$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is

$A$ double slit experiment is immersed in water of refractive index $1.33$. The slit separation is $1 ~mm$ and the distance between the slit and the screen is $1.33 ~m$. The slits are illuminated by light of wavelength $6300 ~Å$. The fringe width is:

$A$ particle is executing simple harmonic motion with an amplitude $A$ and time period $T$. The displacement of the particle after $2T$ time from its initial position is

For the transistor circuit shown below,if $\beta = 100$ and the voltage drop between the emitter and base is $0.7\ V$,then the value of $V_{CE}$ will be.....$V$.

The equation of the pair of tangents to the circle $x^2 + y^2 - 2x + 4y + 3 = 0$ from the point $(6, -5)$ is:

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$,$\vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. $A$ vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$,whose projection on $\vec{c}$ is $\frac{1}{\sqrt{3}}$,is given by