Dec 2016, Booklet B, Ques no.46

Question:
The boundary value problem
x^2 y" - 2x y'+ 2 y = 0, subject to the boundary conditions
y(1)  + a y'(1)  = 1
y(2) + b Y'(2) = 2
has a unique solution if
1. a= -1, b=2
2. a=-1,  b=-2
3. a=-2,  b=2
4. a=-3,  b=2/3
Solution:

DEC 2016 , BOOKLET B, Ques NO. 32

Ques: A function f :  R^2 -> R is defined by f(x,y) = xy. Let V =(1,2) and a = (a1,a2) be two elements of R^2. The directional derivative of f in the direction of v at a is
1.  a1 + 2a2
2. a2 + 2a1
3. a2/2 + a1
4.  a1/2 +a2
Solution:

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