IISC has a mathematics department. Through this department the IISC is offering PHD in mathematics.

The Department of Mathematics, through its Integrated Ph.D. programme, offers exciting opportunities to talented students holding a Bachelor's degree for acquiring a rigorous and modern education in mathematics, and for pursuing research in both pure and applied mathematics.



Previous year question paper for mathematics from IISC








Previous year questions for mathematics from IISC:

1. Consider the following system of linear equations.
x + y + z + w = b1.
x − y + 2z + 3w = b2.
x − 3y + 3z + 5w = b3.
x + 3y − w = b4.
For which of the following choices of b1, b2, b3, b4 does the above system have a
solution?
(A) b1 = 1, b2 = 0, b3 = −1, b4 = 2.
(B) b1 = 2, b2 = 3, b3 = 5, b4 = −1.
(A) b1 = 2, b2 = 2, b3 = 3, b4 = 0.
(A) b1 = 2, b2 = −1, b3 = −3, b4 = 3.

2. Let y : [0, 1] → R be a twice continuously differentiable function such that,
d2y dx2
(x) − y(x) < 0, for all x ∈ (0, 1), and y(0) = y(1) = 0.
Then,
(A) y has at least two zeros in (0, 1).
(B) y has at least on zero in (0, 1).
(C) y(x) > 0 for all x ∈ (0, 1).
(D) y(x) < 0 for all x ∈ (0, 1).

3. Which one of the following boundary value problems has more than one solution?
(A) y 00 + y = 1, y(0) = 1, y(π/2) = 0.
(B) y00 + y = 1, y(0) = 0, y(2π) = 0.
(C) y00 − y = 1, y(0) = 0, y(π/2) = 0.
(D) y00 − y = 1, y(0) = 0, y(π) = 0.
4. Let A be an n × n nonsingular matrix such that the elements of A and A−1 are
all integers. Then, 3
(A) detA must be a positive integer.
(B) detA must be a negative integer.
(C) detA can be +1 or −1.
(D) detA must be +1.

5. Let Q be a polynomial of degree 23 such that Q(x) = −Q(−x) for all x ∈ R with
|x| ≥ 10. If R 1−1
(Q(x) + c) dx = 4 then c equals
(A) 0.
(B) 1.
(C) 2.
(D) 4.