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QUEST TUTORIALS
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1. A question paper is divided into two
parts A and B and each part contains
5 questions . The number of ways in
which a candidate can answer 6
questions selecting atleast two
questions from each part is :
(A) 80 (B) 100
(C) 200 (D) None of these
2. If 15C3r = 15Cr + 3 , then the value of r is
(A) 3 (B) 4
(C) 2 (D) 1
3. 47C4 +
r=
∑
1
5
52 - rC3 =
(A) 47C6(B) 52C5
(C) 52C4(D) None of these
4. If 2nC3 : nC2 = 44 : 3, then for which
of the following values of r, the value
of nCr will be 15 :
(A) r = 3 (B) r = 4
(C) r = 6 (D) r = 5
5. There are four balls of different
colours and boxes of colours same as
those of the balls . The number of
ways in which the balls, one in each
box, could be placed such that a ball
does not go to box of its own colour
is :
(A) 8 (B) 7
(C) 9 (D) None of these
6. The number of numbers that can be
formed with the help of the digits
1, 2, 3, 4, 3, 2, 1 so that odd digits
always occupy odd places, is :
(A) 24 (B) 18
(C) 12 (D) 30
7. Ten different letters of an alphabet are
given . Words with five letters are
formed from these given letters . Then
the number of words which have
atleast one letter repeated is :
(A) 69760 (B) 30240
(C) 99748 (D) None of these
8. Eight chairs are numbered 1 to 8 .
Two women and three men wish to
occupy one chair each . First the
women choose the chairs from
amongst the chairs marked 1 to 4 and
then men select the chairs from
amongst the remaining . The number
of possible arrangements is :
(A) 6C3
×
4C2(B) 4C2
×
4P3
(C) 4P2
×
4P3(D) None of these
9. The number of ways in which the
letters of the word ARRANGE can be
arranged such that both R do not come
together is :
(A) 360 (B) 900
(C) 1260 (D) 1620
10. In how many ways a garland can be
made from exactly 10 flowers ?
(A) 10 !(B) 9 !
(C) 2 (9 !) (D)
9
2
!
11. A student is allowed to select atmost
n books from a collection of (2n + 1)
books . If the total number of ways in
which he can select one book is 63,
then the value of n is :
(A) 2 (B) 3
(C) 4 (D) None of these
12. A box contains two white balls, three
black balls and four red balls . In how
many ways can three balls be drawn
from the box, if atleast one black ball
Permutation & Combinations
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