The question asks for the percentage of self-employed workforce in India for the year 2023-24, according to the Economic Survey Report, 2024-25. This requires knowledge of recent economic data released in official government reports.
B) 58.4% is the correct percentage of the workforce in India that was self-employed in 2023-24, as stated in the Economic Survey Report, 2024-25.
This problem involves decoding a set of relational symbols and then applying them sequentially to determine the relationship between two individuals, P and T. We will break down the given expression 'P ÷ Q + R – S × T' step by step, identifying the relationship at each stage.
Since S is the wife of T, and P is the father of S's mother (Q), P is the father of T's wife's mother. Therefore, P is T's wife's mother's father.
Correct Option: A) Wife's mother's father
The problem asks us to find a pair of letter groups that follows the same pattern as the two given pairs. We need to identify the logical rule or transformation applied to the letters within each pair (e.g., KNR to HKS) and then apply that same rule to the options to find the matching one.
B) FXL : CUM
This pair follows the \(-3, -3, +1\) pattern. Therefore, option B is the correct answer.
The question asks to identify the easternmost international border point of India among the given options. This requires knowledge of the geographical locations of these points within India.
D) Kibithu is a town in Arunachal Pradesh, India, and is recognized as the easternmost inhabited place in India, located at the easternmost tip of the country's international border with China.
The problem involves calculating the difference between simple interest (SI) and compound interest (CI) for the same principal amount, rate, and time period. We can use the standard formulas for SI and CI, or a specific formula for the difference between CI and SI for 2 years, to find the principal amount.
Let the principal amount be \(P\).
The rate of interest \(R = 4\%\) per annum.
The time period \(T = 2\) years.
The difference between CI and SI is given as ₹45.
Calculate Simple Interest (SI):
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ \text{SI} = \frac{P \times 4 \times 2}{100} = \frac{8P}{100} = \frac{2P}{25} \]Calculate Compound Interest (CI):
The formula for the amount \(A\) under compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]\[ A = P \left(1 + \frac{4}{100}\right)^2 = P \left(1 + \frac{1}{25}\right)^2 = P \left(\frac{26}{25}\right)^2 \]\[ A = P \frac{676}{625} \]Compound Interest (CI) is \(A - P\):
\[ \text{CI} = P \frac{676}{625} - P = P \left(\frac{676}{625} - 1\right) = P \left(\frac{676 - 625}{625}\right) = \frac{51P}{625} \]Find the difference between CI and SI:
Given that \(\text{CI} - \text{SI} = 45\).
\[ \frac{51P}{625} - \frac{2P}{25} = 45 \]To subtract the fractions, find a common denominator, which is 625:
\[ \frac{51P}{625} - \frac{2P \times 25}{25 \times 25} = 45 \]\[ \frac{51P}{625} - \frac{50P}{625} = 45 \]\[ \frac{51P - 50P}{625} = 45 \]\[ \frac{P}{625} = 45 \]Solve for \(P\):
\[ P = 45 \times 625 \]\[ P = 28125 \]Alternative Method (Formula for CI - SI for 2 years):
For 2 years, the difference between CI and SI is given by:
\[ \text{CI} - \text{SI} = P \left(\frac{R}{100}\right)^2 \]Substitute the given values:
\[ 45 = P \left(\frac{4}{100}\right)^2 \]\[ 45 = P \left(\frac{1}{25}\right)^2 \]\[ 45 = P \times \frac{1}{625} \]\[ P = 45 \times 625 \]\[ P = 28125 \]The sum invested was ₹28,125.
B) 28,125 is the correct sum invested, as calculated using both methods.
To find the HCF of three numbers given their ratio and LCM, we can represent the numbers using a common factor (HCF). Then, we can use the relationship between the numbers, their HCF, and their LCM to solve for the HCF.
Represent the numbers: Let the HCF of the three numbers be \(x\). Since the numbers are in the ratio \(1:3:5\), we can express the numbers as \(1x\), \(3x\), and \(5x\).
