The equations of the perpendicular bisectors of sides $AB$ and $AC$ of a $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively. If the coordinates of vertex $A$ are $(1, -2)$,then the equation of $BC$ is

$A$ function $y = f(x)$ is given by $x = \frac{1}{1 + t^2}$ and $y = \frac{1}{t(1 + t^2)}$ for all $t > 0$. Then $f$ is:

What is the maximum value of the force $F$ such that the block shown in the arrangement does not move (in $N$)? (Given: $m = \sqrt{3} \ kg$,$\mu = \frac{1}{2\sqrt{3}}$,$\theta = 60^\circ$)

$A$ square is inscribed in the circle $x^{2} + y^{2} - 2x + 4y - 93 = 0$ such that its sides are parallel to the coordinate axes. The coordinates of its vertices are:

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = Young's modulus,$\rho$ = density,$\alpha$ = coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

The binding energy per nucleon of $^{16}O$ is $7.97 \, MeV$ and that of $^{17}O$ is $7.75 \, MeV$. The energy (in $MeV$) required to remove a neutron from $^{17}O$ is: