Data Quantization And Processing

To calculate the number of bytes required to store an image, we need to consider the following: - The image size is 512 × 512 pixels. - Each pixel in the image uses 8 bits (1 byte). Thus, the total number of bytes required to store the image is: Final Answer:

A histogram is a graphical representation of the distribution of a dataset. In a histogram, the data is divided into intervals, called bins, and the frequency (or count) of data points falling into each bin is plotted. When we create a normalized histogram, the frequency values of the bins are adjusted so that the total sum of the histogram equals 1. This means that the heights of the bars in the histogram represent probabilities, not just raw counts.
To understand this more clearly, let's break down the steps involved in normalizing a histogram: Step 1: Understanding the raw histogram.
In a raw histogram, each bar represents the frequency (or count) of data points in a specific bin. The height of the bar is simply the number of data points within that bin. If we have bins, then the total area under the bars would be the total number of data points, denoted as . So, the sum of the raw histogram values would be , where: where represents the frequency of the -th bin, and is the total count of all the data points.
Step 2: Normalizing the histogram.
When we normalize the histogram, we divide each bin’s frequency by the total number of data points . This converts each frequency to a probability, which represents the relative likelihood of a data point falling into that bin. The normalized frequency for each bin is given by: where is the normalized frequency (probability) of the -th bin.
Step 3: Sum of the normalized histogram values.
Since the sum of the frequencies in the raw histogram is , the sum of the normalized frequencies is: Thus, the sum of all the values of a normalized histogram equals 1. This is a fundamental property of probability distributions, where the total probability across all bins must sum to 1.
Final Answer:

The number of cells required to cover a given area can be calculated by dividing the total area by the area of one cell.
For ASTER-GDEM, the resolution is typically 30 m (0.03 km) per cell.
The area of one cell is: Now, to find the number of cells required to cover an area of 9 sq. km, divide the total area by the area of one cell: Thus, the number of cells required is 10000.

To solve this problem, we need to apply the fundamental relationship between the velocity, frequency, and wavelength of electromagnetic waves.
The velocity of an electromagnetic wave is the speed at which the wave propagates through space. The frequency is the number of oscillations or cycles of the wave that pass a point per second, and the wavelength is the distance between two consecutive points in phase, such as two peaks of the wave.
From classical wave theory, we know that the velocity , frequency , and wavelength of any electromagnetic wave are related by the equation:
This means that the velocity of a wave is equal to the product of its frequency and its wavelength. This relationship is true for all types of electromagnetic waves, including light, radio waves, and X-rays.
Let's analyze the options:
- Option (A): is incorrect because it suggests that the velocity is proportional to the square of the frequency, which is not correct.
- Option (B): is also incorrect because it suggests that velocity is the ratio of frequency to wavelength, which contradicts the standard formula.
- Option (C): is correct. This is the fundamental equation that links velocity, frequency, and wavelength.
- Option (D): is incorrect because the square of the wavelength does not appear in the correct formula.
Thus, the correct answer is (C), .

An odometer is an instrument used in surveying to measure the distance traveled by a vehicle or surveyor’s equipment. It is commonly used for measuring distances when performing land surveys or mapping tasks. In surveying, measuring distance accurately is essential for determining boundary lines, elevations, and other key parameters.
Explanation of the Options:
- Option (A) - Azimuth: An azimuth is the angle between a reference direction (such as true north) and the direction of an object, measured clockwise from the reference. An odometer does not measure azimuth, as it is specifically designed for measuring distance, not angles. - Option (B) - Horizontal Angle: Horizontal angles are used to measure the angle between two lines in the horizontal plane. These angles are typically measured with a theodolite or a total station, not an odometer. Therefore, an odometer is not used for measuring horizontal angles. - Option (C) - Vertical Angle: Vertical angles refer to the angles measured between a reference line (typically horizontal) and an object in the vertical plane. These angles are often measured using a theodolite or total station, not with an odometer. Therefore, an odometer is not used to measure vertical angles. - Option (D) - Distance: This is the correct answer. An odometer is a device specifically designed to measure distance. It works by counting the rotations of wheels or sensors to calculate the distance traveled. Odometers are commonly used in both land surveying and road construction to measure horizontal distances accurately over long stretches. Conclusion:
Thus, the correct answer is (D) distance. The odometer is a device used in surveying for accurately measuring distances over a terrain or along a specified path.

The electromagnetic spectrum is divided based on the wavelength of different types of electromagnetic radiation. The order from shortest to longest wavelength is as follows:
- Gamma rays have the shortest wavelengths.
- X-rays follow next.
- Ultraviolet light comes after X-rays.
- Visible light has a longer wavelength than ultraviolet.
- Infrared radiation has a longer wavelength than visible light.
- Microwaves follow infrared.
- Radiowaves have the longest wavelengths.
Step 1: Correct Order of Electromagnetic Waves
By considering the wavelength of each type of radiation, we can order them as:
Step 2: Conclusion
The correct sequence is (D) Gamma rays, X-rays, Ultraviolet, Visible, Infrared, Microwave, Radiowave.