Permutations & Combinations Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If all permutations of the letters of the word AGAIN are arranged as in
dictionary, then fiftieth word is
(a) NAAGI
(b) NAGAI
(c) NAAIG
(d) NAIAG
2. A boat is to be manned by eight men of whom 2 can only row on bow
side and 3 can only row on stroke side, the number of ways in which the
crew can be arranged is
(a) 4360
(b) 5760
(c) 5930
(d) None of these
3. The number of ways in which a mixed doubles game in tennis can be
Page 2


PART-I (Single Correct MCQs)
1. If all permutations of the letters of the word AGAIN are arranged as in
dictionary, then fiftieth word is
(a) NAAGI
(b) NAGAI
(c) NAAIG
(d) NAIAG
2. A boat is to be manned by eight men of whom 2 can only row on bow
side and 3 can only row on stroke side, the number of ways in which the
crew can be arranged is
(a) 4360
(b) 5760
(c) 5930
(d) None of these
3. The number of ways in which a mixed doubles game in tennis can be
arranged from 5 married couples, if no husband and wife play in the
same game, is
(a) 46
(b) 54
(c) 60
(d) None of these
4. Let T
n
 denote the number of triangles which can be formed by using the
vertices of a regular polygon of n sides. If T
n+1
 – T
n
 = 28, then n equals
(a) 4
(b) 5
(c) 6
(d) 8
5. If a denotes the number of permutations of x + 2 things taken all at a
time, b the number of permutations of x things taken 11 at a time and c
the number of permutations of x – 11 things taken all at a time such that
a = 182 bc, then the value of x will be
(a) 12
(b) 10
(c) 8
(d) 6
6. Given five line segments of length 2, 3, 4, 5, 6 units. Then the number
of triangles that can be formed by joining these lines is
(a)
5
C
3 
– 3
(b)
5
C
3 
– 1
(c)
5
C
3
(d)
5
C
3 
– 2
7. There are three coplanar parallel lines. If any p points are taken on each
of the lines, the maximum number of triangles with vertices at these
points is
Page 3


PART-I (Single Correct MCQs)
1. If all permutations of the letters of the word AGAIN are arranged as in
dictionary, then fiftieth word is
(a) NAAGI
(b) NAGAI
(c) NAAIG
(d) NAIAG
2. A boat is to be manned by eight men of whom 2 can only row on bow
side and 3 can only row on stroke side, the number of ways in which the
crew can be arranged is
(a) 4360
(b) 5760
(c) 5930
(d) None of these
3. The number of ways in which a mixed doubles game in tennis can be
arranged from 5 married couples, if no husband and wife play in the
same game, is
(a) 46
(b) 54
(c) 60
(d) None of these
4. Let T
n
 denote the number of triangles which can be formed by using the
vertices of a regular polygon of n sides. If T
n+1
 – T
n
 = 28, then n equals
(a) 4
(b) 5
(c) 6
(d) 8
5. If a denotes the number of permutations of x + 2 things taken all at a
time, b the number of permutations of x things taken 11 at a time and c
the number of permutations of x – 11 things taken all at a time such that
a = 182 bc, then the value of x will be
(a) 12
(b) 10
(c) 8
(d) 6
6. Given five line segments of length 2, 3, 4, 5, 6 units. Then the number
of triangles that can be formed by joining these lines is
(a)
5
C
3 
– 3
(b)
5
C
3 
– 1
(c)
5
C
3
(d)
5
C
3 
– 2
7. There are three coplanar parallel lines. If any p points are taken on each
of the lines, the maximum number of triangles with vertices at these
points is
(a) 3 (p – 1) + 1
(b) 3 (p – 1)
(c) (4p – 3)
(d) None of these
8. In a 12 - storey house ten people enter a lift cabin. It is known that they
will left in groups of 2, 3 and 5 people at different storeys. The number
of ways they can do so if the lift does not stop to the second storey is
(a) 78
(b) 112
(c) 720
(d) 132
9. Given that n is odd, the number of ways in which three numbers in A.P.
can be selected from 1, 2, 3, ..... n is
(a)
(b)
(c)
(d)
10. A contest consists of
predicting the results (win, draw or defeat) of 10
football matches. Then the number of ways in which one entry contains
at least 5 correct answers is :
(a)
(b) – 
(c)
(d)
11. The number of squares that can be formed on a chessboard is
Page 4


