List of practice Questions

The rms velocity of molecules of a gas of density $4~\text{kg m}^{-3}$ and pressure $1.2 \times 10^{5}~\text{N m}^{-2}$ is

0.5 mole of each of $H_{2}$, $SO_{2}$ and $CH_{4}$ are kept in a container. A hole was made in the container. After 3 h, the order of partial pressures in the container will be

The enthalpy of formation of $NH_{3}$ is -46 kJ mol$^{-1}$. The enthalpy change for the reaction $2NH_{3}(g) \longrightarrow N_{2}(g) + 3H_{2}(g)$ is

5 moles of $SO_{2}$ and 5 moles of $O_{2}$ are allowed to react. At equilibrium, it was found that 60% of $SO_{2}$ is used up. If the partial pressure of the equilibrium mixture is one atmosphere, the partial pressure of $O_{2}$ is

\( 2HI(g) \rightleftharpoons H_{2}(g) + I_{2}(g) \). The equilibrium constant of the above reaction is 6.4 at 300 K. If 0.25 mole each of \( H_{2} \) and \( I_{2} \) are added to the system, the equilibrium constant will be

IUPAC name of \( (CH_{3})_{3}CCl \) is

An organic compound on heating with CuO produces \( CO_{2} \) but no water. The organic compound may be

The function of \( Fe(OH)_{3} \) in the contact process is

In which of the following, \( NH_{3} \) is not used?

The magnetic moment of a transition metal ion is \( \sqrt{15} \,\text{BM} \). Therefore, the number of unpaired electrons present in it is

The IUPAC name of \( [Co(NH_{3})_{5}ONO]^{2+} \) ion is

The oxidation state of Fe in the brown ring complex: \( [Fe(H_{2}O)_{5}NO]SO_{4} \) is

If \( f : [2,3] \rightarrow \mathbb{R} \) is defined by \( f(x) = x^{3 + 3x - 2} \), then the range of \( f(x) \) is contained in the interval

\( \{ x \in \mathbb{R} : \frac{2x - 1}{x^{3} + 4x^{2} + 3x} \in \mathbb{R} \} \) equals

Using mathematical induction, the numbers \( a_{n} \) are defined by \( a_{0} = 1,\; a_{n+1} = 3n^{2} + n + a_{n}, \; (n \ge 0) \). Then, \( a_{n} \) is equal to

The number of subsets of \( \{1, 2, 3, \ldots, 9\} \) containing at least one odd number is

The coefficient of \( x^{24} \) in the expansion of \( (1+x^{2})^{12}(1+x^{12})(1+x^{24}) \) is

If \( x \) is numerically so small that \( x^{2} \) and higher powers of \( x \) can be neglected, then \( \left(1+\frac{2x}{3}\right)^{3/2} \cdot (32+5x)^{-1/5} \) is approximately equal to

\( \frac{1}{e^{3x}}(e^{x} + e^{5x}) = a_{0} + a_{1}x + a_{2}x^{2} + \cdots \Rightarrow 2a_{1} + 2^{3}a_{3} + 2^{5}a_{5} + \cdots \) is equal to

Let \( f(x) = x^{2} + ax + b \), where \( a, b \in \mathbb{R} \). If \( f(x)=0 \) has all its roots imaginary, then the roots of \( f(x) + f'(x) + f''(x) = 0 \) are

If \( \alpha, \beta, \gamma \) are the roots of \( x^{3} + 4x + 1 = 0 \), then the equation whose roots are \[ \frac{\alpha^{2}}{\beta+\gamma}, \quad \frac{\beta^{2}}{\gamma+\alpha}, \quad \frac{\gamma^{2}}{\alpha+\beta} \] is

If \( f(x) = 2x^{4} - 13x^{2} + ax + b \) is divisible by \( x^{2} - 3x + 2 \), then \( (a, b) \) is equal to

If one of the roots of \( \begin{vmatrix} 3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3 \end{vmatrix} = 0 \), then the other roots are

If \( x, y, z \) are all positive and are the \( p \)th, \( q \)th and \( r \)th terms of a geometric progression respectively, then the value of the determinant \( \begin{vmatrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{vmatrix} \) equals

If \( \begin{bmatrix} 1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1 \end{bmatrix} \) has no inverse, then the real value of \( x \) is