The question asks for the best method to dispose of biological wastes from hospitals. Hospital waste, especially biological waste, is hazardous and requires specific disposal methods to prevent the spread of infections and protect public health and the environment.
B) incineration — Incineration is the process of burning waste materials at high temperatures (typically 850-1100 °C) to convert them into ash, flue gas, and heat. For biological and medical waste, incineration is highly effective because the high temperatures destroy pathogenic microorganisms, including bacteria, viruses, and spores, thereby preventing the spread of infectious diseases. Modern incinerators are equipped with advanced pollution control devices to minimize the release of harmful emissions into the atmosphere, making it a controlled and safe method for hazardous waste disposal.
This problem involves trigonometry, specifically the concept of angles of depression. We are given the height of a tower and the angle of depression to a vehicle. We need to find the horizontal distance of the vehicle from the base of the tower. We can form a right-angled triangle where the height of the tower is the perpendicular side, the distance to the vehicle is the base, and the angle of depression corresponds to an angle of elevation from the vehicle to the top of the tower.
Let the height of the tower be \(h\). Given \(h = 150 \text{ m}\).
Let the horizontal distance of the vehicle from the base of the tower be \(x\).
The angle of depression from the top of the tower to the vehicle is given as \(45^\circ\). When we consider the right-angled triangle formed by the tower, the ground, and the line of sight to the vehicle, the angle of elevation from the vehicle to the top of the tower will also be \(45^\circ\) (alternate interior angles).
In the right-angled triangle, we have the opposite side (height of the tower) and we want to find the adjacent side (distance to the vehicle). The trigonometric ratio that relates the opposite and adjacent sides is the tangent function:
\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]Substitute the given values into the formula:
\[ \tan(45^\circ) = \frac{h}{x} \]We know that \(\tan(45^\circ) = 1\). So, the equation becomes:
\[ 1 = \frac{150 \text{ m}}{x} \]Solve for \(x\):
\[ x = 150 \text{ m} \]The distance of the vehicle from the tower is 150 m.
What will the value of the following expression be?
\(\frac{6+3}{3}\) - 5 × (4+5)
To solve this expression, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS. This stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
The given expression is: \(\frac{6+3}{3} - 5 \times (4+5)\)
First, calculate the sum inside the parentheses: \((4+5) = 9\)
The expression becomes: \(\frac{6+3}{3} - 5 \times 9\)
Next, calculate the sum in the numerator of the fraction: \((6+3) = 9\)
The expression becomes: \(\frac{9}{3} - 5 \times 9\)
Now, perform the division: \(\frac{9}{3} = 3\)
The expression becomes: \(3 - 5 \times 9\)
Next, perform the multiplication: \(5 \times 9 = 45\)
The expression becomes: \(3 - 45\)
Finally, perform the subtraction: \(3 - 45 = -42\)
Correct Option: B) -42
To find the Highest Common Factor (HCF) of a set of numbers, we first need to express each number as a product of its prime factors. Then, the HCF is the product of the common prime factors, each raised to the lowest power it appears in any of the factorizations.
The numbers are \(12 \times 15\), \(15 \times 21\), and \(21 \times 12\).
The HCF is the product of these common prime factors raised to their lowest powers. In this case, it is just \(3^2\).
\[ \text{HCF} = 3^2 = 9 \]
A) 9 is the HCF of \(12 \times 15\), \(15 \times 21\), and \(21 \times 12\).
This problem involves calculating the total number of votes based on the percentage of votes received by one candidate and the difference in votes between the two candidates. We will determine the percentage of votes the winning candidate received, then find the percentage difference, and finally use this percentage difference to calculate the total votes.
Let the total number of votes cast be \(T\).
The losing candidate received 37% of the total votes.
\[ \text{Votes for losing candidate} = 0.37 \times T \]Since there are only two contestants, the winning candidate received the remaining percentage of votes.
\[ \text{Percentage for winning candidate} = 100\% - 37\% = 63\% \]So, the votes for the winning candidate are:
\[ \text{Votes for winning candidate} = 0.63 \times T \]The difference in votes between the winning candidate and the losing candidate is given as 520,000 votes.
\[ \text{Difference in votes} = (0.63 \times T) - (0.37 \times T) \]\[ 520000 = (0.63 - 0.37) \times T \]\[ 520000 = 0.26 \times T \]Now, we can solve for \(T\), the total number of votes.
\[ T = \frac{520000}{0.26} \]\[ T = \frac{520000}{\frac{26}{100}} \]\[ T = \frac{520000 \times 100}{26} \]\[ T = \frac{52000000}{26} \]\[ T = 2000000 \]Thus, the total number of votes cast in that election is 2,000,000.
