Evaluate  .

Prove that  is an orthogonal matrix.

Solve the following system of equations using Cramer's rule.

x + 3y + 2z = 6, -x + 4y + 5z = 8, 2x + 5y + 3z = 10

If the first term of an AP is 5 and 101 term of the AP is 1005 then

common difference

of the AP will be 105.

If probability of an event E is 1/2 and probability of the event  is 1/6, then probability of the event F is 1/3, where events E and F are independent.

If  and  they are perpendicular to each other.

If A is a matrix of order 2 by 3 and B is a matrix of order 3 by 2, then order of the matrix A + B is 2 by 3.

Derivative of  with respect to x is 1.

Define thermal conductivity. Why the thermal conductivity of gases is independent of pressure up to a reasonably high pressure.

Why is conductivity not a suitable quantity to compare the conduction behaviour of different electrolytic solutions?

Using the Fick's first law of diffusion, derive the mathematical expression that provides the link between the phenomenological and thermodynamic treatment of diffusion phenomenon.

What are the limitations of phenomenological approach to transport properties?

Explain the principle for the experimental determination of activity and activity coefficient from solubility measurements.

Explain the principle for the experimental determination of activity and activity coefficient from solubility measurements.

List different methods of experimental determination of activity coefficients.

Calculate the ionic strength of

i) 0.08 mol kg¹ solutions of Ca(NO3)2 and

ii) the solution consisting of 6.3 g of MgCl2, 5 g of AlCl3 and 500 g of water.

Write the basic assumptions of the Debye-Huckel theory.

Derive the mathematical rate expression for competitive enzyme inhibition and give the graphical representation of Lineweaver-Burk plot.

Derive the mathematical rate expression for competitive enzyme inhibition and give the graphical representation of Lineweaver-Burk plot.

What is the difference between competitive and uncompetitive enzyme inhibition?