List of practice Questions

A balloon contains 2.0 g of hydrogen gas. A second balloon contains 4.0 g of helium gas. Both balloons are at the same temperature and pressure. Pick the false statement from the following list.

The vapour pressure of pure water is 23.5 mm Hg. Then, the vapour pressure of an aqueous solution which contains 5 mass percent of urea is (Molar mass of urea is 60).

Choose the one false statement.

What is the minimum number of moles of Pb(NO3) must be added to 0.10L of a solution that is 1.0M in MgCl2 and 1.0 M in KCl? The compound PbCl2 precipitates.

The \( K_{sp} \) for Mn(OH)\(_2\) is \( 1.6 \times 10^{-13} \). What is the molar solubility of this compound in water?

Choose the most appropriate options. Arrange the following in the decreasing order of basic character: I. p-toluidine II. N,N-dimethyl-p-toluidine III. p-nitroaniline IV. Aniline

In how many ways can 10 identical objects be put in 8 distinct boxes in such that no box is empty?

Choose the most appropriate option. \(\lim_{x \to 1} x^{(1-x)}\) is equal to:

In how many ways can 3 blue, 4 white and 2 red balls be distributed into 4 distinct boxes?

Choose the most appropriate option. \[ \int_{-2}^{2} \frac{3x^7 - 2x^5 + x^3 - 3}{x^4 + 3x^2 + 1} \, dx \]

Is equal to $$ \left| \begin{matrix} b^2 + c^2 & c^2 + b^2 \\ c^2 & c^2 + a^2 \\ b^2 & a^2 + b^2 \end{matrix} \right| $$ 

Choose the most appropriate option. If \(y = a^b x\), then

Choose the most appropriate options. Let \( P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \} \) and \( Q = \{ \theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \} \). Then,

If the arithmetic mean of the following data is 7, then \( a + b = \) \[ \begin{array}{|c|c|c|c|c|} \hline x_i & 4 & 6 & 7 & 9 \\ f_i & a & 4 & b & 5 \\ \hline \end{array} \]

Evaluate the limit: \[ \lim_{x \to a} \frac{\log{(x^{a-1})}}{x-a} \]

Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x} \]