The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x-3 y+5}{6 x-9 y+7}$ is

Two charged particles of mass 1 g each are placed 1 m apart. If each of these possesses 1 femto coulomb of charge, then the dominant force of interaction between them is

A physical quantity $S$ is related to four observables $a, b, c$ and $d$ as $S=\frac{\sqrt{a b}}{c^3 d^4}$. If the percentage errors of measurement in $a, b, c$ and $d$ are $2 \%, 1 \%, 1 \%$ and $1 \%$ respectively, then percentage error in the quantity $S$ is

A particle moves along a straight line, such that its displacement $x$ varies with time $t$ as $x=\alpha t^3+\beta t^2+\gamma$, where $\alpha, \beta$ and $\gamma$ are constants, $v_1$ is the average velocity of the particle during its journey between $t=1 \mathrm{~s}$ and $t=3 \mathrm{~s} . v_2$ is the instantaneous velocity of the particle at $t=3 \mathrm{~s}$. The ratio $\frac{v_1}{v_2}$ is