IIT JEE 2006

The edge length of unit cell of a metal having molecular weight \(75 \mathrm{~g} \mathrm{~mol}^{-1}\) is 5 \(\mathop A\limits^o\) which crystallizes in cubic lattice. If the density is \(2 \mathrm{~g} / \mathrm{cc}\), find the radius of metal atom. \(\left(\mathrm{N}_{\mathrm{A}}=6 \times 10^{23}\right)\). Give the answer in \(\mathrm{pm}\).

A circular disc with a groove along its diameter is placed horizontally. A block of mass 1 kg is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu=\frac{2}{5}$. The disc has an acceleration of $25 \mathrm{~m} / \mathrm{s}^2$. Find the acceleration of the block with respect to disc.

For the reaction, $2 \mathrm{CO}+\mathrm{O}_2 \rightarrow 2 \mathrm{CO}_2 ; \Delta \mathrm{H}=-560 \mathrm{~kJ}$. Two moles of CO and one mole of $\mathrm{O}_2$ are taken in a container of volume 1 L . They completely form two moles of $\mathrm{CO}_2$, the gases deviate appreciably from ideal behaviour. If the pressure in the vessel changes from 70 to 40 atm , find the magnitude (absolute value) of $\Delta \mathrm{U}$ at 500 K . $(1 \mathrm{~L} \mathrm{~atm}=0.1 \mathrm{~kJ})$

If \(f(x)\) is a twice differentiable function such that \(f(A)=0, f(B)=2, f(C)=-1, f(D)=2\), \(f(e)=0\), where \(a < b < c < d < e\), then the minimum number of zeroes of \(g(x)=\left(f'(x)\right)^{2}+f''(x) f(x)\) in the interval \([a, e]\) is :

In an insulated vessel, 0.05 kg steam at 373 K and 0.45 kg of ice at 253 K are mixed. Then, find the final temperature of the mixture.