Let the vector $$\overrightarrow {PQ} ,\overrightarrow {QR} ,\overrightarrow {RS} ,\overrightarrow {ST} ,\overrightarrow {TU} $$ and $$\overrightarrow {UP} $$, represent the sides of a regular hexagon.

Statement 1 : $$\overrightarrow {PQ} \times \left( {\overrightarrow {RS} + \overrightarrow {ST} } \right) \ne \overrightarrow 0 $$

Statement 2 : $$\overrightarrow {PQ} \times \overrightarrow {RS} = \overrightarrow 0 $$ and $$\overrightarrow {PQ} \times \overrightarrow {ST} \ne \overrightarrow 0 $$

Let F(x) be an indefinite integral of $$\sin^2x$$.

Statement 1 : The function F(x) satisfies F($$x+\pi$$) = F($$x$$) for all real x.

Statement 2 : $${\sin ^2}(x + \pi ) = {\sin ^2}x$$ for all real x.

Let V$$_r$$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ($$2r-1$$). Let $${T_r} = {V_{r + 1}} - {V_r} - 2$$ and $${Q_r} = {T_{r + 1}} - {T_r}$$ for r = 1, 2, ...

The sum V$$_1$$ + V$$_2$$ + ... + V$$_n$$ is

Let V$$_r$$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ($$2r-1$$). Let $${T_r} = {V_{r + 1}} - {V_r} - 2$$ and $${Q_r} = {T_{r + 1}} - {T_r}$$ for r = 1, 2, ...

T$$_r$$ is always