that those 'jugs' which are 'stoves' are also 'engines'. Therefore, there is an overlap between 'engines' and 'stoves'. This conclusion logically follows.
The statement "All jugs are cans" means that every jug is also a can. This inherently implies that there are some cans that are jugs (specifically, all the jugs are cans, so the cans that are jugs are the jugs themselves). This conclusion logically follows.
B) Both conclusions I and II follow.
As explained in the step-by-step analysis, both Conclusion I ("Some engines are stoves") and Conclusion II ("Some cans are jugs") can be logically deduced from the given statements.
The question asks to identify which function among the given options does NOT fall under the jurisdiction of local bodies in India. Local bodies, such as Panchayats and Municipalities, are responsible for local governance and administration of specific services as defined by the Constitution (73rd and 74th Amendment Acts).
Correct Option: B) Law and Order — Maintaining law and order, including policing, is a primary responsibility of the State Government, not local bodies. Local bodies are concerned with local governance and civic amenities, not the enforcement of criminal law or maintaining public order directly through police forces.
The question asks to identify the Indian state where the 'Solung' festival is celebrated. This requires knowledge of the cultural festivals of different Indian states, a common topic in general knowledge sections of competitive exams.
Correct Option: A) Arunachal Pradesh is the correct answer because the Solung festival is a major agricultural festival of the Adi tribe, who are indigenous to Arunachal Pradesh. It is celebrated to seek a good harvest, prosperity, and protection from evil spirits.
Seven friends, Chandan, Aman, Falak, Manoj, Mahima, Bony and Fatima, are standing in a line facing east but not necessarily in the same order. Chandan is to the immediate right of Fatima. Fatima is fourth to the right of Falak. Manoj is an immediate neighbour of both Aman and Bony. Falak, who is third to the left of Aman, is standing at one of the extreme ends.
What is the correct position of Mahima?
To the immediate left of Bony
Immediate neighbour of Bony and Fatima
To the immediate left of Chandan
Fourth to the right of Manoj
This is a linear arrangement puzzle. We need to deduce the exact positions of seven friends (Chandan, Aman, Falak, Manoj, Mahima, Bony, and Fatima) standing in a line facing East based on the given clues. We will build the arrangement step-by-step, starting with the most definitive clues.
Clue 1: Falak, who is third to the left of Aman, is standing at one of the extreme ends.
Since they are facing East, 'left' means to the North and 'right' means to the South. If Falak is at an extreme end and is third to the left of Aman, Falak must be at the leftmost end. Let's represent the positions from left to right as 1 to 7.
Arrangement so far:
\[ \text{Falak} \quad \_ \quad \_ \quad \text{Aman} \quad \_ \quad \_ \quad \_ \]
Positions: \(\text{1} \quad \text{2} \quad \text{3} \quad \text{4} \quad \text{5} \quad \text{6} \quad \text{7}\)
Clue 2: Fatima is fourth to the right of Falak.
Starting from Falak at position 1, the fourth position to the right is position 5.
Arrangement so far:
\[ \text{Falak} \quad \_ \quad \_ \quad \text{Aman} \quad \text{Fatima} \quad \_ \quad \_ \]
Positions: \(\text{1} \quad \text{2} \quad \text{3} \quad \text{4} \quad \text{5} \quad \text{6} \quad \text{7}\)
Clue 3: Chandan is to the immediate right of Fatima.
If Fatima is at position 5, Chandan must be at position 6.
Arrangement so far:
\[ \text{Falak} \quad \_ \quad \_ \quad \text{Aman} \quad \text{Fatima} \quad \text{Chandan} \quad \_ \]
Positions: \(\text{1} \quad \text{2} \quad \text{3} \quad \text{4} \quad \text{5} \quad \text{6} \quad \text{7}\)
Clue 4: Manoj is an immediate neighbour of both Aman and Bony.
This means Manoj is between Aman and Bony. From our current arrangement, Aman is at position 4. The only available position next to Aman is position 3. So, Manoj must be at position 3, and Bony must be at position 2.
Arrangement so far:
\[ \text{Falak} \quad \text{Bony} \quad \text{Manoj} \quad \text{Aman} \quad \text{Fatima} \quad \text{Chandan} \quad \_ \]
Positions: \(\text{1} \quad \text{2} \quad \text{3} \quad \text{4} \quad \text{5} \quad \text{6} \quad \text{7}\)
Final Arrangement:
All friends except Mahima have been placed. The only remaining position is 7. Therefore, Mahima must be at position 7.
