AIEEE 2003 (Maths) Mock Test

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is:

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by:

If $1,\omega ,{\omega }^2$ are the cube roots of unity, then$\Delta =\left|\begin{array}{ccc}1& {\omega }^n& {\omega }^{2n}\\ {\omega }^n& {\omega }^{2n}& 1\\ {\omega }^{2n}& 1& {\omega }^n\end{array}\right|$ is equal to:

If ${}^n{C}_r$ denotes the number of combinations of $n$ things taken $r$ at a time, then the expression ${}^n{C}_{r+1}+{}^n{C}_{r-1}+2\times {}^n{C}_r$ equals:

The number of integral terms in the expansion of $(\sqrt{3}+\sqrt[8]{5}{)}^{256}$ is: