Ques 1.

 Explain the necessary and sufficient conditions in case of unconstrained optimisation.

Ques 2.

 Consider a consumer who buys two goods, x and y with utility function u(x, y) = 2√x + y. The consumer's income is 20 and price of y is 4. Compute the optimal consumption bundle when the price of x is equal to 1 using constrained optimisation. 

Ques 3.

With respect to the applications of dynamic optimisation, explain the optimal rate of extraction of exhaustible resources by monopoly. 

Ques 4.

What is a discontinuous function? Discuss the two types of discontinuous functions along with their diagrams.  

Ques 5.

 Explain the concept of a stationary point and inflexion point. Is a stationary point always a point of inflexion? Why or why not? 

Ques 6.

What do you understand by the term ‘joint distribution’ and ‘marginal distribution’? Discuss with the help of an example. 

Ques 7.

What is a sample? Explain with the help of an example. Discuss any two types of sampling techniques. 

Ques 8.

 One-tailed and two-tailed tests 

Ques 9.

 One to one and onto functions 

Ques 10.

Hyperbola 

Ques 11.

 Local minima