BUET Admission Test 2014-2015

1. An electric power station annually burns $3.1 \times 10^{7} \mathrm{~kg}$ of coal containing $2.4 \%$ rhombic Sulphur by mass. Calculate the volume of $\mathrm{SO}_{2}$ produced at STP.

2. The capacity of a closed cylindrical can made of tin is $1 \mathrm{~L}\left(1000 \mathrm{~cm}^{3}\right)$ of liquid. What should be the height and radius of the can so that the amount of tin needed to manufacture it will be minimum?

3. Find a nonzero value of the constant $\mathrm{k}$ that makes the following function continuous at $\mathrm{x}=0$. Justify your answer.

$f(x)=\left\{\begin{array}{ll} \frac{\tan k x}{x}, & x<0 \\ 3 x+2 k^{2}, & x \geq 0 \end{array}\right.$

4. The half-life of $\mathrm{U}^{238}$ is $1.42 \times 10^{17} \mathrm{~s}$. How many disintegrations per second occurs in $1 \mathrm{~g}$ of $\mathrm{U}^{238}$ ?

[Avogadro's number, $\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-1}$ ]

5. Write with reactions, how aqua regia dissolves platinum.