The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is :

Let A₁, A₂, A₃, ....... be an increasing geometric progression of positive real numbers. If A₁A₃A₅A₇ = $${1 \over {1296}}$$ and A₂ + A₄ = $${7 \over {36}}$$, then the value of A₆ + A₈ + A₁₀ is equal to

Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral $$\int\limits_0^1 {[ - 8{x^2} + 6x - 1]dx} $$ is equal to :

Let f : R $$\to$$ R be defined as

$$f(x) = \left[ {\matrix{ {[{e^x}],} & {x < 0} \cr {a{e^x} + [x - 1],} & {0 \le x < 1} \cr {b + [\sin (\pi x)],} & {1 \le x < 2} \cr {[{e^{ - x}}] - c,} & {x \ge 2} \cr } } \right.$$

where a, b, c $$\in$$ R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?