List of practice Questions

A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of \( 0.02 \, \text{cm/s} \). The rate of increase of its volume when the radius is \( 10 \, \text{cm} \) is:

The interval in which the function \( f(x) = \frac{4x^2 + 1}{x} \) is decreasing is:

The eccentricity of the ellipse whose major axis is three times the minor axis is:

The equation of the hyperbola with vertices \( (3, 0), (-3, 0) \) and semi-latus rectum 4 is given by:

Amplitude of \( \frac{1 + \sqrt{3}i}{\sqrt{3} + 1} \) is:

The value of \[ \lim_{x \to 0} \frac{x^3 \cot x}{1 - \cos x} \] is:

The connective in the statement: \[ "2 + 7>9 \, \text{or} \, 2 + 7<9" \] is:

The number of ways in which 3 prizes can be distributed to 4 children, so that no child gets all the three prizes, are:

If \( A \) and \( B \) are events such that \( P(A) = 0.42 \), \( P(B) = 0.48 \), and \( P(A \cap B) = 0.16 \), then: I. \( P(\text{not } A) = 0.58 \)
II. \( P(\text{not } B) = 0.52 \)
III. \( P(A \cup B) = 0.47 \)

The focus of the curve \( y^2 + 4x - 6y + 13 = 0 \) is:

Which one of the following statements is correct?

In case of nitrogen, \( \text{NCl}_3 \) is possible but not \( \text{NCl}_5 \), while in case of phosphorus, \( \text{PCl}_3 \) as well as \( \text{PCl}_5 \) is possible. It is due to:

For the reaction: \[ \text{BaO} (s) + \text{O}_2(g) \rightarrow \text{BaO}_2(s) \] \( \Delta H = +ve \), In equilibrium condition, pressure of \( O_2 \) is dependent on:

In the series of reaction \[ \text{C}_6\text{H}_5\text{NH}_2 \xrightarrow{\text{NaNO}_2/\text{HCl}} X \quad \text{and} \quad X \xrightarrow{\text{HNO}_3, \text{H}_2\text{O}} Y + \text{N}_2 + \text{HCl}, \] X and Y are respectively:

In \( \text{XeF}_2 \), \( \text{XeF}_4 \), \( \text{XeF}_6 \), the number of lone pairs on Xe are respectively:

In Williamson synthesis if tertiary alkyl halide is used than:

If \( 12 \cot^2 \theta - 31 \csc \theta + 32 = 0 \), then the value of \( \sin \theta \) is:

The energies \( E_1 \) and \( E_2 \) of two radiations are 25 eV and 50 eV, respectively. The relation between their wavelengths i.e., \( \lambda_1 \) and \( \lambda_2 \), will be:

In the reaction:

The nucleotide in DNA are linked by:

The correct order of the thermal stability of hydrogen halides (H-X) is:

The values of \( \Delta H \) and \( \Delta S \) for the reaction, \[ \text{C(graphite)} + \text{CO}_2(g) \rightarrow 2\text{CO}(g), \] are 170 kJ and 170 J/K, respectively. This reaction will be spontaneous at:

The following carbohydrate is:

Given that the equilibrium constant for the reaction \( 2SO_3(g) + O_2(g) \rightleftharpoons 2SO_2(g) \) has a value of \( 2.78 \times 10^{3} \) at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature? \[ SO_3(g) \rightleftharpoons SO_2(g) + \frac{1}{2}O_2(g) \]

An organic compound \( \text{C}_6\text{H}_9\text{N} \) (A), when treated with nitrous acid, gave an alcohol and \( \text{N}_2 \) gas was evolved. (A) on warming with \( \text{CHCl}_3 \) and caustic potash gave (C), which on reduction gave isopropylmethylamine. Predict the structure of (A):