The probability that a person is not a sportsperson is $\frac{1}{6}$. Then the probability that out of the 6 members of the family, 5 are sportspersons is

If $\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$, then $\sin \left(\frac{\pi}{4}+\theta\right)=$

The line MN whose equation is $x-y-2=0$ cuts the X -axis at M and co-ordinates of N are $(4,2)$. The line MN is rotated about M through $45^{\circ}$ in anticlockwise direction. The equation of the line MN in the new position is

The money invested in a company is compounded continuously. If $Rs\, 400$ invested today becomes ₹800 in 6 years, then at the end of 30 years, it will become (in ₹)