The reading of the ammeter in the circuit shown will be: (in $A$)

The magnetic needle of a vibration magnetometer makes $12$ oscillations per minute in the horizontal component of the earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line,it makes $15$ oscillations per minute. If the poles of the bar magnet are interchanged,the number of oscillations it makes per minute is

Which of the following is the only taxonomic category that has a real existence?

The image of the pair of lines represented by $ax^2 + 2hxy + by^2 = 0$ by the line mirror $y = 0$ is

$A$ liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is $r$ and the angular velocity of rotation is $\omega$,then the difference in the heights of the liquid at the centre of the vessel and the edge is

If the plane $7x + 11y + 13z = 3003$ meets the coordinate axes at $A, B, C$, then the centroid of the $\triangle ABC$ is