When a bucket is half full,the weight of the bucket and the water is $10 \ kg$. When the bucket is two-thirds full,the total weight is $11 \ kg$. What is the total weight (in $kg$),when the bucket is completely full?

Three waves of equal frequency having amplitudes $10\, \mu m, 4\, \mu m$ and $7\, \mu m$ arrive at a given point with successive phase difference of $\pi/2$. The amplitude of the resulting wave in $\mu m$ is given by

$A$ convex lens $A$ of focal length $20 \ cm$ and a concave lens $B$ of focal length $5 \ cm$ are kept along the same axis with a distance $d$ between them. If a parallel beam of light falling on $A$ leaves $B$ as a parallel beam,then the distance $d$ in $cm$ will be

$A$ radioactive nucleus undergoes a series of decays according to the scheme:
$A \xrightarrow{\alpha} A_1 \xrightarrow{\beta} A_2 \xrightarrow{\alpha} A_3 \xrightarrow{\gamma} A_4$
If the mass number and atomic number of $A$ are $180$ and $72$ respectively,what are these numbers for $A_4$?

An object is projected with a velocity of $20 \ m/s$ making an angle of $45^\circ$ with the horizontal. The equation for the trajectory is $h = Ax - Bx^2$,where $h$ is height,$x$ is horizontal distance,and $A$ and $B$ are constants. The ratio $A : B$ is $(g = 10 \ m/s^2)$.

The two thigh bones (femurs),each of cross-sectional area $10 \,cm^2$,support the upper part of a person of mass $50 \,kg$. The average pressure sustained by the femurs is ........... $N/m^2$.