JEE Advanced Model Paper 3 with solutions for online practice

x2 + 1 > 0 , x ∊ R ..... (i)
(a - 1) x2 - (a + |a - 1| + 2) x + 1 ≥ 0 ..... (2)
Solution of equation (2) is x ∊ R
a - 1 > 0 and Δ ≤ 0
a > 1 and (a+a−1+2)2 - 4 (a - 1) ≤ 0
4a2 + 5 ≤ 0
∴ which is not possible for any real value of a
∴ Hence number of integral value of a is zero.