All the letters of the word "GTWENTY" are written in all possible ways with or without meaning, and these words are arranged as in a dictionary. The serial number of the word "GTWENTY" is:
A body starts moving from rest with constant acceleration and covers displacement \(S_1\) in the first \((p - 1)\) seconds and \(S_2\) in the first \(p\) seconds. The displacement \(S_1 + S_2\) will be made in time:
For a reaction taking place in three steps at the same temperature, the overall rate constant \( K = \frac{K_1 K_2}{K_3} \). If \( E_{a1} \), \( E_{a2} \), and \( E_{a3} \) are 40, 50, and 60 kJ/mol respectively, the overall \( E_a \) is ____ kJ/mol.
A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the coefficient of friction between the surfaces is 0.4, then the work done against friction (in J) is:
For \( 0 < a < 1 \), the value of the integral \[ \int_{0}^{\frac{\pi}{2}} \frac{dx}{1 - 2a \cos x + a^2} \] is: