The question asks about the primary focus of the Ramsar Convention. To answer this, one needs to recall the specific environmental domain that this international treaty addresses.
Correct Option: D) The Ramsar Convention is an international treaty for the conservation and sustainable use of wetlands. It was signed in Ramsar, Iran, in 1971 and came into force in 1975. Its primary objective is to halt the worldwide loss of wetlands and to conserve those that remain.
The question asks about the location of the G7 environment ministers' meeting in 2019 where they discussed a report on the state of the planet. This requires knowledge of specific international events and their venues.
C) France — The G7 Environment Ministers met in Metz, France, in May 2019. During this meeting, they addressed the alarming report on the state of the planet, particularly the IPBES global assessment report on biodiversity and ecosystem services.
To determine the day of the week on 7th March 2019, given that 4th March 2018 was a Wednesday, we need to calculate the number of odd days between these two dates. The number of odd days determines how many days the week advances.
The year 2018 is a normal year (not a leap year) because it is not divisible by 4. A normal year has 365 days.
The number of odd days is the remainder when the total number of days is divided by 7.
\[ \text{Odd days} = \frac{\text{Total days}}{7} \text{ (remainder)} \]\[ \text{Odd days for 2018} = \frac{365}{7} = 52 \text{ weeks and } 1 \text{ day} \]So, there is 1 odd day between 4th March 2018 and 4th March 2019.Since 4th March 2018 was a Wednesday and there is 1 odd day, we add 1 day to Wednesday.
\[ \text{Wednesday} + 1 \text{ day} = \text{Thursday} \]So, 4th March 2019 will be a Thursday.From 4th March to 7th March, there are \(7 - 4 = 3\) days.
If 4th March 2019 is a Thursday, then:
D) Sunday is the correct day of the week for 7th March 2019.
The question asks to identify which of the given percentages is NOT a Goods and Services Tax (GST) rate slab in India. To answer this, one needs to be familiar with the standard GST rate structure implemented in India.
Correct Option: C) 10% is not a standard GST rate slab in India. The main GST rate slabs are 0%, 5%, 12%, 18%, and 28%.
The problem asks us to identify which of the given assumptions are implicit in the statement: "RTE has mandated compulsory enrolment of all children of the age 6 to 14 years in the schools." We need to analyze each assumption to see if it is a necessary underlying thought or belief for the statement to be made.
C) Neither assumption I nor assumption II is implicit.
What is the value of sin 15°?
\(\frac{\sqrt{6}-\sqrt{2}}{2}\)
\(\frac{\sqrt{6}-\sqrt{2}}{3}\)
\(\frac{\sqrt{6}-\sqrt{2}}{4}\)
\(\frac{\sqrt{3}-\sqrt{2}}{4}\)
To find the value of \(\sin 15^\circ\), we can use the trigonometric identity for the sine of the difference of two angles, which is \(\sin(A - B) = \sin A \cos B - \cos A \sin B\). We need to choose two standard angles whose difference is \(15^\circ\) and whose sine and cosine values are known.
Correct Option: C) \(\frac{\sqrt{6}-\sqrt{2}}{4}\)
The question asks for an alternative name for the August Kranti. This requires knowledge of key movements in Indian history and their associated names.
The August Kranti is famously known as the Quit India Movement, which was launched by Mahatma Gandhi on August 8, 1942, demanding an end to British rule in India.
A) Quit India — The Quit India Movement, also known as the August Movement or August Kranti, was a pivotal civil disobedience movement launched in India in August 1942 by Mahatma Gandhi. It demanded an immediate end to British rule.
The problem provides a system of three linear equations with three variables (x, y, z). We need to find the value of a linear expression involving these variables. The most straightforward approach is to solve the system of equations to find the individual values of x, y, and z, and then substitute them into the target expression.
