1.Algebra Booster

5.18 Algebra Booster
16. A 5-digit number divisible by 3 is to be formed using
the numbers 0, 1, 2, 3, 4 and 5 without repetition. Find
the total number of ways this can be done.
[IIT-JEE, 1989]
17. In an examination, the maximum marks for each three
papers are 50 each. Maximum marks for 4th paper are
100. Find the number of ways in which the candidate
can score 60 % marks in the aggregate.
[IIT-JEE, 1989]
No questions asked in 1990.
18. 18 guests have to be seated, half on each side of a long
table. 4 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?
[IIT-JEE, 1991]
19. There are four balls of different colours and four boxes
of colours same as those of different colours. Find 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. [IIT-JEE, 1992]
No questions asked in 1993.
20. 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 5
women have to be included in a committee
(i) the women are in majority?
(ii) the men are in majority?
[IIT-JEE, 1994]
No questions asked in 1995.
kk ( + 1)
21. Let n and k be positive integers such that n ≥ .
2
The number of solutions (x 1
, x 2
, …, x k
), x 1
≥ 1, x 2
≥ 2,
…, x k
≥ k all integers, satisfying x 1
+ x 2
+ … + x k
= n,
is...
[IIT-JEE, 1996]
22. Find the number of ways of selecting 5 letters from the
letters of the word INDEPENDENT.
[IIT-JEE, 1997]
23. The number of divisors of the form 4n + 2 (≥ 0) of the
integer 240 is
(a) 4 (b) 8 (c) 10 (d) 3
[IIT-JEE, 1998]
24. An n-digit number is a positive number with exactly
n digits. Nine hundred distinct n-digit numbers are to
be formed using only the three digits 2, 5 and 7. The
smallest value of n for which this is possible is
(a) 6 (b) 7 (c) 8 (d) 9
[IIT-JEE, 1998]
25. In a college of 300 students, every students reads 5
newspapers and every newspaper is read by 60 students.
The number of newspapers is
(a) at least 30 (b) atmost 20
(c) exactly 25 (d) none
[IIT-JEE, 1998]
26. The number of ways in which 5 male and 2 female
members of a committee can be seated around a round
table so that the two females are not seated together is
(a) 480 (b) 600 (c) 720 (d) 840.
[IIT-JEE, 1999]
27. How many different nine-digit numbers can be formed
from the number 223355888 by re-arranging its digits
so that the odd digits occupy even positions?
(a) 16 (b) 36 (c) 60 (d) 80
[IIT-JEE, 2000]
Ênˆ Ê n ˆ Ê n ˆ
28. For 2 £ r £ n, Á + 2 +
Ër˜ ¯
Á
Ër -1˜ ¯
Á
Ër
-2˜
¯
(a)
(c)
Ên
+ 1ˆ
Á
Ër
- 1˜
¯
Ên
+ 2ˆ
Á
Ë r ˜
¯
(b)
(d)
Ên
+ 1ˆ
2Á
Ër
+ 1˜
¯
Ê 2
2 n + ˆ
Á
Ë r ˜
¯
[IIT-JEE, 2000]
29. Let T n
denote the number of triangles which can be
formed using the vertices of a regular polygon of n
sides.
If T n+1
– T n
= 21, then n equals
(a) 5 (b) 7 (c) 6 (d) 4
[IIT-JEE, 2001]
30. The arrangement of the letters of the word BANANA
in which the two N’s do not appear adjacently.
(a) 40 (b) 60 (c) 80 (d) 100
[IIT-JEE, 2002]
No questions asked in 2003.
31. If n – 1 C r
= (k 2 – 3) n C r + 1
, then the value of k is
(a) (– , 2] (b) (2, )
(c) [- 3, 3] (d) ( 3,2]
[IIT-JEE, 2004]
32. A rectangle with sides (2n – 1) and (2m – 1) is divided
into square of unit length. The number of rectangles
which can be formed with sides of odd length is
(a) (m + n – 1) 2 (b) 4 m–n–1
(c) m 2 n 2 (d) mn(m + 1)(n + 1)
[IIT-JEE, 2005]
33. If the L.C.M of p, q is r 2 t 4 s 2 , where r, s, t are prime
numbers and p, q are the +ve integers, the number of
ordered pairs (p, q) is
(a) 252 (b) 254 (c) 225 (d) 224
[IIT-JEE, 2006]
34. The letters of the word COCHIN are permuted and all
the permutations are arranged in an alphabetical order
as in an english dictionary. The number of words that
appear before the word COCHIN.
(a) 360 (b) 192 (c) 96 (d) 48
[IIT-JEE, 2007]