Class – 12 -
---
Subject – Mathematics Topic –P&C(solution) DPP - revision final 3 Date: 29.03.2020
Permutation and combination (Level – I) Date:28.03.2020
Level - II
22. How many different nine digit numbers can be formed from the number 223344888 by rearranging its digits so that odd digits
occupy even places
(A) 16 (B) 36
(C) 60 (D) 180
p
23. The number of rational numbers , where p, q {1, 2, 3, 4, 5, 6,} is
q
(A) 23 (B) 32
(C) 36 (D) none of these
24. The number of ordered pairs (m, n) (m, n {1, 2, …., 20} ) such that 3m + 7n is a multiple of 10, is
(A) 100 (B) 200
(C) 4! 4! (D) none of these
25. The number of arrangement of the letters of the word ‘BANANA’ in which two N’ and do not appear adjacently is
(A) 40 (B) 60
(C) 80 (D) 100
26. The number of positive integral solutions of the equation x 1 x2 x3 = 60 is
(A) 54 (B) 27
(C) 81 (D) None of these.
27. The number of permutations of the letters a, b, c, d, e, f, g such that neither the pattern ‘beg’ nor the pattern ‘cad’ appears
is
(A) 4106 (B) 4806
(C) 4776 (D) 5120
Narayana Academy : Above Family Bazar, Near CMS School, Saheed Path, Gomtinagar Extension - 226010 1
28. The number of non-negative integral solutions of x1 + x2 + x3 + 4x4 = 20 is
(A) 236 (B) 336
(C) 436 (D) 536
29. The number of ordered triplets of positive integers which are solutions of the equation x + y + z = 100 is
(A) 5081 (B) 6005
(C) 4851 (D) none of these.
30. The number of numbers less than 1000 that can be formed out of the digits 0, 1, 2, 3, 4, and 5, no digit being repeated, is
(A) 130 (B) 131
(C) 156 (D) none of these.
31. Let (0, 0), (21, 0) and (0, 21) be the vertices of a triangle. The number of points having integral co-ordinates which are strictly
inside the given triangle are
(A) 231 (B) 105
(C) 190 (D) 133
32. The sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is.
(A) 18 (B) 108
(C) 432 (D) 144.
33. ‘m’ men and ‘n’ women are to be seated in a row so that no two women sit together. If m> n, then the number of ways in
which they can be seated is
m !n ! m ! (m + 1) !
(A) (B)
(m + n) ! (m − n + 1) !
m ! m !
(C) (C) none of these
(m − n + 1) !
34. The total number of all proper factors of 75600 is
(A) 120 (B) 119
Narayana Academy : Above Family Bazar, Near CMS School, Saheed Path, Gomtinagar Extension - 226010 2
(C) 118 (D) none of these
35. The number of ways in which a batsman can score 14 runs in 6 balls not scoring more than 4 runs in any ball is
(A) 19C5 - 6.14C5 + 15.9C5 (B) 19C5 + 6.14C5 - 15.9C5
(C) 386 (D) 286
36. How many six digits numbers can be formed in decimal system in which every succeeding digit is greater than its preceding
digit
(A) 9P6 (B) 10P6
(C) 9C3 (D) none of these
37. There are n numbered seats around a round table. In how many ways can m (< n) persons sit around the round table
(A) nCm.m! (B) nCm.(m –1)!
n
Cm .(m-1)!
(C) (D) none of these
2
38. The number of n-digit numbers which contain the digits 2 and 7, but not the digits 0, 1, 8, 9 is
(A) 2n + 2n/2 - 2n/4 (B) 6n - 2.5n + 4n
(C) 6n - 2.4n + 5n (D) 6n - 2.4n + 5n
ANSWERS:
22. A 23. A 24. A
25. A 26. A 27. B 28. D
29. C 30. B 31. C 32. B
33. B 34. C 35. A 36. C
37. A 38. B
Narayana Academy : Above Family Bazar, Near CMS School, Saheed Path, Gomtinagar Extension - 226010 3