Final arrangement:
\[ \text{Falak} \quad \text{Bony} \quad \text{Manoj} \quad \text{Aman} \quad \text{Fatima} \quad \text{Chandan} \quad \text{Mahima} \]
Positions: \(\text{1} \quad \text{2} \quad \text{3} \quad \text{4} \quad \text{5} \quad \text{6} \quad \text{7}\)
Check Mahima's position:
Mahima is at position 7. Let's evaluate the given options.
D) Fourth to the right of Manoj
The number 0.3\(\overline{35}\) can be represented in the form of \( \frac{p}{q} \)
(where p and q are natural numbers) as:
\(\frac{332}{895}\)
\(\frac{332}{990}\)
\(\frac{332}{995}\)
\(\frac{332}{980}\)
To convert a recurring decimal into a fraction of the form \( \frac{p}{q} \), we follow a standard algebraic method. We assign the decimal to a variable, multiply it by powers of 10 to align the repeating part, and then subtract the equations to eliminate the repeating decimal.
Correct Option: B) \( \frac{332}{990} \)
The question asks about the product formed during a precipitation reaction. We need to understand the definition of a precipitation reaction and the nature of the product formed.
A) an insoluble ionic solid
Precipitation reactions are defined by the formation of an insoluble solid, known as a precipitate, when two aqueous solutions are mixed. This solid is an ionic compound.
We are given the discount percentage, profit percentage, and the absolute profit amount. We need to find the marked price. We can use the relationships between Cost Price (CP), Selling Price (SP), Marked Price (MP), discount, and profit to solve this problem.
C) Rs 12,000 is the correct answer. We calculated the Cost Price using the profit amount and percentage, then found the Selling Price, and finally used the discount percentage to determine the Marked Price.
The question asks to identify the sportsperson who received the Padma Bhushan award in 2022 among the given options. This requires knowledge of recent national awards conferred upon prominent Indian athletes.
Correct Option: B) Devendra Jhajharia
Devendra Jhajharia is a Paralympic javelin thrower who has won multiple medals, including two gold medals at the Paralympics. He was honored with the Padma Bhushan in 2022, making him the first para-athlete to receive India's third-highest civilian award.
The problem involves calculating the simple interest rate based on a loan with partial repayment. We need to track the principal amount and the interest accumulated over different time periods. The key is to understand that simple interest is calculated on the original principal for the entire duration or on the outstanding principal for each period.
Initial Loan Amount:
Let the principal borrowed be \(P = \text{Rs } 7,000\).
Interest for the first 3 years:
Let the rate of interest be \(R\%\) per annum.
Simple Interest for 3 years, \(I_1 = \frac{P \times R \times T_1}{100}\)
\[ I_1 = \frac{7000 \times R \times 3}{100} = 210R \]Amount due after 3 years:
Amount due = Principal + Interest = \(7000 + 210R\).
Payment after 3 years:
Johnny pays Rs 4,000. This amount is adjusted as repayment of part of the principal borrowed. This implies that the interest accumulated till this point is still outstanding, and the payment reduces the principal amount for future interest calculations.
Outstanding Principal after 3 years = Original Principal - Payment
\[ P' = 7000 - 4000 = 3000 \]Interest for the next 2 years (from year 3 to year 5):
The remaining period is \(5 - 3 = 2\) years.
The interest for this period will be calculated on the outstanding principal \(P' = 3000\).
Simple Interest for the next 2 years, \(I_2 = \frac{P' \times R \times T_2}{100}\)
\[ I_2 = \frac{3000 \times R \times 2}{100} = 60R \]Total amount to be paid to settle the account:
At the end of 5 years, Johnny pays Rs 4,350 to settle the account. This amount must cover the outstanding principal and all accumulated interest.
Total amount to settle = Outstanding Principal + Total Interest
Total Interest = Interest for first 3 years + Interest for next 2 years
\[ \text{Total Interest} = I_1 + I_2 = 210R + 60R = 270R \]Formulate the equation:
The amount paid to settle the account (Rs 4,350) must be equal to the outstanding principal (Rs 3,000) plus the total interest accumulated (Rs \(270R\)).
\[ 4350 = 3000 + 270R \]Solve for R:
\[ 270R = 4350 - 3000 \]\[ 270R = 1350 \]\[ R = \frac{1350}{270} \]\[ R = 5 \]The rate of interest is \(5\%\).
D) 5 % is the correct rate of interest calculated based on the simple interest method and the given repayment schedule.