Find the work done by the force, F = 5î + 2ĵ + 3k̂ when its point of application moves from A(1, -2, -2) to B(3, 1, 1).

(a) Show that the set of following vectors form the sides of a right-angled triangle. 

2î - ĵ + k̂

î - 3ĵ - 5k̂

3î - 4ĵ - 4k̂

 1.50 mol of PCl₅(g) is decomposes at room temperature to form PCl₃(g) and Cl₂(g). Determine their concentration at equilibrium, when K_c = 1.80. 

Define subjective, injective, and bijective functions with the examples. 

(a) Which of the following sets are finite, and which are infinite? 

(i) The set of points on the circumference of a circle.

(ii) ]0, 1[

(iii) [-1, 1]

(iv) {1, 2, ..., 100}

(b) If A = {1, 2, 3}, B = {2, 3, 4, 5}, and C = {1}, determine A ∪ B ∪ C and also verify

A ∪ B ∪ C = (A ∪ B) ∪ C = A ∪ (B ∪ C) 

 (a) Which of the following sets are finite, and which are infinite? 

(i) The set of points on the circumference of a circle.

(ii) ]0, 1[

(iii) [-1, 1]

(iv) {1, 2, ..., 100}

Discuss the Recommendation of the Second Administrative Reforms Commission.

 Describe the meaning and significance of Promotion.

 Explain the Types of Bureaucracy.

Discuss the objectives of Training.

Describe the meaning and Types of Recruitment.

 Explain the Political Rights of Public Servants.

 Describe the organisation and functions of Union Public Service Commission.

Discuss the Nature and scope of Personnel Administration.

Explain the Role, organisation and Functions of Union Public Service commission.

 Describe the meaning, Functions and Significance of Personnel Administration.

Describe the nature of NGOs.

Write a note on Nehru's defense and Foreign Policies.

Explain the nature of Political Process Approach.

Bring out impact of Globalist theory on State.