To find the population in 1950, we need to calculate the population after two successive decades, with each decade experiencing a 95% increase. This is a compound growth problem.
Alternatively, we can use the compound growth formula: \(P_n = P_0 (1 + r)^n\), where \(P_n\) is the population after \(n\) periods, \(P_0\) is the initial population, \(r\) is the growth rate per period, and \(n\) is the number of periods.
In this case, \(P_0 = 3,48,000\), \(r = 0.95\), and \(n = 2\) decades.
\[ P_{1950} = 3,48,000 \times (1 + 0.95)^2 \] \[ P_{1950} = 3,48,000 \times (1.95)^2 \] \[ P_{1950} = 3,48,000 \times 3.8025 \] \[ P_{1950} = 13,23,270 \]Correct Option: B) 13,23,270
The question asks to identify the Princely State that established a representative assembly as early as 1881. This requires knowledge of the administrative and political reforms undertaken by various Indian Princely States during the British Raj.
Correct Option: C) Mysore
The Princely State of Mysore was indeed the first to establish a representative assembly, known as the Mysore Representative Assembly, in 1881. This was a significant step towards modern governance and public participation in administration in an Indian state.
The problem describes a circular arrangement puzzle. We need to deduce the seating arrangement of seven people (A, B, C, D, R, S, T) around a circular table based on the given clues and then determine the number of people between B and R when counted from the left of R.
Initial Setup: There are 7 people around a circular table facing the center. Let's denote the positions as 1 to 7 in a clockwise manner.
Clue 1: T sits to the immediate right of D.
Let's place D at position 1. Then T will be at position 2 (immediate right).
_ _ _ _ _ _ _ | | | D T | | | _ _ _ _ _ _ _
Clue 2: Only three people sit between T and S when counted from the left of T.
Counting from the left of T (anti-clockwise):
If T is at position 2, the people to its left are at positions 1, 7, 6, 5, 4, 3.
Counting 3 people from the left of T: Position 1 (D), Position 7, Position 6. So, S must be at Position 5.
Current arrangement:
D (1), T (2), _ (3), _ (4), S (5), _ (6), _ (7)
_ _ _ _ _ _ _ | | | D T | | S | _ _ _ _ _ _ _
Clue 3: Only three people sit between D and C.
There are 7 people, so if 3 people sit between D and C, it means D and C are opposite to each other (7 - 3 - 1 = 3 people on the other side).
Counting from D's left (anti-clockwise): D (1), _ (7), _ (6), _ (5). So C is at position 4.
Current arrangement:
D (1), T (2), _ (3), C (4), S (5), _ (6), _ (7)
_ _ _ _ _ _ _ | | | D T | | C S | _ _ _ _ _ _ _
Clue 4: A sits to the immediate right of R.
The remaining empty seats are 3, 6, 7. The remaining people are A, B, R.
The only consecutive empty seats are 6 and 7. So, R must be at position 6 and A at position 7 (immediate right of R).
Current arrangement:
D (1), T (2), _ (3), C (4), S (5), R (6), A (7)
_ _ _ _ _ _ _ | A | | D T | | C S | _ _ _ _ R _ _
Final Placement: The last remaining person is B, and the last remaining seat is 3.
Final arrangement:
D (1), T (2), B (3), C (4), S (5), R (6), A (7)
_ _ _ A _ _ | | | D T | | B C S | _ _ _ R _ _
Answer the Question: How many people sit between B and R when counted from the left of R?
R is at position 6. Counting from the left of R (anti-clockwise):
The people to the left of R are S (5), C (4), B (3), T (2), D (1), A (7).
Counting from the left of R until B:
R (6) → S (5) (1st person) → C (4) (2nd person) → B (3).
So, there are two people (S and C) between B and R when counted from the left of R.
B) Two
To solve this problem, we need to calculate the effective capital invested by each person (X, Y, and Z) for the entire year. The profit distribution will be in the ratio of their effective capital investments. We will first determine the initial shares, then adjust for withdrawals, and finally calculate the total investment for each person over the year. Once we have the ratio of their total investments, we can distribute the total profit accordingly.
Assume initial shares: Let the initial shares of X, Y, and Z be \(3k\), \(4k\), and \(10k\) respectively, for some constant \(k\).
