- The total number of flags with three horizontal
strips, in order, that can be formed using 2 identical red,
2 identical green and 2 identical white strips, is equal
to
(a) 4! (b) 3.(4!)
(c) 2.(4!) (d) none of these - The sides AB, BC, CA of a triangle ABC have 3, 4,
5 interior points respectively on them. Total number
of triangles that can be formed using these points as
vertices, is equal to
(a) 135 (b) 145 (c) 178 (d) 205 - ‘n 1 ’ men and ‘n 2 ’ women are to be seated in a row
so that no two women sit together. If n 1 > n 2 , then total
number of ways in which they can be seated, is equal
to
(a) n^1 Cn 2 (b) n^1 Cn nn 2 (!)( !) 12
(c) n^1 Cnnn 2 + 11 (!)( !) 2 (d) n^1 +^1 Cn nn 2 (!)( !) 12
- There are ‘n’ numbered seats around a round table.
Total number of ways in which n 1 (n 1 < n ) persons can
sit around the table, is equal to
(a) nCn 1 (b) nPn 1
(c) nCn 1 − 1 (d) nPn 1 − 1
- Three boys of class X, 4 boys of class XI and 5 boys
of class XII, sit in a row. Total number of ways in which
these boys can sit so that all the boys of same class sit
together, is equal to
(a) (3!)^2 (4!) (5!) (b) (3!) (4!)^2 (5!)
(c) (3!) (4!) (5!) (d) (3!) (4!) (5!)^2 - Total number of ways in which the letters of the
word ‘MISSISSIPPI’ be arranged, so that any two S’s are
separated, is equal to
(a) 7350 (b) 3675
(c) 6300 (d) none of these - The number of ways in which a mixed double game
can be arranged amongst nine married couples so that
no husband and his wife play in the same game, is equal
to
(a)^9 C 2 ·^7 C 2 (b)^9 C 2 ·^7 C 2 ·^2 C 1
(c)^9 P 2 ·^7 P 2 (d)^9 P 2 ·^7 P 2 ·^2 P 1 - A candidate is required to answer 7 out of 10
questions, which are divided into two groups, each
containing 5 questions. He is not permitted to attempt
more than 4 questions from each group. Total number
of different ways in which the candidate can answer the
paper, is equal to
(a) 2 ·^5 C 3 ·^5 C 4 (b) 2.^5 P 3 ·^5 P 4
(c)^5 C 3 ·^5 C 4 (d)^5 P 3 ·^5 P 4- The total number of six digit numbers x 1 x 2 x 3 x 4 x 5 x 6
having the property that x 1 < x 2 ≤ x 3 < x 4 < x 5 ≤ x 6
is equal to
(a)^10 C 6 (b)^12 C 6
(c)^11 C 6 (d) none of these - The total number of three digit numbers, the sum
of whose digits is even, is equal to
(a) 450 (b) 350 (c) 250 (d) 325 - ‘n’ different toys have to be distributed among ‘n’
children. Total number of ways in which these toys can
be distributed so that exactly one child gets no toy, is
equal to
(a) n! (b) n! nC 2
(c) (n – 1)! nC 2 (d) n! n – 1 C 2 - Total number of permutations of ‘k’ different
things, in a row, taken not more than ‘r’ at a time (each
thing may be repeated any number of times) is equal to
(a) kr – 1 (b) kr
(c) k
kr−
−1
1(d) kk
k()r
()−
−1
1- Total number of 4 digit numbers that are greater
than 3000 and can be formed using the digits 1, 2, 3, 4, 5, 6
(no digit is being repeated in any number ) is equal to
(a) 120 (b) 240 (c) 480 (d) 80 - A teacher takes 3 children from her class to the zoo
at a time as often as she can, but she doesn’t take the
same set of three children more than once. She finds out
that she goes to the zoo 84 times more than a particular
child goes to the zoo. Total number of students in her
class in equal to
(a) 12 (b) 14 (c) 10 (d) 11 - A person predicts the outcome of 20 cricket
matches of his home team. Each match can result either
in a win, loss or tie for the home team. Total number
of ways in which he can make the predictions so that
exactly 10 predictions are correct, is equal to
(a)^20 C 10 · 2^10 (b)^20 C 10 · 3^20
(c)^20 C 10 · 3^10 (d)^20 C 10 · 2^20 - A team of four students is to be selected from a
total of 12 students. Total number of ways in which
team can be selected such that two particular students
refuse to be together and other two particular students
wish to be together only, is equal to
(a) 220 (b) 182
(c) 226 (d) none of these