List of practice Questions

The coefficient of \( x^{20} \) in the expansion of \( (1 + x^2)^{40} \left( x^2 + 2 + \frac{1}{x^2} \right)^{-5} \) is:

If \( x \) is positive then the sum to infinity of the series \[ \frac{1}{1+3x} - \frac{1}{1+3x^2} + \frac{1}{1+3x^3} - \dots \, \infty \] is:

Which of the following is soluble in yellow ammonium sulphide?

Let A and B be two sets then \( (A \cup B) \cup (A \cap B) \) is equal to:

Let \( x \) and \( y \) be two natural numbers such that \( x \cdot y = 12(x + y) \) and \( x \leq y \). Then the total number of pairs \( (x, y) \) is:

In \( \sin \theta + \sin^2 \theta = 1/2 \), cos\( 2\theta + \) cos\( \theta = 3/2 \), then cos\( \theta - \phi \) is equal to:

Let \( T(k) \) be the statement \( 1 + 3 + 5 + \dots + (2k - 1) = k^2 + 10 \). Which of the following is correct?

The amplitude of \( \sin \frac{\pi}{5} + i \left( 1 - \cos \frac{\pi}{5} \right) \) is:

The helical structure of protein is stabilized by:

Complete hydrolysis of cellulose gives:

Alizarin is an example of:

2,4-Dichlorophenoxyacetic acid is used as:

0.45 g of acid molecular weight 90 is neutralized by 20 mL of 0.5N caustic potash. The basicity of the acid is:

In the reaction of KMnO\(_4\) with an oxalate in acidic medium, MnO\(_4^-\) is reduced to Mn\(^{2+}\) and C\(_2\)O\(_4^{2-}\) is oxidized to CO\(_2\). Hence, 50 mL of 0.02 M KMnO\(_4\) is equivalent to:

Among the following, the lowest degree of paramagnetism per mole of the compound at 298 K will be shown by:

Which of the following processes is used for the preparation of acetone?

The preparation of ethyl acetoacetate involves:

Which one of the following pairs is not correctly matched?

The ionic conductance of \( \text{Ba}^{2+} \) and \( \text{Cl}^- \) respectively are 127 and 76 \( \text{S} \, \text{cm}^{-1} \) at infinite dilution. The equivalent conductance of \( \text{BaCl}_2 \) at infinite dilution will be:

\( 2N_2O_5 \to 4NO_2 + O_2 \) If rate and rate constant for above reaction are \( 2.40 \times 10^{-5} \, \text{mol L}^{-1} \text{s}^{-1} \) and \( 3 \times 10^{-5} \, \text{s}^{-1} \), respectively, then calculate the concentration of \( N_2O_5 \):

Which of the following gives maximum value of enthalpy of physiolysis?

Which of the following will be most effective in the coagulation of \( \text{Fe(OH)}_3 \) (soil)?

When chlorine water is exposed to sunlight, \( \text{O}_2 \) is liberated. Hence,

An extremely hot copper wire reacts with steam to give:

Which alkene on ozonolysis gives \( \text{CH}_2 \text{CHO} \) and \( \text{CH}_3 \text{CO} \)?