--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/using_sage/questions.rst	Wed Dec 01 16:51:35 2010 +0530
@@ -0,0 +1,99 @@
+Objective
+---------
+
+1. How do you find the limit of the function ``x/sin(x)`` as ``x`` tends to
+   ``0`` from the negative side.
+
+   Answer: lim(x/sin(x), x=0, dir="below")
+
+#. Find the third differential of the function ``exp(sin(x)*cos(x^2))``
+ 
+   Answer: diff(exp(sin(x)*cos(x^2), x, 3)
+
+#. Solve the system of linear equations::
+
+     x-2y+3z = 7
+     2x+3y-z = 5
+     x+2y+4z = 9
+
+   Answer::
+
+     A = Matrix([[1, -2, 3], 
+                 [2, 3, -1], 
+                 [1, 2, 4]])
+
+     b = vector([7, 5, 9])
+
+     solve_right(A, b)
+
+#. How do you get the factorized form of ``x^4 - 4x^2 + x^3 + 2x + 7`` 
+
+   Answer::
+
+      factor( x^4 + x^3 - 4*x^2 + 2*x + 7 )
+
+#. list all the primes between 2009 and 2900
+
+   Answer: prime_range(2009, 2901)
+
+#. Which function is used to check primality
+
+   a. isPrime
+   #. isprime
+   #. is_prime
+   #. prime
+
+   Answer: is_prime
+
+#. How do you list all the combinations of ``[1, 2, 3, 4]``
+
+
+   Answer::
+
+     c1 = Combinations([1, 2, 3, 4])
+     c1.list()
+
+#. How do you list all the permutations of ``[1, 3, 2, 3]``
+
+    Answer::
+
+      p1 = Permutations([1, 3, 2, 3])
+      p2.list()
+
+
+Programming
+-----------
+
+1. Obtain the sum of primes between 1 million and 2 million. 
+
+   Answer::
+
+     prime_sum = 0
+     for i in range(1000001, 2000000, 2):
+         if is_prime(i):
+         prime_sum += i
+        
+     prime_sum
+
+   OR
+   ::
+
+     sum(prime_range(1000000, 2000000))
+
+2. ``graphs.WorldMap()`` gives the world map in the form of a
+   graph. ::
+
+       G = graphs.WorldMap()
+       G.vertices()
+
+  
+   Suppose, I wish to go from India to France by Road, find out the
+   least number of Visas that I'll have to obtain. 
+
+   Answer::
+
+      G.distance("India", "France")
+
+      
+
+