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1

### IIT-JEE 2005

Subjective
If total number of runs scored in n matches is $$\left( {{{n + 1} \over 4}} \right)\,\,({2^{n + 1}} - n - 2)\,$$ where $$n > 1$$, and the runs scored in the $${k^{th}}$$ match are given by k. $$\,{2^{n + 1 - k}}$$, where $$1 \le k \le n$$. Find n.

7
2

### IIT-JEE 2004

Subjective
Prove by permulation or otherwise $${{({n^2})!} \over {{{(n!)}^n}}}$$ is an integer $$(n \in {1^ + })$$.

solve it.
3

### IIT-JEE 1994

Subjective
A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have to included in a committee? In how many of these committees? In how may of these committees
(a) The women are in majority?
(b) The men are in majority?

6072, (a) 2702, (b) 1008
4

### IIT-JEE 1991

Subjective
Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made.

$${}^{11}{C_5} \times 9\,!\, \times \,9\,!$$

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Class 12