Calculate X's investment for the year: Since X did not withdraw any share, X's investment of \(3k\) was for the full 12 months.
\[ \text{X's total investment} = 3k \times 12 = 36k \]Calculate Y's investment for the year: Y invested \(4k\) for the first 6 months. After 6 months, Y withdrew 50% of his share, meaning he withdrew \(0.50 \times 4k = 2k\). So, his remaining share was \(4k - 2k = 2k\). This remaining share was invested for the next \(12 - 6 = 6\) months.
\[ \text{Y's total investment} = (4k \times 6) + (2k \times 6) = 24k + 12k = 36k \]Calculate Z's investment for the year: Z invested \(10k\) initially. Z withdrew 40% of his share 9 months prior to the completion of the year. This means Z withdrew his share after \(12 - 9 = 3\) months. The amount withdrawn was \(0.40 \times 10k = 4k\). So, his remaining share was \(10k - 4k = 6k\). This remaining share was invested for the next \(12 - 3 = 9\) months.
\[ \text{Z's total investment} = (10k \times 3) + (6k \times 9) = 30k + 54k = 84k \]Determine the ratio of total investments: The ratio of X's, Y's, and Z's total investments is:
\[ \text{X} : \text{Y} : \text{Z} = 36k : 36k : 84k \]Divide by \(12k\) to simplify the ratio:
\[ \text{X} : \text{Y} : \text{Z} = 3 : 3 : 7 \]Calculate Z's share in the profit: The total profit at the end of the year is ₹23,400. The sum of the ratio parts is \(3 + 3 + 7 = 13\).
\[ \text{Z's share} = \frac{\text{Z's ratio part}}{\text{Sum of ratio parts}} \times \text{Total profit} \] \[ \text{Z's share} = \frac{7}{13} \times 23,400 \] \[ \text{Z's share} = 7 \times 1,800 \] \[ \text{Z's share} = 12,600 \]A) The share of Z in the profit is ₹12,600, which matches our calculation.
The problem requires us to modify a given number based on specific rules for odd and even digits, then identify two specific digits in the new number, and finally calculate their difference. We will first apply the given rules to each digit of the original number to form the new number. Then, we will locate the second digit from the left and the second digit from the right in this new number and find their difference.
Identify the original number: The given number is 7648135.
Apply the rules to each digit:
Let's process each digit:
Form the new number: Combining the modified digits, the new number is 8426246.
Identify the second digit from the left: In the new number 8426246, the second digit from the left is 4.
Identify the second digit from the right: In the new number 8426246, counting from the right, the first digit is 6, and the second digit is 4.
Calculate the difference: The difference between the second digit from the left (4) and the second digit from the right (4) is:
\[ 4 - 4 = 0 \]Correct Option: C) 0
The difference between the second digit from the left (4) and the second digit from the right (4) in the new number is 0.
The question asks to identify the political leader who bestowed the title 'Rani Gaidinliu' upon Gaidinliu Pamei, a prominent Naga spiritual and political leader who led a revolt against British rule.
D) Jawaharlal Nehru gave the title 'Rani Gaidinliu' to Gaidinliu Pamei, recognizing her as a symbol of resistance against British rule and a leader of her people.
To find the total surface area of a solid hemisphere, we need to sum the curved surface area and the area of its circular base. The radius of the hemisphere is given, and we will use the standard formulas for these areas.
Correct Option: D) 768π cm²
The problem presents a number series, and we need to find the next term. We will analyze the relationship between consecutive terms to identify the pattern and then apply it to find the missing number.
The differences are \(7, 14, 28, 56\). It is clear that each difference is double the previous difference:
This indicates a pattern where the difference between consecutive terms is doubling each time.
The next difference in the series should be \(56 \times 2 = 112\).
Add this next difference to the last given term:
\[ 107 + 112 = 219 \]The next number in the series is 219.
D) 219 — As determined by following the pattern of doubling differences, \(107 + (56 \times 2) = 107 + 112 = 219\).
The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others, based on the English alphabetical order. We need to find a common rule or relationship between the letters within each pair and between the two clusters of letters in each option.
Let's assign numerical values to the letters:
Now let's analyze each option:
Upon re-examining the pattern, it seems the relationship is between the absolute difference of the letters in the first cluster and the absolute difference of the letters in the second cluster. Let's re-evaluate with this in mind.
The consistent pattern among options A, B, and D is that the absolute difference between the letters in the second cluster is an integer multiple of the absolute difference between the letters in the first cluster.
C) BZ – KF — In this option, the absolute difference for BZ is \(|2 - 26| = 24\), and for KF is \(|11 - 6| = 5\). \(24\) is not an integer multiple of \(5\). This breaks the pattern observed in the other options.
The question asks about the maximum imprisonment term that a Chief Judicial Magistrate (CJM) can award. This is a direct question related to the powers of judicial magistrates as defined under the Code of Criminal Procedure (CrPC) in India. To answer this, one needs to recall the specific provisions of the CrPC concerning the sentencing powers of different classes of magistrates.
A) 7 years is the correct answer. As per Section 29(3) of the CrPC, a Chief Judicial Magistrate cannot award a sentence of imprisonment exceeding seven years.