$^{29}C_5 + \sum_{r=0}^{4} {^{(33-r)}C_4} =$

If $^n{P_r} = 840$ and $^n{C_r} = 35$,then $n$ is equal to

If for some $m, n$,${ }^6 C_{m}+2({ }^6 C_{m+1})+{ }^6 C_{m+2} > { }^8 C_3$ and ${ }^{n-1} P_3 : { }^n P_4 = 1 : 8$,then ${ }^n P_{m+1} + { }^{n+1} C_m$ is equal to

There are three sections in a question paper,each containing $4$ questions. If a candidate has to answer only $5$ questions from this paper without leaving any section,then the number of ways the candidate can make the choice of questions is:

The number of four-digit numbers formed by using the digits $0, 2, 4, 5$ (without repetition) which are not divisible by $5$ is:

If all the numbers which are greater than $6000$ and less than $10000$ are formed with the digits $3, 5, 6, 7, 8$ without repetition of the digits,then the difference between the number of odd numbers and the number of even numbers among them is