The question asks to identify the head of the Commission appointed in April 2007 to suggest measures for improvement in Centre-State relations in India. This requires knowledge of significant commissions and their chairpersons related to Indian federalism.
A) M.M.Punchhi
The Government of India appointed a Commission on Centre-State Relations under the chairmanship of Justice Madan Mohan Punchhi (M.M. Punchhi), a former Chief Justice of India, in April 2007. This commission was tasked with examining and reviewing the working of the existing arrangements between the Union and States, various pronouncements of the courts in regard to powers, functions, and responsibilities in all spheres, including legislative, administrative, and financial relations, and to recommend such changes or other measures as may be appropriate. The commission submitted its report in 2010.
The question asks to identify the country whose President delivered an underwater speech in 2019 to advocate for stronger ocean protection. This is a specific event-based general knowledge question.
A) Seychelles — In April 2019, then-President Danny Faure of Seychelles delivered a groundbreaking speech from a submersible 124 meters below the surface of the Indian Ocean. His address called for stronger international action to protect the world's oceans from climate change and overfishing, making Seychelles the correct answer.
The sum of two numbers is 25 and the product is 35. The sum of their reciprocals is:
\( \frac{3}{7} \)
\( \frac{6}{7} \)
\( \frac{4}{7} \)
\( \frac{5}{7} \)
This problem involves basic algebra. We are given the sum and product of two numbers and asked to find the sum of their reciprocals. We can represent the two numbers with variables and set up equations based on the given information. Then, we can manipulate these equations to find the required sum of reciprocals.
Let the two numbers be \(x\) and \(y\).
According to the problem statement, the sum of the two numbers is 25. So, we can write the equation:
\[ x + y = 25 \quad \text{(Equation 1)} \]The product of the two numbers is 35. So, we can write the equation:
\[ xy = 35 \quad \text{(Equation 2)} \]We need to find the sum of their reciprocals. The reciprocals of \(x\) and \(y\) are \( \frac{1}{x} \) and \( \frac{1}{y} \), respectively. Their sum is:
\[ \frac{1}{x} + \frac{1}{y} \]To add these fractions, we find a common denominator, which is \(xy\):
\[ \frac{1}{x} + \frac{1}{y} = \frac{y}{xy} + \frac{x}{xy} = \frac{x + y}{xy} \]Now, substitute the values from Equation 1 and Equation 2 into this expression:
\[ \frac{x + y}{xy} = \frac{25}{35} \]Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\[ \frac{25 \div 5}{35 \div 5} = \frac{5}{7} \]Thus, the sum of their reciprocals is \( \frac{5}{7} \).
Correct Option: D) \( \frac{5}{7} \)
The question asks for the full form of the acronym "ALU" in computer terminology. This is a fundamental concept in computer architecture.
Correct Option: A) Arithmetic Logic Unit. The ALU is a fundamental digital circuit within the CPU that performs arithmetic and bitwise logical operations. It handles operations like addition, subtraction, multiplication, division, and logical operations such as AND, OR, NOT, XOR.
The problem presents a series of letter-clusters. We need to identify the pattern in the given clusters and apply it to find the missing cluster. The pattern usually involves the positional values of the letters in the English alphabet.
D) VXZ is the correct cluster as determined by applying the pattern of adding 7 to the positional value of each corresponding letter in the previous cluster.
The question asks about the current status of the 'right to property' in India. Understanding the historical changes to this right in the Indian Constitution is crucial to answering this question.
Correct Option: C) Legal right
The right to property is currently a legal right under Article 300A of the Indian Constitution. While it is a constitutional right, it is not a fundamental right. This change was brought about by the 44th Amendment Act of 1978.
To find the mean profit for the last 10 days, we need to first calculate the total profit for the entire month and the total profit for the first 20 days. Then, we can subtract the profit of the first 20 days from the total monthly profit to get the profit for the last 10 days. Finally, divide this amount by 10 to find the mean profit for the last 10 days.
Calculate the total profit for the entire month (30 days):
The mean daily profit for 30 days was ₹450.
\[ \text{Total profit for 30 days} = \text{Mean profit} \times \text{Number of days} \] \[ \text{Total profit for 30 days} = 450 \times 30 = \text{₹}13500 \]Calculate the total profit for the first 20 days:
The mean profit for the first 20 days was ₹300.
\[ \text{Total profit for first 20 days} = \text{Mean profit} \times \text{Number of days} \] \[ \text{Total profit for first 20 days} = 300 \times 20 = \text{₹}6000 \]Calculate the total profit for the last 10 days:
The profit for the last 10 days is the total profit for the month minus the profit for the first 20 days.
\[ \text{Profit for last 10 days} = \text{Total profit for 30 days} - \text{Total profit for first 20 days} \] \[ \text{Profit for last 10 days} = 13500 - 6000 = \text{₹}7500 \]Calculate the mean profit for the last 10 days:
Divide the total profit for the last 10 days by the number of days (10).
\[ \text{Mean profit for last 10 days} = \frac{\text{Profit for last 10 days}}{\text{Number of days}} \] \[ \text{Mean profit for last 10 days} = \frac{7500}{10} = \text{₹}750 \]Correct Option: A) ₹750
To solve this problem, we need to perform the addition and subtraction of decimal numbers in the given order. It's crucial to align the decimal points correctly when adding or subtracting.
