If $\log 2=a, \log 3=b, \log 7=c$ and $6^x=7^{x+4}$,then $x$ is equal to:

If $\omega$ is a complex cube root of unity,then $\sin \left\{\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right\}$ is equal to

$A$ large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water,the quantities of water flowing out per second from both the holes are the same. Then $R$ is equal to

Which of the following organisms belongs to the Kingdom $Monera$?

Which of the following can be used to extinguish a fire caused by alkali metals?

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is