Theory of Equat...

Number of positive integers n for which n ² + 96 is a perfect square is

Statement – 1: If x ⊂ R (2, 3) then x² – 5x + 6 > 0

Statement – 2: If α < x < β, and a have opposite signs (α , β)

Statement– 1: The set of all numbers a such that a² + 2a, 2a + 3 and a² + 3a + 8 are the sides of a triangle is (5, ∞)

Statement– 2: In a triangle sum of two sides is greater than the other and also sides are always positive.

Let a ≠ – 2 and ( a + 2 ) x² + 2 ( a + 1 ) x a = 0 has integral roots.

Statement – 1: a can take four distinct integral values.

Statement – 2: a/a +2 must be integer.

If a < b < c < d, then for any real non– zero λ, the quadratic equation (x – a) (x – c) + λ (x – b) (x – d) = 0 has

If x² – 2x + sin² α = 0, then x may lie in the set