Write down the given equations:
\[ 2x + y = 15 \quad \text{(1)} \]\[ y + 2z = 17 \quad \text{(2)} \]\[ x + 2y = 9 \quad \text{(3)} \]From equation (1), express \(y\) in terms of \(x\):
\[ y = 15 - 2x \quad \text{(4)} \]Substitute equation (4) into equation (3):
\[ x + 2(15 - 2x) = 9 \]\[ x + 30 - 4x = 9 \]\[ -3x = 9 - 30 \]\[ -3x = -21 \]\[ x = \frac{-21}{-3} \]\[ x = 7 \]Substitute the value of \(x = 7\) back into equation (4) to find \(y\):
\[ y = 15 - 2(7) \]\[ y = 15 - 14 \]\[ y = 1 \]Substitute the value of \(y = 1\) into equation (2) to find \(z\):
\[ 1 + 2z = 17 \]\[ 2z = 17 - 1 \]\[ 2z = 16 \]\[ z = \frac{16}{2} \]\[ z = 8 \]Now that we have the values \(x=7\), \(y=1\), and \(z=8\), substitute them into the expression \(4x + 3y + z\):
\[ 4x + 3y + z = 4(7) + 3(1) + 8 \]\[ = 28 + 3 + 8 \]\[ = 31 + 8 \]\[ = 39 \]C) 39 is the correct value for the expression \(4x + 3y + z\).
Find the value of 3(x+y) if x = \(\frac{\sqrt{3}+1}{\sqrt{3}-1}\) and y =\(\frac{\sqrt{3}-1}{\sqrt{3}+1}\)
To find the value of \(3(x+y)\), we first need to simplify the expressions for \(x\) and \(y\). This involves rationalizing the denominators of both fractions. After simplifying \(x\) and \(y\), we will calculate their sum \(x+y\) and then multiply the result by 3.
Simplify \(x\):
Given \(x = \frac{\sqrt{3}+1}{\sqrt{3}-1}\). To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is \(\sqrt{3}+1\).
\[ x = \frac{\sqrt{3}+1}{\sqrt{3}-1} \times \frac{\sqrt{3}+1}{\sqrt{3}+1} \]Using the identity \((a-b)(a+b) = a^2 - b^2\) in the denominator and \((a+b)^2 = a^2 + 2ab + b^2\) in the numerator:
\[ x = \frac{(\sqrt{3})^2 + 2(\sqrt{3})(1) + (1)^2}{(\sqrt{3})^2 - (1)^2} \] \[ x = \frac{3 + 2\sqrt{3} + 1}{3 - 1} \] \[ x = \frac{4 + 2\sqrt{3}}{2} \] \[ x = 2 + \sqrt{3} \]Simplify \(y\):
Given \(y = \frac{\sqrt{3}-1}{\sqrt{3}+1}\). To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is \(\sqrt{3}-1\).
\[ y = \frac{\sqrt{3}-1}{\sqrt{3}+1} \times \frac{\sqrt{3}-1}{\sqrt{3}-1} \]Using the identity \((a+b)(a-b) = a^2 - b^2\) in the denominator and \((a-b)^2 = a^2 - 2ab + b^2\) in the numerator:
\[ y = \frac{(\sqrt{3})^2 - 2(\sqrt{3})(1) + (1)^2}{(\sqrt{3})^2 - (1)^2} \] \[ y = \frac{3 - 2\sqrt{3} + 1}{3 - 1} \] \[ y = \frac{4 - 2\sqrt{3}}{2} \] \[ y = 2 - \sqrt{3} \]Calculate \(x+y\):
Now, add the simplified values of \(x\) and \(y\):
\[ x + y = (2 + \sqrt{3}) + (2 - \sqrt{3}) \] \[ x + y = 2 + \sqrt{3} + 2 - \sqrt{3} \] \[ x + y = 4 \]Calculate \(3(x+y)\):
Finally, multiply the sum by 3:
\[ 3(x+y) = 3(4) \] \[ 3(x+y) = 12 \]Correct Option: A) 12
The question asks to identify the largest producer of Uranium in the world in 2019. This requires knowledge of global mineral production statistics, specifically for Uranium.
According to the World Nuclear Association and other geological surveys, Kazakhstan has consistently been the world's largest producer of uranium since 2009. In 2019, Kazakhstan produced approximately 22,808 tonnes of uranium, accounting for about 43% of the world's total production.
B) Kazakhstan was the largest producer of Uranium in the world in 2019, producing over 22,000 tonnes and accounting for a significant portion of global output.