If two of the lines represented by $2x^3 + x^2y + y^3 = 0$ are mutually perpendicular,then the slope of the third line is

If the coefficients of the $(2r+1)$-th term and the $(r+2)$-th term in the expansion of $(1+x)^{43}$ are equal,then $r$ is equal to:

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.

Beats are produced by two waves $y_1 = a \sin(1000\pi t)$ and $y_2 = a \sin(998\pi t)$. The number of beats heard per second is:

If the lines $4x + 3y - 1 = 0$,$x - y + 5 = 0$,and $kx + 5y - 3 = 0$ are concurrent,then $k$ is equal to:

Which one of the following statements is not correct?