Where is the Natural History Museum located?

Two ions having masses in the ratio $1: 1$ and charges $1: 2$ are projected into a uniform magnetic field perpendicular to the field with speeds in the ratio $2: 3$. The ratio of the radii of circular paths along which the two particles move is :

The number of normals drawn to the parabola $y^2 = 4x$ from the point $(1, 0)$ is

If $\int e^x \left( \frac{1-\sin x}{1-\cos x} \right) dx = f(x) + \text{constant}$,then $f(x)$ is equal to

Which of the following statements is $NOT$ correct?

In a competition,$A, B$,and $C$ are participating. The probability that $A$ wins is twice that of $B$,and the probability that $B$ wins is twice that of $C$. What is the probability that $A$ loses?