List of practice Questions

If D is the set of all real x such that \( 1 - e^{(1/x)} \) is positive, then D is equal to:

Find the value of the limit \[ \lim_{x \to 0} \frac{\sqrt{1 - \cos x}}{x} \]

Evaluate \[ \int \frac{x^2 + 4}{x^4 + 16} \, dx \]

Evaluate \[ \int_{ \frac{\pi}{4} }^{ \frac{3\pi}{4} } \frac{1}{1 + \cos x} \, dx \]

If one AM 'A' and two GM \( p \) and \( q \) are inserted between two given numbers, then find the value of \[ \frac{p^2}{q} + \frac{q^2}{p} \]

To the lines \( ax^2 + 2hxy + by^2 = 0 \), the line \( ax^2 + 2h(a+b)xy + b^2y^2 = 0 \) are:

If \( R \) be a relation from \( A = \{1, 2, 3, 4\} \) to \( B = \{1, 3, 5\} \) such that \( (a, b) \in R \) if \( a<b \), then ROR is:

If \( x + y = (1 + i \sqrt{3})^{100} \), then find \( (x, y) \):

For a GP, \( a_n = 3(2^n) \), \( n \in \mathbb{N} \), Find the common ratio.

If \( a, b, c \) are in HP, then \( \frac{a}{b+c} = \frac{b}{c+a} = \frac{c}{a+b} \) will be in:

If \( x^2 + 2x + 7<6 \), \( x \in \mathbb{R} \), then:

The number of ways of painting the faces of a cube of six different colours is:

For the reaction \( 2A + B \rightleftharpoons C \), \( \Delta H = x \) cal, which one of the following conditions would favour the yield of C on the basis of Le-Chatelier's principle?

The EMF of the cell, \[ \text{Mg}^{2+}(0.01M) \parallel \text{Sn}^{2+}(0.1M) \parallel \text{Sn at 298K} \] is:

Heat of formation, \( \Delta H_f \), of an explosive compound like NC\( _3 \) is:

For the reaction, \[ C_3H_8(g) + 5O_2(g) \rightarrow 3CO_2(g) + 4H_2O(l) \] at constant temperature, \( \Delta H = \Delta E \) is:

The favourable conditions for a spontaneous reaction are:

Compound A and B are treated with dil. HCl separately. The gases liberated are Y and Z respectively. Y turns acidified dichromate paper green while Z turns lead acetate paper black. The compound A and B are respectively:

Which of the following is the correct comparison of the stability of the molecules?

Consider the following equation, which represents the reaction in the extraction of chromium from its ore: \[ \text{Fe}_2\text{O}_3 + 4\text{Na}_2\text{Cr}_2\text{O}_7 + 3O_2 \rightarrow 2\text{Fe}_2\text{O}_3 + 4\text{Na}_2\text{CrO}_4 + 3O_2 \] Which of the following statements about the oxidation states of the substances is correct?

In the reversible reaction, \[ 2NO_2 \rightleftharpoons \text{N}_2\text{O}_4 \] the rate of disappearance of \( NO_2 \) is equal to:

A chemical reaction was carried out at 300 K and 280 K. The rate constants were found to be \( k_1 \) and \( k_2 \) respectively. Then

The rate constant of a reaction at temperature 200 K is 10 times less than the rate constant at 400 K. What is the activation energy of the reaction?

A vessel at 1000 K contains CO\(_2\) with a pressure of 0.5 atm. Some of the CO\(_2\) is converted into CO on the addition of graphite. The value of K if the total pressure at equilibrium is 0.8 atm, is:

The radio-isotope used for treatment of thyroid disorders is: