Particles and their anti-particles have

The equation of the hyperbola which passes through the point $(2,3)$ and has the asymptotes $4x+3y-7=0$ and $x-2y-1=0$ is

$\int_0^1 x^{3/2} \sqrt{1-x} \, dx$ is equal to

If the curves $x^2 - 6x + y^2 + 8 = 0$ and $x^2 - 8y + y^2 + 16 - k = 0$ $(k > 0)$ touch each other at a point,then the largest value of $k$ is

When a wave traverses a medium,the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$,where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then, the probability for the ball chosen to be white is: