Lenz's law is a consequence of the law of conservation of

The volume of the tetrahedron formed by the coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is $3$. Then the volume of the parallelepiped formed by the coterminous edges $\vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}$ is

The locus of the centre of the circle,which cuts the circle $x^2+y^2-20x+4=0$ orthogonally and touches the line $x=2$,is

$A$ small ball of mass $m$ is released at a height $R$ above the Earth's surface,as shown in the figure. The ball enters a narrow groove and reaches a maximum depth of $R/2$ inside the Earth before coming to rest momentarily. The groove contains an ideal spring of spring constant $K$ and natural length $R$. Find the value of $K$. ($R$ is the radius of the Earth and $M$ is the mass of the Earth).

If $f(2)=4$ and $f^{\prime}(2)=1$,then $\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}$ is equal to

What are the oxidation numbers of nitrogen in $NH_4NO_3$?