The number of points in $(-\infty, \infty)$,for which $x^2-x \sin x-\cos x=0$,is

The integral $\int \frac{3x^{13} + 2x^{11}}{(2x^4 + 3x^2 + 1)^4} dx$ is equal to (where $C$ is a constant of integration)

Choose the incorrect statement from the following:
$S1:$ The efficiency of a heat engine can be $1$,but the coefficient of performance of a refrigerator can never be infinity.
$S2:$ The first law of thermodynamics is basically the principle of conservation of energy.
$S3:$ The second law of thermodynamics does not allow several phenomena consistent with the first law.
$S4:$ $A$ process,whose only result is to transfer heat from a colder to a hotter object,is impossible.

Which of the following hormones is used to induce callus formation from shoot tips?

The major product $A$ is:

Oxidation number of $P$ in $Mg_2P_2O_7$ is