Find the LCM of the numbers in terms of \(x\): To find the LCM of \(x\), \(3x\), and \(5x\), we can factor out \(x\). The remaining numbers are \(1\), \(3\), and \(5\). These are prime to each other (or pairwise coprime). Therefore, the LCM of \(1\), \(3\), and \(5\) is \(1 \times 3 \times 5 = 15\). So, the LCM of \(x\), \(3x\), and \(5x\) is \(x \times 1 \times 3 \times 5 = 15x\).
Use the given LCM to find \(x\): We are given that the LCM of the three numbers is \(285\). So, we have the equation:
\[ 15x = 285 \]Solve for \(x\): Divide both sides by \(15\):
\[ x = \frac{285}{15} \] \[ x = 19 \]Since \(x\) represents the HCF, the HCF of the three numbers is \(19\).
The HCF of the three numbers is found to be \(19\).
The question asks to identify the Chairman of ISRO appointed in January 2025. This requires knowledge of recent appointments in key scientific organizations in India.
Correct Option: A) V Narayanan. While there is no public record of V Narayanan being appointed as the Chairman of ISRO in January 2025, and the current Chairman S. Somanath's term is expected to end around that time, if 'A' is the designated correct answer, it implies a specific (possibly internal or hypothetical) context for the question. Without further information, this answer is difficult to verify publicly.
The problem involves finding an unknown value 'A' by equating two proportional relationships: the fourth proportion of three given numbers and the third proportion of 'A' and another number. We will first calculate the fourth proportion, then set up the equation for the third proportion, and finally solve for 'A'.
If \(a, b, c, d\) are in proportion, then \[\frac{a}{b} = \frac{c}{d}\]. Here, \(a=9\), \(b=3\), \(c=27\), and \(d\) is the fourth proportion.
\[ \frac{9}{3} = \frac{27}{d} \]\[ 9d = 3 \times 27 \]\[ 9d = 81 \]\[ d = \frac{81}{9} \]\[ d = 9 \]If \(x, y, z\) are in third proportion, then \[\frac{x}{y} = \frac{y}{z}\]. Here, \(x=A\), \(y=24\), and \(z\) is the third proportion. The problem states that the fourth proportion (which we found to be 9) is the same as the third proportion to A and 24. So, \(z=9\).
\[ \frac{A}{24} = \frac{24}{9} \]Now, we solve the equation from step 2 for A.
\[ 9A = 24 \times 24 \]\[ 9A = 576 \]\[ A = \frac{576}{9} \]\[ A = 64 \]The value of A is 64.
D) 64 — As calculated in the step-by-step solution, the value of A is 64.
To find the area of the rhombus, we first need to calculate the lengths of its diagonals using the given expressions and the values of \(x\) and \(y\). Once the diagonal lengths are determined, we can use the formula for the area of a rhombus, which is half the product of its diagonals.
Identify the given information:
Calculate the length of the first diagonal (\(d_1\)):
Substitute \(x = 2\) and \(y = 1\) into the expression for \(d_1\):
\[ d_1 = (1 + (2)(1) + 5) \text{ m} \]\[ d_1 = (1 + 2 + 5) \text{ m} \]\[ d_1 = 8 \text{ m} \]Calculate the length of the second diagonal (\(d_2\)):
Substitute \(x = 2\) and \(y = 1\) into the expression for \(d_2\):
\[ d_2 = (1 - (2)(1) + 7) \text{ m} \]\[ d_2 = (1 - 2 + 7) \text{ m} \]\[ d_2 = (-1 + 7) \text{ m} \]\[ d_2 = 6 \text{ m} \]Calculate the area of the rhombus:
The formula for the area of a rhombus is:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]Substitute the calculated diagonal lengths into the area formula:
\[ \text{Area} = \frac{1}{2} \times 8 \text{ m} \times 6 \text{ m} \]\[ \text{Area} = \frac{1}{2} \times 48 \text{ m}^2 \]\[ \text{Area} = 24 \text{ m}^2 \]Correct Option: D) 24 m²
The area of the rhombus is \(24 \text{ m}^2\).