Thus, the final result is \(41.046\).
Correct Option: C) 41.046
If sinA = \( \frac{a}{b} \), then find the value of cosA.
\(\frac{\sqrt{b^2-a^2}}{b}\)
\(\frac{b}{a}\)
\(\frac{a}{\sqrt{b^2-a^2}}\)
\(\frac{b}{a^2+b^2}\)
We are given the value of \(\sin A\) and need to find the value of \(\cos A\). We can use the fundamental trigonometric identity \(\sin^2 A + \cos^2 A = 1\) or construct a right-angled triangle to find the adjacent side.
Using the Pythagorean Identity:
The fundamental trigonometric identity is:
\[ \sin^2 A + \cos^2 A = 1 \]We are given \(\sin A = \frac{a}{b}\). Substitute this into the identity:
\[ \left(\frac{a}{b}\right)^2 + \cos^2 A = 1 \] \[ \frac{a^2}{b^2} + \cos^2 A = 1 \]Now, isolate \(\cos^2 A\):
\[ \cos^2 A = 1 - \frac{a^2}{b^2} \]Combine the terms on the right side:
\[ \cos^2 A = \frac{b^2 - a^2}{b^2} \]Take the square root of both sides to find \(\cos A\):
\[ \cos A = \sqrt{\frac{b^2 - a^2}{b^2}} \]Since \[\sqrt{\frac{X}{Y}} = \frac{\sqrt{X}}{\sqrt{Y}}\], we get:
\[ \cos A = \frac{\sqrt{b^2 - a^2}}{\sqrt{b^2}} \] \[ \cos A = \frac{\sqrt{b^2 - a^2}}{b} \]Using a Right-Angled Triangle:
Consider a right-angled triangle with angle \(A\). We know that \[\sin A = \frac{\text{Opposite}}{\text{Hypotenuse}}\].
Given \(\sin A = \frac{a}{b}\), we can say:
Let the adjacent side be \(x\). By the Pythagorean theorem:
\[ (\text{Opposite})^2 + (\text{Adjacent})^2 = (\text{Hypotenuse})^2 \] \[ a^2 + x^2 = b^2 \]Solve for \(x^2\):
\[ x^2 = b^2 - a^2 \]So, the adjacent side \(x\) is:
\[ x = \sqrt{b^2 - a^2} \]Now, \[\cos A = \frac{\text{Adjacent}}{\text{Hypotenuse}}\]:
\[ \cos A = \frac{\sqrt{b^2 - a^2}}{b} \]Correct Option: A) \(\frac{\sqrt{b^2-a^2}}{b}\)
The value of \(\frac{0.064+0.027}{0.16-0.12+0.09}\) is:
The question asks us to simplify a fraction containing decimal numbers in both the numerator and denominator. We need to perform the addition and subtraction operations separately, then divide the resulting values to obtain the final answer.
Identify the given expression:
\[ \frac{0.064+0.027}{0.16-0.12+0.09} \]We first simplify the numerator and denominator separately.
Simplify the numerator:
Add the two decimal numbers:
\[ 0.064+0.027=0.091 \]Therefore, the numerator is 0.091.
Simplify the denominator:
Perform the subtraction first:
\[ 0.16-0.12=0.04 \]Now add 0.09:
\[ 0.04+0.09=0.13 \]Therefore, the denominator is 0.13.
Divide the numerator by the denominator:
Substituting the simplified values:
\[ =\frac{0.091}{0.13} \]Multiply the numerator and denominator by 1000 to remove the decimal points:
\[ =\frac{91}{130} \]Simplifying by dividing both the numerator and denominator by 13:
\[ =\frac{7}{10} \] \[ =0.7 \]Determine the final answer:
The value of the given expression is 0.7.
Correct Option: C) 0.7 — Adding the numbers in the numerator gives 0.091, while simplifying the denominator gives 0.13. Therefore:
\[ \frac{0.064+0.027}{0.16-0.12+0.09} =\frac{0.091}{0.13} =\frac{91}{130} =0.7 \]
Hence, Option C is the correct answer.
A) 0.09: This is incorrect because it does not represent the quotient of the simplified numerator 0.091 and denominator 0.13.
B) 0.16: This is incorrect because 0.16 is only one of the values in the denominator, not the result of the complete expression.
D) 0.9: This is incorrect because dividing 0.091 by 0.13 gives 0.7, not 0.9.