Perhydrol is an aqueous solution of

In order to shift a body of mass $m$ from a circular orbit of radius $3R$ to a higher radius $5R$ around the Earth,the work done is:

Let $\alpha \neq 1$ be a real root of the equation $x^3-ax^2+ax-1=0$,where $a \neq -1$ is a real number. Then,a root of this equation,among the following,is

An infinitely long conductor $PQR$ is bent to form a right angle as shown. $A$ current $I$ flows through $PQR$. The magnetic field due to this current at the point $M$ is $H_1$. Now,another infinitely long straight conductor $QS$ is connected at $Q$ such that the current in $PQ$ remains unchanged. The magnetic field at $M$ is now $H_2$. The ratio $H_1/H_2$ is given by

$A$ bar magnet of magnetic moment $M$ and moment of inertia $I$ is freely suspended such that the magnetic axial line is in the direction of the magnetic meridian. If the magnet is displaced by a very small angle $\theta$,the angular acceleration is (Magnetic induction of earth's horizontal field $= B_H$)

The value of $\lambda$ with $|\lambda| < 16$ such that $2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0$ represents a pair of straight lines,is