This is a coding-decoding problem where we need to find the codes for individual words by comparing the given coded statements. We will identify common words and their corresponding common codes across the statements to deduce the code for each word.
Correct Option: A) na sy
To find the height of the conical tent, we need to use the given information about the space on the ground (area) and the air to breathe (volume) required per person. We will first calculate the total base area and total volume of the tent, then use the formulas for the area of the base of a cone and the volume of a cone to find the height.
Calculate the total base area required:
Each person requires \(5 \text{ m}^2\) of space on the ground. There are 30 persons.
Calculate the total volume required:
Each person requires \(120 \text{ m}^3\) of air to breathe. There are 30 persons.
Relate base area to the radius of the cone:
The base of a conical tent is a circle. The area of the base of a cone is given by the formula \(A = \pi r^2\), where \(r\) is the radius of the base.
Relate volume to the radius and height of the cone:
The volume of a cone is given by the formula \(V = \frac{1}{3} \pi r^2 h\), where \(h\) is the height of the cone.
Substitute the value of \(r^2\) into the volume formula:
We found \(r^2 = \frac{150}{\pi}\) from step 3. Substitute this into the volume equation from step 4.
Solve for the height \(h\):
\[ h = \frac{3600}{50} \]\[ h = 72 \text{ m} \]Correct Option: D) 72
To find the original number, we need to understand that an increase of 50% means the new number is 150% of the original number. We can set up an equation where the original number (let's call it \(x\)) increased by 50% equals 2820.
Thus, the original number is 1880.
Correct Option: C) 1880
The question asks for the process used to prepare sodium hydroxide (NaOH). We need to identify the correct industrial process among the given options.
Correct Option: B) Chlor-alkali process is the industrial process used for the preparation of sodium hydroxide, along with chlorine and hydrogen gas, by the electrolysis of brine solution.
To determine how voltage is distributed across resistors in a series combination, we will use Ohm's Law and the properties of series circuits. In a series circuit, the current flowing through each component is the same, and the total voltage is the sum of the individual voltage drops across each component.
Therefore, the voltage is distributed directly proportional to the resistance of each resistor.
D) Directly proportional to resistance. In a series circuit, the current is the same through all resistors. According to Ohm's Law (\(V = IR\)), if \(I\) is constant, then \(V\) is directly proportional to \(R\).
To find the area of an isosceles triangle, we can use the formula for the area of a triangle, which is \( \frac{1}{2} \times \text{base} \times \text{height} \). Since the height is not given, we first need to calculate it using the Pythagorean theorem. In an isosceles triangle, the altitude drawn to the base bisects the base, creating two right-angled triangles.
Identify the given dimensions:
Find the height of the triangle:
In an isosceles triangle, the altitude from the vertex between the equal sides to the base bisects the base. So, if we draw an altitude \(h\) to the base, it divides the base into two equal segments, each of length \( \frac{b}{2} \).
\[ \frac{b}{2} = \frac{56 \text{ cm}}{2} = 28 \text{ cm} \]
Now, we have a right-angled triangle with the hypotenuse as one of the equal sides (\(100 \text{ cm}\)), one leg as half the base (\(28 \text{ cm}\)), and the other leg as the height (\(h\)).
Using the Pythagorean theorem (\( \text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2 \)):
\[ a^2 = \left(\frac{b}{2}\right)^2 + h^2 \]
\[ 100^2 = 28^2 + h^2 \]
\[ 10000 = 784 + h^2 \]
\[ h^2 = 10000 - 784 \]
\[ h^2 = 9216 \]
\[ h = \sqrt{9216} \]
To find the square root of 9216:
We can estimate: \(90^2 = 8100\) and \(100^2 = 10000\). The number ends in 6, so the unit digit of the square root must be 4 or 6. Let's try \(96^2\).
\[ 96 \times 96 = (100 - 4) \times (100 - 4) = 10000 - 2 \times 4 \times 100 + 16 = 10000 - 800 + 16 = 9216 \]
So, \(h = 96 \text{ cm}\).
Calculate the area of the triangle:
The area of a triangle is given by:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
\[ \text{Area} = \frac{1}{2} \times 56 \text{ cm} \times 96 \text{ cm} \]
\[ \text{Area} = 28 \times 96 \text{ cm}^2 \]
\[ \text{Area} = 2688 \text{ cm}^2 \]
Correct Option: B) 2688
The calculated area of the triangle is \(2688 \text{ cm}^2\).
The question asks to identify the balanced chemical equation for the complete combustion of methane. Complete combustion of a hydrocarbon involves its reaction with oxygen to produce carbon dioxide and water.
Correct Option: A) \(\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}\) is the balanced chemical equation for the complete combustion of methane.
To find the average of a series of natural numbers, we can use the formula for the average of an arithmetic progression. The series of natural numbers from 1 to 92 is an arithmetic progression with a common difference of 1. For such a series, the average is simply the sum of the first and last term divided by 2.
Identify the series: The natural numbers from 1 to 92 are \(1, 2, 3, \dots, 92\).
Recognize the type of series: This is an arithmetic progression (AP) because the difference between consecutive terms is constant (which is 1).
Recall the formula for the average of an AP: For an arithmetic progression, the average is given by:
\[ \text{Average} = \frac{\text{First Term} + \text{Last Term}}{2} \]Identify the first and last terms:
Apply the formula:
\[ \text{Average} = \frac{1 + 92}{2} \] \[ \text{Average} = \frac{93}{2} \] \[ \text{Average} = 46.5 \]Correct Option: C) 46.5
Hritik ranked 20th from the bottom and 30th from the top in his class. How many students are there in his class?
To find the total number of students in the class, we can use the formula that relates a person's rank from both ends of a line. When a person's rank from the top and bottom (or left and right) is known, the total number of people can be calculated by adding the two ranks and subtracting 1 (because the person themselves is counted twice).
Therefore, there are 49 students in the class.
Correct Option: D) 49
The question asks to identify the method of plant reproduction that involves only a single parent. We need to evaluate each option based on the number of parents involved in the reproductive process.
Correct Option: B) Asexual reproduction is a method of reproduction in plants where only a single parent is involved. The offspring produced are genetically identical to the parent.