KVPY Government Jobs Exams

The number of solutions (x, y, z) to the system of equations
x + 2y + 4z = 9, 4yz + 2xz + xy = 13, xyz = 3 Such that at least two of x, y, z are integers is
option
(A) 3
(B) 5
(C) 6
(D) 4

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KVPY Other Question

Let a, b, c be positive integers such that
b^2 c
a^2 b
+
+ is a rational number,
then which of the following is always an integer In a triangle ABC, it is known that AB = AC. Suppose D is the mid- point of AC and BD = BC = 2. Then the area of the triangle ABC is
option
(A) 2
(B) 2 2
(C) 7
(D) 2 7