$$\mathop {\lim }\limits_{x \to 0} {{\int_0^x {t\sin \left( {10t} \right)dt} } \over x}$$ is equal to

Let S be the set of all real roots of the equation,
3^x(3^x – 1) + 2 = |3^x – 1| + |3^x – 2|. Then S :

If $$A = \left( {\matrix{ 2 & 2 \cr 9 & 4 \cr } } \right)$$ and $$I = \left( {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right)$$ then 10A^–1 is equal to :

If $$I = \int\limits_1^2 {{{dx} \over {\sqrt {2{x^3} - 9{x^2} + 12x + 4} }}} $$, then :