The equation of the line passing through the point of intersection of the lines $x-3y+2=0$ and $2x+5y-7=0$ and perpendicular to the line $3x+2y+5=0$ is:

If the area of an equilateral triangle inscribed in the circle $x^2+y^2+10x+12y+c=0$ is $27\sqrt{3}$ sq. units,then $c$ is equal to:

The equations of the tangents to the circle $x^2 + y^2 = 13$ at the points whose abscissa is $2$,are

The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of vessel $A$ is $\alpha$,the coefficient of linear expansion of vessel $B$ is

If $\sin ^{-1}\left(\frac{3}{x}\right)+\sin ^{-1}\left(\frac{4}{x}\right)=\frac{\pi}{2}$,then $x$ is equal to

In an $LCR$ circuit,the capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged,the inductance should be changed from $L$ to: