Let $f : [0,1]\,\to R$ be such that $f\,(xy) = f\,(x)\,f\,(y)$ for all $x,y\,\in [0,1],$ and $f \,(0)\,\ne 0.$ If $y=y\,(x)$ satisfies the differential equation,$\frac{{dy}}{{dx}} = f(x)$ with $y(0) = 1,$ then $y\left( {\frac{1}{4}} \right) + y\left( {\frac{3}{4}} \right)$ is equal to
→If $4i + 7j + 8k,\,\,\,2i + 3j + 4k\,$ and $2i + 5j + 7k$ are the position vectors of the vertices $ A, B$ and $C$ respectively of triangle $ABC$ . The position vector of the point where the bisector of angle $A$ meets $BC$ is
→If $f\left( x \right)\left\{ {\begin{array}{*{20}{c}}
{\frac{{\sin \,\left( {p + 1} \right)x + \sin \,x}}{x},\,\,}&{x < 0} \\
{q\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,}&{x = 0} \\
{\frac{{\sqrt {x + {x^2}} - \sqrt x }}{{x/2}},}&{x > 0}
\end{array}} \right.$ Is continuous at $x = 0$, then the ordered pair $(p, q)$ is equal to
→If $(2,3,9),(5,2,1),(1, \lambda, 8)$ and $(\lambda, 2,3)$ are coplanar, then the product of all possible values of $\lambda$ is.
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