D) 2000000
The question asks about the primary focus of the 'Green Revolution'. To answer this, one needs to recall the historical context and objectives of the Green Revolution, particularly in countries like India.
Correct Option: B) The 'Green Revolution' is fundamentally related to increasing food and grain production, primarily wheat and rice, through the adoption of new agricultural technologies and practices.
The question asks about the substance in the air that causes silver articles to turn black. This phenomenon is known as tarnishing, which is a chemical reaction between silver and certain atmospheric components.
Correct Option: C) Sulphur
What is the value of \(\frac{4+\sqrt{2}}{\sqrt{2}+1}\)?
2 - 3\(\sqrt{2}\)
3\(\sqrt{2}\) - 2
3\(\sqrt{2}\)
3\(\sqrt{2}\) + 2
To simplify the given expression, we will rationalize the denominator. Rationalizing the denominator involves multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of \(\sqrt{a} + b\) is \(\sqrt{a} - b\).
The given expression is:
\[ \frac{4+\sqrt{2}}{\sqrt{2}+1} \]The denominator is \(\sqrt{2}+1\). Its conjugate is \(\sqrt{2}-1\).
Multiply the numerator and the denominator by the conjugate of the denominator:
\[ \frac{4+\sqrt{2}}{\sqrt{2}+1} \times \frac{\sqrt{2}-1}{\sqrt{2}-1} \]Expand the numerator:
\[ (4+\sqrt{2})(\sqrt{2}-1) = 4(\sqrt{2}) - 4(1) + \sqrt{2}(\sqrt{2}) - \sqrt{2}(1) \]\[ = 4\sqrt{2} - 4 + 2 - \sqrt{2} \]\[ = (4\sqrt{2} - \sqrt{2}) + (-4 + 2) \]\[ = 3\sqrt{2} - 2 \]Expand the denominator using the identity \((a+b)(a-b) = a^2 - b^2\):
\[ (\sqrt{2}+1)(\sqrt{2}-1) = (\sqrt{2})^2 - (1)^2 \]\[ = 2 - 1 \]\[ = 1 \]Combine the simplified numerator and denominator:
\[ \frac{3\sqrt{2} - 2}{1} = 3\sqrt{2} - 2 \]Correct Option: B) \(3\sqrt{2} - 2\)
The problem presents a series consisting of alternating letters and numbers. To find the missing element, we need to identify the pattern in both the letter sequence and the number sequence separately.
Correct Option: A) T is the correct letter that follows Q in the established pattern of adding 3 to the alphabetical position.
To find the ratio of volumes of two spheres given the ratio of their curved surface areas, we need to recall the formulas for the curved surface area and volume of a sphere. We will use the given ratio to find the ratio of their radii, and then use the ratio of radii to find the ratio of their volumes.
Let the radii of the two spheres be \(r_1\) and \(r_2\).
The formula for the curved surface area (CSA) of a sphere is \(4\pi r^2\).
So, the curved surface areas of the two spheres are \(CSA_1 = 4\pi r_1^2\) and \(CSA_2 = 4\pi r_2^2\).
The problem states that the ratio of their curved surface areas is 1 : 4.
\[ \frac{CSA_1}{CSA_2} = \frac{4\pi r_1^2}{4\pi r_2^2} = \frac{r_1^2}{r_2^2} = \frac{1}{4} \]From the ratio of surface areas, we can find the ratio of their radii:
\[ \frac{r_1^2}{r_2^2} = \frac{1}{4} \]\[ \left(\frac{r_1}{r_2}\right)^2 = \frac{1}{4} \]\[ \frac{r_1}{r_2} = \sqrt{\frac{1}{4}} = \frac{1}{2} \]The formula for the volume (V) of a sphere is \(\frac{4}{3}\pi r^3\).
So, the volumes of the two spheres are \(V_1 = \frac{4}{3}\pi r_1^3\) and \(V_2 = \frac{4}{3}\pi r_2^3\).
Now, we find the ratio of their volumes:
\[ \frac{V_1}{V_2} = \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} = \frac{r_1^3}{r_2^3} = \left(\frac{r_1}{r_2}\right)^3 \]Substitute the ratio of radii we found in step 4:
\[ \frac{V_1}{V_2} = \left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8} \]Therefore, the ratio of the volumes of the two spheres is 1 : 8.
Correct Option: C) 1 : 8