The configurations of the complexes of manganese A, B respectively are \(t_{2 g}^3 e_g^1, t_{2 g}^4 e_g^0\). Then \(A, B\) are

For which of the following processes entropy change \((\Delta \mathrm{S})\) is negative ?
I) Sublimation of dry ice
II) Freezing of water
III) Crystallisation of the dissolved substance
IV) Burning of rocket fuel

Which of the following expression is correct

At \(\mathrm{T}(\mathrm{K}), \mathrm{K}_{\mathrm{c}}\) value of \(\mathrm{AO}_2(\mathrm{~g})+\mathrm{BO}_2(\mathrm{~g}) \rightleftharpoons \mathrm{AO}_3(\mathrm{~g})+\mathrm{BO}(\mathrm{g})\) is 16. In a closed 1 L flask, one mole each of \(\mathrm{AO}_2, \mathrm{BO}_2, \mathrm{AO}_3\) and BO are taken and heated to \(\mathrm{T}(\mathrm{K})\). Identify the correct statements about this equilibrium.
I) Total number of moles at equilibrium is 4
II) At equilibrium, the ratio of moles of \(\mathrm{AO}_2\) and \(\mathrm{AO}_3\) is \(1: 4\)
III) Total number of moles of \(\mathrm{AO}_2\) and \(\mathrm{BO}_2\) at equilibrium is 0.8

The common name of isopropyl benzene is

Which of the following reactions is not correct?

Arrange the following in increasing order of their acidic strength

The upper half of an inclined plane with an angle of inclination \(\phi\), is smooth while the lower half is rough. A body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is

\(\frac{1}{2}-\frac{1}{2 \cdot 2^2}+\frac{1}{3 \cdot 2^3}-\frac{1}{4 \cdot 2^4}+\ldots\) is equal to

If a force \(F\) is applied on a body and it moves with a velocity \(v\), the power will be

The magnetic field at the centre of a long solenoid having 400 turns per unit length and carrying a current ' \(i\) ' is \(6.24 \times 10^{-2} \mathrm{~T}\). The magnetic field at the centre of another long solenoid having 200 turns per unit length and carrying a current \(\frac{' i^{\prime}}{2}\) is

If \(\theta\) is the angle between the unit vectors \(\mathbf{a}\) and \(\mathbf{b}\), then \(\sin \frac{\theta}{2}\) is equal to

The scalar product of the vector $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}$ with a unit vector along the sum of the vectors $\overrightarrow{b}=2\hat{i}+4\hat{j}-5\hat{k}$ and $\overrightarrow{c}=\lambda \hat{i}+2\hat{j}+3\hat{k}$ is equal to one. Then. $\lambda =$