Ref: QAT1002110
QUANTITATIVE ABILITY TEST
(Permutations & Combinations)
Time: 30 min.
Directions for questions 1 to 25: For the Multiple Choice Questions, select the correct alternative from the given
choices. For the Non-Multiple Choice Questions, write your answer in the box provided.
1.
In how many ways can the letters of the word
VARIETY be arranged so that exactly two vowels
are together?
(A) 2880
(B) 5184
(C) 1440
(D) 2160
2.
Eight books are to be distributed among eight
students. In how many ways can it be done
if a particular student has to receive exactly 3
specific books?
(A) 57
(B) 75
(C) 7C5
(D) 35
3.
4.
5.
How many 8-digit numbers can be formed using the
digits 1, 2 and 3 so that the number contains at least
one of each of the three digits?
(A) 243
(B) 112(36) (C) 5696
(D) 5796
A question paper has 40 questions. Each question
has four answer choices and only one of them is
correct. In the first four questions, Raju answered
one question correctly. Starting from the first
question that he got right, he answered every fourth
question correctly. If Raju answered all the
40 questions, in how many ways could he have
answered the paper?
(A) 330
(B) 4(330) (C) 2(330) (D) 331
C

B

A
There is a rectangular grid consisting of uniform
cells as shown. One needs to travel from A to C.
One can travel only rightwards or upwards. In how
many ways can one go from A to C without travelling
via B?
6.
There are 8 parallel lines in a plane. Eight other
lines lying in the same plane, and parallel to each
other, intersect these lines. The number of
parallelograms formed is
7.
In how many ways can ten identical oranges be
placed in three distinct baskets if at least
two oranges are placed in each basket?
(A) 10
(B) 15
(C) 30
(D) 80
8.
Find the sum of all possible 4-digit numbers that can
be formed using the digits 1, 2, 3 and 4. (repetition
of digits allowed).
(A) 28,44,160
(B) 66,160
(C) 66,660
(D) 7,11,040
9.
A bag contains 5 identical white balls, 6 identical
green balls and 4 identical red balls. In how many
ways can these balls be arranged in a row such that
all the red balls are together and no two green balls
are together?
10. In how many ways is it possible to express 36 as
a product of 3 positive integers?
(A) 8
(B) 6
(C) 12
(D) None of these
11. How many words can be formed using all the letters
of the word EQUATION, such that no word begins
with E or ends with N?
(A) 28,940
(B) 38,690
(C) 30,960
(D) 39,710
12. Two numbers are selected from the first 50 natural
numbers. In how many ways can this be done, such
that the first number is less than the second number
and the sum of the numbers is divisible by 5?
13. The letters of the word BANANA are permuted in all
possible ways and listed in alphabetical order as in
a dictionary. What is the rank of the word NANAAB?
(A) 50
(B) 39
(C) 51
(D) 49
14. Three numbers are selected from the first 15 natural
numbers. How many such triplets will be in
arithmetic progression?
(A) 64
(B) 169
(C) 49
(D) 81
15. Three, four and five points are marked on the sides
AB, BC and CA respectively of ABC. None of the
12 points coincide with A, B or C. How many
triangles can be formed using these 12 points
as vertices?
(A) 220
(B) 217
(C) 210
(D) 205
16. Bag A contains 7 maths books, bag B contains
5 physics books and bag C contains x chemistry
books. The number of ways of selecting three books
such that two books are from one bag and the third
book is from a different bag is 541. The value
of x is
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17. In how many ways can we choose two white
squares (1 cm  1 cm) from an 8 cm  8 cm
chessboard, so that they are neither in the same row
nor in the same column?
(A) 800
(B) 992
(C) 400
(D) 1024
18. My mother gave me 5 rasgullas and went out
at 7:00 p.m. She is expected to return at 8:00 p.m.
She knew that I would eat them all and so she
told me to give a gap of at least 5 minutes between
any two rasgullas. Assuming that I can
instantaneously eat a rasgulla and I eat them only at
the middle of a minute, what is the number of
combinations of times at which I could have eaten
my rasgullas (of course all) during that one hour?
(A) 39C5
(B) 40C5
(C) 41C5
(D) 44C5
19. For how many integers between 1 and 1,000 is the
sum of the digits 16?
20. In how many ways can six books be distributed
among three students A, B and C, such that A and B
receive at least one book each?
(A) 603
(B) 602
(C) 601
(D) 665
21. Find the number of points (x, y, z) in space
with negative integral coordinates such that
x + y + z + 20 = 0.
22. Five boys including Suresh and five girls including
Suneeta have to be seated around a circular table
such that no two boys are adjacent and Suneeta is
not adjacent to Suresh. In how many ways can this
be done?
(A) 4!  5!
(B) (4!)2
2
(C) 3  (4!)
(D) 3  (5!)2
23. A bag contains ten different green balls and eight
different red balls. In how many ways can 4 balls be
drawn such that among them there is at least
one green ball and at least one red ball?
(A) 3060
(B) 2780
(C) 2220
(D) 2740
24. Find the number of ways in which 14 boys and
10 girls can be seated in a row such that no two girls
sit adjacent to each other and a particular boy and
a particular girl sit adjacent to each other.
(14 ! )2
14 ! 13 !
(A)
(B)
120
60
(C)
14 !2
120
(D)
14 ! 13 !
60
25. How many 9-digit multiples of 6 can be formed using
only the digits 8 or 9?
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