## Fill in the Blanks

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Total number of ways in which six ' + ' and four ' - ' signs can be arranged in a line such that no two ' - ' signs occu...
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 w...
IIT-JEE 1988
The side AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles t...
IIT-JEE 1984
In a certain test, $${a_i}$$ students gave wrong answers to atleast i questions, where i = 1, 2,..., k. No student gave ...
IIT-JEE 1982

## Numerical

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Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand cons...
JEE Advanced 2015 (Offline)
Let $${n_1}\, ... JEE Advanced 2014 (Offline) Let$${n \ge 2}$$be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colo... JEE Advanced 2014 (Offline) Consider the set of eight vectors$$V = \left\{ {a\,\hat i + b\,\hat j + c\hat k:a,\,b,\,c\, \in \left\{ { - 1,\,1} \rig...
JEE Advanced 2013 (Offline)

## MCQ (Single Correct Answer)

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A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel ...
IIT-JEE 2005 Screening
If the LCM of p, q is $${r^2}\,{r^4}\,{s^2}$$, where r, s, t are prime numbers and p, q are the positive integers then n...
IIT-JEE 2005 Screening
The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is
IIT-JEE 2002 Screening
Let $${T_n}$$ denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If ...
IIT-JEE 2001 Screening
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd ...
IIT-JEE 2000 Screening
A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The tota...
IIT-JEE 1989
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the nu...
IIT-JEE 1982
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chai...
IIT-JEE 1982
The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}}$$ is equal to
IIT-JEE 1982
$${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84\,\,and\,\,{}^n{C_{r + 1}} = 126$$, then r is :
IIT-JEE 1979
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an Engl...
IIT-JEE 2007
A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select from this club including the selection...
JEE Advanced 2016 (Offline)
Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope ...
JEE Advanced 2014 (Offline)
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person ge...
IIT-JEE 2012
Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no conse...
IIT-JEE 2012
Let $${{a_n}}$$ denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no conse...
IIT-JEE 2012
the number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, i...
IIT-JEE 2009
Consider all possible permutations of the letters of the word ENDEANOEL. Match the statements / Expressions in Column I ...
IIT-JEE 2008

## MCQ (More than One Correct Answer)

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An n-digit number is a positive number with exactly digits. Nine hundred distinct n-digit numbers are to be formed using...
IIT-JEE 1998

## Subjective

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If total number of runs scored in n matches is $$\left( {{{n + 1} \over 4}} \right)\,\,({2^{n + 1}} - n - 2)\,$$ where \$...
IIT-JEE 2005
Prove by permulation or otherwise $${{({n^2})!} \over {{{(n!)}^n}}}$$ is an integer $$(n \in {1^ + })$$.
IIT-JEE 2004
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the...
IIT-JEE 1986
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 o...
IIT-JEE 1983
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 ...
IIT-JEE 1994
Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one partic...
IIT-JEE 1991
Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how ma...
IIT-JEE 1981
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 ma...
IIT-JEE 1978
7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gen...
IIT-JEE 1985

## True or False

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The product of any r consecutive natural numbers is always divisible by r!
IIT-JEE 1985

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