Find the asymptotes of the following functions: 

(i) (3x-4)/(2x+6)

(ii) (x²-2x-8)/(x-1)

Find the equation of tangent and normal to the curve f(x) = x³ - 3x² + 6x - 1 at x = 2. 

(a) Find all the second order partial derivatives of the following function. 

f(x, y) = x² - 8xy + y²

Find the derivative of the following functions with respect to x: (2+2)

(i) (x⁻¹ᐟ² - x¹ᐟ²)/(x⁻¹ᐟ² + x¹ᐟ²)

(ii) 3x/√(5+2x²)

(a) Evaluate the following limit. 

(b) If the law of motion of a particle is given as: s = -t³ + 3t² + 25, then (2+1)

i) find its velocity and acceleration.

ii) find the distance covered by the particle in time t = 5 units

Prove, with the help of vectors, that the diagonals of a parallelogram bisect each other. 

 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.