Hey as per your demand here I am giving you details of IISC Aptitude Questions for your practice

Here I am giving you IISC Aptitude Questions

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

Let y : [0, 1] → R be a twice continuously differentiable function such that,

(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) y
00 + y = 1, y(0) = 0, y(2π) = 0.
(C) y
00 − y = 1, y(0) = 0, y(π/2) = 0.
(D) y
00 − y = 1, y(0) = 0, y(π) = 0

Let A be an n × n nonsingular matrix such that the elements of A and A−1 are
all integers. Then,
(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.