The value of $r$ for which $^{20}{C_r}^{20}{C_0}{ + ^{20}}{C_{r - 1}}^{20}{C_1}{ + ^{20}}{C_{r - 2}}^{20}{C_2} + ...{ + ^{20}}{C_0}^{20}{C_r}$ is maximum is
$15$
$20$
$11$
$10$
Number of positive integral solution of the equation $xyz = 90$ is equal to :-
In how many ways a team of $10$ players out of $22$ players can be made if $6$ particular players are always to be included and $4$ particular players are always excluded
If for some $\mathrm{m}, \mathrm{n} ;{ }^6 \mathrm{C}_{\mathrm{m}}+2\left({ }^6 \mathrm{C}_{\mathrm{m}+1}\right)+{ }^6 \mathrm{C}_{\mathrm{m}+2}>{ }^8 \mathrm{C}_3$ and ${ }^{n-1} P_3:{ }^n P_4=1: 8$, then ${ }^n P_{m+1}+{ }^{n+1} C_m$ is equal to
The number of words from the letters of the word $'RAJASTHAN' $ by taking all the letters at a time in which vowels are alternate, are
If $^n{P_3}{ + ^n}{C_{n - 2}} = 14n$, then $n = $