Consider the two sets :
A = {m $$ \in $$ R : both the roots of
x² – (m + 1)x + m + 4 = 0 are real}
and B = [–3, 5).
Which of the following is not true?

If y² + log_e (cos²x) = y,
$$x \in \left( { - {\pi \over 2},{\pi \over 2}} \right)$$, then :

The value of (2.¹P₀ – 3.²P₁ + 4.³P₂ .... up to 51^th term)
+ (1! – 2! + 3! – ..... up to 51^th term) is equal to :

The function, f(x) = (3x – 7)x^2/3, x $$ \in $$ R, is increasing for all x lying in :