2005
JEE Advanced
Numerical
IIT-JEE 2005
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.
Correct Answer: 7
2004
JEE Advanced
Numerical
IIT-JEE 2004
Prove by permulation or otherwise ${{({n^2})!} \over {{{(n!)}^n}}}$ is an integer $(n \in {1^ + })$.
Correct Answer: solve it.
1994
JEE Advanced
Numerical
IIT-JEE 1994
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?
(a) The women are in majority?
(b) The men are in majority?
Correct Answer: 6072, (a) 2702, (b) 1008
1991
JEE Advanced
Numerical
IIT-JEE 1991
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.
Correct Answer: $${}^{11}{C_5} \times 9\,!\, \times \,9\,!$$
1986
JEE Advanced
Numerical
IIT-JEE 1986
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?
Correct Answer: 64
1985
JEE Advanced
Numerical
IIT-JEE 1985
7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relatives and 3 of the wife's relatives?
Correct Answer: 485
1983
JEE Advanced
Numerical
IIT-JEE 1983
m men and n women are to be seated in a row so that no two women sit together. If $m > n$, then show that the number of ways in which they can be seated is $\,{{m!(m + 1)!} \over {(m - n + 1)!}}$
Correct Answer: solve it.
1981
JEE Advanced
Numerical
IIT-JEE 1981
Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how many different ways can be place the balls so that no box remains emply?
Correct Answer: 300
1978
JEE Advanced
Numerical
IIT-JEE 1978
Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be done.
Correct Answer: 26
1988
JEE Advanced
Numerical
IIT-JEE 1988
Total number of ways in which six ' + ' and four ' - ' signs can be arranged in a line such that no two ' - ' signs occur together is.....................................
Correct Answer: 35
1988
JEE Advanced
Numerical
IIT-JEE 1988
There are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in which the balls, one each in a box, could be placed such that a ball does not go to a box of its own colour is.......................
Correct Answer: 9
1984
JEE Advanced
Numerical
IIT-JEE 1984
The side AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles that can be constructed using these interior points as vertices is .......................
Correct Answer: 205
1982
JEE Advanced
Numerical
IIT-JEE 1982
In a certain test, ${a_i}$ students gave wrong answers to atleast i questions, where i = 1, 2,..., k. No student gave more than k wrong answers. The total number of wrong answers given is.....................................
Correct Answer: $${a_1} + {a_2} + ...... + {a_k}$$
1985
JEE Advanced
MCQ
IIT-JEE 1985
The product of any r consecutive natural numbers is always divisible by r!
A.
TRUE
B.
FALSE