If ${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$,then the minimum value of $n$ is

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then the value of $\lambda$ is

$A$ mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency $\omega$. The mass $M$ moves with steady speed in a circular path of constant radius $r$. The angular momentum of $M$ about point $A$ is $L_A$,which lies in the positive $z$-direction,and the angular momentum of $M$ about point $B$ is $L_B$. Which of the following statements is correct for this system?

Identify the incorrect pair from the following:

Which has the maximum number of molecules among the following?

The solution of $\frac{dy}{dx} = (\frac{x}{y})^{-1/3}$ is