Modern cereal $Triticale$ is developed by crossing between

$A$ block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope,the force exerted by the rope on the block is-

If $I$ is the identity matrix of order $2$ and $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$,then for $n \geq 1$,mathematical induction gives

$A$ wire of length $l$ is bent into a circular coil of one turn of radius $R_1$. Another wire of the same material,same area of cross-section,and same length is bent into a circular coil of two turns of radius $R_2$. When the same current flows through the two coils,the ratio of magnetic induction at the centres of the two coils is

During the reaction of permanganate with thiosulphate,the change in oxidation state of manganese occurs by a value of $3$. Identify which of the below media will favour the reaction.

$\int \frac{dx}{\sqrt{x-x^2}}$ is equal to