Solid $Ba(NO_3)_2$ is gradually dissolved in a $1.0 \times 10^{-3} \ M \ Na_2CO_3$ solution. At what concentration of $Ba^{2+}$ will a precipitate begin to form? ($K_{sp}$ for $BaCO_3 = 5.1 \times 10^{-9}$)

There is some change in length when a $33000 ~N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} ~m^2$. The change of temperature required to produce the same elongation,if the steel rod is heated,is (The modulus of elasticity is $3 \times 10^{11} ~N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ} C$). (in $^{\circ} C$)

$A$ large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water,the quantities of water flowing out per second from the two holes are the same. Then the value of $R$ is

In angiosperms,the functional megaspore develops into which of the following?

Which of the following has the lowest melting point?

$X$-rays are used in: