1.Algebra Booster

Permutations and Combinations 5.13
18. The rank of the word IIT according to English dictionary
is
(a) 2 (b) 1 (c) 3 (d) 4
19. In how many ways, can the letters of the word ARRANGE
be arranged so that two Rs are never together is
(a) 800 (b) 600 (c) 900 (d) 700
20. The number of ways in which 10 candidates A 1
, A 2
, …,
A 10
can be ranked so that A 1
always above A 2
is
(10)!
(a) (10)!
(b)
(c) (9)!
(d)
2
(9)!
2
21. There are 4 letters and 4 directed envelopes. The number
of ways in which all the letters can be put in the
wrong envelope is
(a) 8 (b) 9 (c) 16 (d) 20
22. 6 boys and 6 girls sit along a line alternately in x ways
and along a circle in y ways, then
(a) x = y
(b) y = 12x
(c) x = 10y
(d) x = 12y
23. The number of ways in which 7 persons can be arranged
at a round table if two particular persons may
not sit together is
(a) 480 (b) 120 (c) 80 (d) 100
24. A round table conference is to be held between 20 delegates
of 20 countries. The number of ways can they be
seated if two particular delegates sit together is
(a) 2 ¥ (17)! (b) 2 ¥ (19)!
(c) 2 ¥ (18)! (d) 2 ¥ (20)!
25. The number of positive integral solutions of xyz = 20 is
(a) 9 (b) 27 (c) 81 (d) 243
26. The number of positive integral solutions of x + y + z =
10 is
(a) 33 (b) 55 (c) 66 (d) 44
27. The number of positive integral solutions of
2x + 2y + z = 10 is
(a) 33 (b) 55 (c) 66 (d) 44
28. The number of points of intersection of 5 circles is
(a) 30 (b) 20 (c) 66 (d) 40
29. The number of points of intersection of 8 lines and 4
circles is
(a) 32 (b) 64 (c) 76 (d) 104
30. The number of rectangles of size 6 ¥ 4 is
(a) 110 (b) 160 (c) 210 (d) 150
31. The number of rectangles of any size in a chess board is
(a) 216 (b) 1296 (c) 64 (d) 1024.
32. The number of squares of any size in a rectangle of size
8 ¥ 5 is
(a) 150 (b) 130 (c) 100 (d) 160
33. The number of zeroes at the end of (2013)! is
(a) 400 (b) 501 (c) 250 (d) 160
34. The number of ways of 52 cards can be equally divided
among 4 persons is
(a)
(52)!
(52)!
(b)
4
4
(13!) ¥ 4
(13!)
(c)
(52)!
(52)!
(d)
4
4
(13!) ¥ 4!
(13!) ¥ 2!
35. The number of ways 12 balls can be divided between 2
boys, one receiving 5 and the other gets 7 is
(a) 1584 (b) 1284 (c) 1384 (d) 1484
36. The number of non-negative integral solutions of
3x + y + z = 24i
(a) 115 (b) 117 (c) 119 (d) 121
37. The number of solutions of x + y + z = 6, where x, y, z
ΠN, is
(a) 180 (b) 280 (c) 380 (d) 480
38. The number of ways 5 different balls can be arranged
into 3 different boxes, so that no box remains empty, is
(a) 420 (b) 620 (c) 720 (d) 520
39. The number of ways 5 identical balls can be distributed
into 3 different boxes, so that no box remains empty, is
(a) 5 (b) 6 (c) 10 (d) 15
40. The number of ways 16 identical balls can be distributed
among 4 persons, if each person get at least 3 things
is
(a) 55 (b) 25 (c) 35 (d) 45
41. The sum of all odd divisors of 360 is
(a) 75 (b) 76 (c) 78 (d) 88
42. The number of ways the number 18900 can be resolved
as a product of two factors is
(a) 25 (b) 30 (c) 36 (d) 40
43. The number of ways 18900 can be split into two factors,
which are relatively prime, is
(a) 8 (b) 10 (c) 12 (d) 6
44. The number of ways to put 5 letters in 5 addressed envelopes
so that all are in wrong envelopes is
(a) 22 (b) 33 (c) 44 (d) 55
45. The number of ways to put 6 letters in 6 addressed envelopes
so that all are in wrong envelopes is
(a) 262 (b) 363 (c) 265 (d) 565
46. The number of permutations of the letters a, b, c and d
such that b does not follow a, c does not follow b, and
d does not follow c, is
(a) 12 (b) 11 (c) 14 (d) 13
47. The number of function f from the set {1, 2, 3, 4, 5}
into the set {1, 2, 3, 4, 5} such that f(i) π i, is
(a) 30 (b) 44 (c) 9 (d) 63
48. The number of ways distributing 12 identical oranges
among 4 children so that every child gets at least one
and no child gets more than 4 is
(a) 31 (b) 32 (c) 35 (d) 42
49. In how many ways can 20 oranges can be given to four
children if each child get at least one orange?
(a) 969 (b) 691 (c) 891 (d) 979