Let $$f:[0,\infty ) \to [0,\infty )$$ be defined as $$f(x) = \int_0^x {[y]dy} $$

where [x] is the greatest integer less than or equal to x. Which of the following is true?

The values of a and b, for which the system of equations

2x + 3y + 6z = 8

x + 2y + az = 5

3x + 5y + 9z = b

has no solution, are :

Let 9 distinct balls be distributed among 4 boxes, B₁, B₂, B₃ and B₄. If the probability than B₃ contains exactly 3 balls is $$k{\left( {{3 \over 4}} \right)^9}$$ then k lies in the set :

The number of real roots of the equation $${e^{6x}} - {e^{4x}} - 2{e^{3x}} - 12{e^{2x}} + {e^x} + 1 = 0$$ is :