Objective Questions
-------------------

.. A mininum of 8 questions here (along with answers)

1. How do you define a name 'y' as a symbol?


   Answer: var('y')

2. List out some constants pre-defined in sage?

   Answer: pi, e ,euler_gamma

3. List the functions for differentiation and integration in sage?

   Answer: diff and integral

4. Get the value of pi upto precision 5 digits using sage?

   Answer: n(pi,5)

5.  Find third order differential of function.

    f(x)=sin(x^2)+exp(x^3)

    Answer: diff(f(x),x,3) 

6. What is the function to find factors of an expression?

   Answer: factor

7. What is syntax for simplifying a function f?

   Answer f.simplify_full()

8. Find the solution for x between pi/2 to pi for the given equation?
   
   sin(x)==cos(x^3)+exp(x^4)
   find_root(sin(x)==cos(x^3)+exp(x^4),pi/2,pi)

9. Create a simple two dimensional matrix with two symbolic variables?

   var('a,b')
   A=matrix([[a,1],[2,b]])

Larger Questions
----------------

.. A minimum of 2 questions here (along with answers)

1.Find the points of intersection of the circles

 x^2 + y^2 - 4x = 1 
 x^2 + y^2 - 2y = 9  

2. Integrate the function 

x^2*cos(x)

between 1 to 3.