Which factor affect the degree of ionization of weak electrolyte. Explain in brief. 

 Consider the following reaction
$
In which direction, towards reactants and towards products, does the reaction shift if the equilibrium is stressed by each change? (i) H₂ is added (ii) NH₃ is added (iii) NH₃ is removed.

 In the equilibrium mixture of three ideal gases A, B, C  obtained by dissociation of A to the extent of  at a total pressure of , what are the partial pressure of A, B and C. 

एक एंजाइम उत्प्रेरित अभिक्रिया में  ग्लूकोस के दो अणु संघनित होकर डाइसैकेराइड, माल्टोस का एक अणु बनाते हैं, अभिक्रिया की एन्थैल्पी का परिकलन करें।  पर क्रिस्टलीय  ग्लूकोस और माल्टोस की दहन एन्थैल्पियाँ क्रमशः  और  हैं। 

 What is the chemical potential? Explain it with its significance. 

रूद्धोष्म प्रक्रिया के लिए तापमान और आयतन के बीच संबंध ज्ञात कीजिए।  ताप पर हीलियम गैस के एक मोल का उत्क्रमणीय समतापी प्रसार प्रारंभिक आयतन  से  तक होने दिया जाता है। यह मानते हुए कि हीलियम आदर्श गैस की तरह व्यवहार करती है, गैस का अंतिम ताप ज्ञात करें। दिया है:  

Differentiate between enthalpy driven and entropy driven reactions with the help of suitable examples.

 Two molecule of  condense in enzyme catalyzed reaction to give a molecule of disaccharide, maltose. Calculate the enthalpy of the reaction. The enthalpies of combustion of crystalline  and maltose at  are  and , respectively. 

 Derive a relation between temperature and volume for an adiabatic process.  of helium gas at temperature of  undergoes reversible adiabatic expansion from an initial volume of  to . Calculate the final temperature of the gas by assuming that the helium behaves ideally and has . 

List the differences between thermodynamically reversible and irreversible processes with the suitable examples Derive a relation between temperature and volume for an adiabatic process.  of helium gas at temperature of  undergoes reversible adiabatic expansion from an initial volume of  to . Calculate the final temperature of the gas by assuming that the helium behaves ideally and has

List the differences between thermodynamically reversible and irreversible processes with the suitable examples

Define homomorphisms. When do the homomorphisms become endomorphism and isomorphism?

Obtain the Fourier cosine transformation of the function:
 

ऊष्मागतिकीय उत्क्रमणीय और अनुत्क्रमणीय प्रक्रियाओं के बीच के अंतरों को उपयुक्त उदाहरणों सहित सूचीबद्ध कीजिए। 

 Consider a triangle T in the z-plane with vertices at i, 1 - i, 1 + i. Determine the triangle T₀ into which T is mapped under the transformations

Evaluate the integral

by the method of residues when -1 < p < 1.

 Evaluate the value of the contour integral  where C is a circle defined by .

 Obtain the Laurent series expansion of  about . Determine the type of singularity and the region of convergence.

 Show that the Series  converges for |z| < 1 and find its sum.

Calculate the value of the integral  when C is the circle .