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

Correct increasing order of spin magnetic moment (in $B.M.$) for the following complexes is:
$(I) [FeF_6]^{-3}$
$(II) [V(H_2O)_6]^{+2}$
$(III) [Fe(H_2O)_6]^{+2}$

$A$ uniform rope of mass $0.1 ~kg$ and length $2.45 ~m$ hangs from a rigid support. The time taken by the transverse wave formed in the rope to travel through the full length of the rope is (Assume $g=9.8 ~m/s^2$) (in $~s$)

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is

The lines $x-y-2=0$,$x+y-4=0$ and $x+3y=6$ meet at a common point:

Which of the following is not an ore of magnesium?