Calculate the probability that the speed of a chlorine molecule will lie between 200 m s⁻¹ and 220 m s^-1 at 300 K. Given that mass of chlorine molecule = 70u, k_B = 1.38 × 10^-23 JK^-1 and N_A = 6.02 × 10²⁶ kmol^-1 .

A researcher is interested to check the relationship between the salaries of workers involved in the production process of a company. To accomplish this, she/he has decided to develop a multiple regression model to predict their weekly salaries. For this purpose, he/she has selected a random sample of 50 workers involved in the production process. The information on their current monthly salaries in hundreds (Y), lengths of employment in months (X1), and job classifications (X2; 0 for technical job and 1 for clerical job) are summarised in the following table:

i) Prepare a scatter plot to get an idea about the relationship among the variables.

ii) Fit a linear regression model and its related analysis at 1% level of significance.

iii) Does the fitted regression model satisfy the linearity and normality assumptions?

iv) Also, draw both fitted regression lines on the scatter plot.  

A publisher recorded the total number of pages in 25 published books and also the number of typing errors that have been made in preparing the final print of the books. The results are given in the following table:

The publisher needs to set up a suitable control chart for the number of errors to check whether the number of errors in a state of control or not. Also computes the revised control limits, if necessary 

The marketing manager of a transportation network company offering taxi services in a metro city wanted to study the waiting times of customers to get a taxi during the peak hours. A subgroup of 15 customers was selected (one at each ten minutes interval during the hour) and the time in minutes was measured from the point each customer booked the taxi to when he or she began the trip. The results of 40 days period were as under.

The manager of this company needs to construct the suitable control charts for variability as well as average to infer whether the waiting times of customers for getting a taxi is under control or not. If it is out-of-control, also construct the revised control charts 

Explain with the help of a diagram, the operation of a photovoltaic solar cell.

Describe the different types of polymerization processes with an example of each.

A germanium crystal with doping of 10¹⁸ arsenic atoms per cm³ is required. For initial Ge load of 20 kg, calculate the mass of arsenic to be added. Assume that the value of k₀ remains constant throughout the growth process. Consider the density of molten germanium to be 5.7 g cm^-3 and atomic weight of arsenic 74.934u.

What are the features of magnetic hysterisis loop? Explain how the shape of the loop determines the application of a magnetic material.

A superconducting material has a critical temperature of 4.1 K at zero magnetic field. The critical field at 0 K is 0.04 Tesla. Determine the critical field at 2 K.

In Hall experiment, the current density due to the applied electric field is 2A m^-2 and Hall constant is measured to be - 1.5 10^-10 Vm³ A ^-1 Tesla^-1 . Calculate drift velocity of the change carriers.

For an intrinsic semiconductor with energy gap Eg = 0.85 eV, determine the position of the Fermi level at 300 K if    6me . Also calculate the density of electrons and holes at 300 K.

The density of copper is 8.92 10³ kg m^-3 and its atomic weight is 63.5. Assuming that each copper atom provides one conduction (free) electron, calculate the density of conduction electrons. Also estimate the relaxation time for free electrons applying classical free electron theory. What is the corresponding mean free path? Take the electrical conductivity of copper to be 6.8 10⁷   m^-1 .

The unit cell size of KCl is 6.3 Å and the Young’s modulus in the [100] direction is 3.8 10¹⁰ Nm^-2 . Estimate the wavelength at which electromagnetic radiation is strongly reflected by a crystal [Atomic weight of K = 39 and Cl = 37].

Calculate the heat capacity of Hf at 200 K, given that its Debye temperature is 242 K.

Derive an expression for the velocity of the transverse wave in the [100] direction in a cubic crystal.

The lattice energy for an ion is given by

where and  are constants and is the Madelung constant. Find an expression for the cohesive energy.

The primitive lattice vectors of a lattice are given by

Determine the volume of the primitive cell and the reciprocal lattice vectors.

The first order Bragg reflection angle from the (111) planes in an fcc metal is 19.2° for an x-ray beam with λ = 1.54 Å. Calculate the density of the metal if its atomic weight is 26.98 u.

Calculate the atomic packing fraction for a bcc lattice.

Suppose that a customer service manager of a mall wants to evaluate the service of the eight food counters in the mall. She/he hires seven evaluators with varied experience in food-service evaluation to act as raters. To reduce the effect of the variability from rater to rater, a randomised block design is applied considering raters serving as the blocks. The seven raters evaluate the service of each of the eight food counters in a randomorder. A rating scale from 0 (low) to 100 (high) is used. The following table summarises the results:

The effect of evaluation of each rater on the service of food counters is normally distributed with approximately equal variances.

i) Analyse the design at 2% level of significance.

ii) Is the average service of the eight food counters significantly different? If the difference between the averages services of the eight restaurants is significant, do the pair-wise comparison between them