The number of real roots of the equation,
e^4x + e^3x – 4e^2x + e^x + 1 = 0 is :

Let the observations x_i (1 $$ \le $$ i $$ \le $$ 10) satisfy the
equations, $$\sum\limits_{i = 1}^{10} {\left( {{x_1} - 5} \right)} $$ = 10 and $$\sum\limits_{i = 1}^{10} {{{\left( {{x_1} - 5} \right)}^2}} $$ = 40.
If $$\mu $$ and $$\lambda $$ are the mean and the variance of the
observations, x₁ – 3, x₂ – 3, ...., x₁₀ – 3, then
the ordered pair ($$\mu $$, $$\lambda $$) is equal to :

If ƒ'(x) = tan^–1(secx + tanx), $$ - {\pi \over 2} < x < {\pi \over 2}$$,
and ƒ(0) = 0, then ƒ(1) is equal to :

If for some $$\alpha $$ and $$\beta $$ in R, the intersection of the following three places
x + 4y – 2z = 1
x + 7y – 5z = b
x + 5y + $$\alpha $$z = 5
is a line in R³, then $$\alpha $$ + $$\beta $$ is equal to :