One litre of oxygen at a pressure of $1\, atm$ and two litres of nitrogen at a pressure of $0.5\, atm$ are introduced into a vessel of volume $1\, L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) is

$A$ vertical $U-$tube of uniform inner cross-section contains mercury in both sides of its arms. $A$ glycerin (density $= 1.3 \ g/cm^3$) column of length $10 \ cm$ is introduced into one of its arms. Oil of density $0.8 \ g/cm^3$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column. (Density of mercury $= 13.6 \ g/cm^3$) (in $cm$)

The upper half of an inclined plane with an angle of inclination $\phi$ is smooth, while the lower half is rough. $A$ body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is

Which of the following substances,if introduced into the blood stream,causes coagulation of blood at the site of its introduction?

The orthocentre of the triangle formed by the lines $x+3y=10$ and $6x^2+xy-y^2=0$ is

The lengths of tangent,subtangent,normal,and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are $A, B, C$,and $D$ respectively. Then their increasing order is: