The materials suitable for making electromagnets should have

The equation of a line which makes an angle of $45^{\circ}$ with each of the pair of lines $xy-x-y+1=0$ is

If $f$ is an even function defined on the interval $(-5, 5)$,then four real values of $x$ satisfying the equation $f(x) = f\left( \frac{x + 1}{x + 2} \right)$ are

Three numbers are chosen at random from $1$ to $20$. The probability that they are consecutive is

The work function of nickel is $5 \text{ eV}$. When light of wavelength $2000 \text{ \AA}$ falls on it, it emits photoelectrons. The potential difference necessary to stop the fastest electrons emitted is (given $h = 6.67 \times 10^{-34} \text{ J-s}$): (in $\text{ V}$)

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).