PART-I (Single Correct MCQs)
1. If all permutations of the letters of the word AGAIN are arranged as in
dictionary, then fiftieth word is
(a) NAAGI
(b) NAGAI
(c) NAAIG
(d) NAIAG
2. A boat is to be manned by eight men of whom 2 can only row on bow
side and 3 can only row on stroke side, the number of ways in which the
crew can be arranged is
(a) 4360
(b) 5760
(c) 5930
(d) None of these
3. The number of ways in which a mixed doubles game in tennis can be
arranged from 5 married couples, if no husband and wife play in the
same game, is
(a) 46
(b) 54
(c) 60
(d) None of these
4. Let T
n
 denote the number of triangles which can be formed by using the
vertices of a regular polygon of n sides. If T
n+1
 – T
n
 = 28, then n equals
(a) 4
(b) 5
(c) 6
(d) 8
5. If a denotes the number of permutations of x + 2 things taken all at a
time, b the number of permutations of x things taken 11 at a time and c
the number of permutations of x – 11 things taken all at a time such that
a = 182 bc, then the value of x will be
(a) 12
(b) 10
(c) 8
(d) 6
6. Given five line segments of length 2, 3, 4, 5, 6 units. Then the number
of triangles that can be formed by joining these lines is
(a)
5
C
3 
– 3
(b)
5
C
3 
– 1
(c)
5
C
3
(d)
5
C
3 
– 2
7. There are three coplanar parallel lines. If any p points are taken on each
of the lines, the maximum number of triangles with vertices at these
points is
(a) 3 (p – 1) + 1
(b) 3 (p – 1)
(c) (4p – 3)
(d) None of these
8. In a 12 - storey house ten people enter a lift cabin. It is known that they
will left in groups of 2, 3 and 5 people at different storeys. The number
of ways they can do so if the lift does not stop to the second storey is
(a) 78
(b) 112
(c) 720
(d) 132
9. Given that n is odd, the number of ways in which three numbers in A.P.
can be selected from 1, 2, 3, ..... n is
(a)
(b)
(c)
(d)
10. A contest consists of
predicting the results (win, draw or defeat) of 10
football matches. Then the number of ways in which one entry contains
at least 5 correct answers is :
(a)
(b) – 
(c)
(d)
11. The number of squares that can be formed on a chessboard is
(a) 64
(b) 160
(c) 224
(d) 204
12. The number of triangles whose vertices are at the vertices of an octagon
but none of whose sides happen to come from the sides of the octagon
is
(a) 24
(b) 52
(c) 48
(d) 16
13. Six persons A, B, C, D, E and F are to be seated at a circular table. The
number of ways, this can be done if A must have either B or C on his
right and B must have either C or D on his right is
(a) 36
(b) 12
(c) 24
(d) 18
14. If m
1
 and m
2
 satisfy the relation
 ,
then  m
1
 + m
2
 is equal to
(a) 10
(b) 9
(c) 13
(d) 17
15. A teaparty is arranged for 16 people along two sides of a large table
with 8 chairs on each side. Four men want to sit on one particular side
and two on the other side. The number of ways in which they can be
seated is
(a)
Page 5


PART-I (Single Correct MCQs)
1. If all permutations of the letters of the word AGAIN are arranged as in
dictionary, then fiftieth word is
(a) NAAGI
(b) NAGAI
(c) NAAIG
(d) NAIAG
2. A boat is to be manned by eight men of whom 2 can only row on bow
side and 3 can only row on stroke side, the number of ways in which the
crew can be arranged is
(a) 4360
(b) 5760
(c) 5930
(d) None of these
3. The number of ways in which a mixed doubles game in tennis can be
arranged from 5 married couples, if no husband and wife play in the
same game, is
(a) 46
(b) 54
(c) 60
(d) None of these
4. Let T
n
 denote the number of triangles which can be formed by using the
vertices of a regular polygon of n sides. If T
n+1
 – T
n
 = 28, then n equals
(a) 4
(b) 5
(c) 6
(d) 8
5. If a denotes the number of permutations of x + 2 things taken all at a
time, b the number of permutations of x things taken 11 at a time and c
the number of permutations of x – 11 things taken all at a time such that
a = 182 bc, then the value of x will be
(a) 12
(b) 10
(c) 8
(d) 6
6. Given five line segments of length 2, 3, 4, 5, 6 units. Then the number
of triangles that can be formed by joining these lines is
(a)
5
C
3 
– 3
(b)
5
C
3 
– 1
(c)
5
C
3
(d)
5
C
3 
– 2
7. There are three coplanar parallel lines. If any p points are taken on each
of the lines, the maximum number of triangles with vertices at these
points is
(a) 3 (p – 1) + 1
(b) 3 (p – 1)
(c) (4p – 3)
(d) None of these
8. In a 12 - storey house ten people enter a lift cabin. It is known that they
will left in groups of 2, 3 and 5 people at different storeys. The number
of ways they can do so if the lift does not stop to the second storey is
(a) 78
(b) 112
(c) 720
(d) 132
9. Given that n is odd, the number of ways in which three numbers in A.P.
can be selected from 1, 2, 3, ..... n is
(a)
(b)
(c)
(d)
10. A contest consists of
predicting the results (win, draw or defeat) of 10
football matches. Then the number of ways in which one entry contains
at least 5 correct answers is :
(a)
(b) – 
(c)
(d)
11. The number of squares that can be formed on a chessboard is
(a) 64
(b) 160
(c) 224
(d) 204
12. The number of triangles whose vertices are at the vertices of an octagon
but none of whose sides happen to come from the sides of the octagon
is
(a) 24
(b) 52
(c) 48
(d) 16
13. Six persons A, B, C, D, E and F are to be seated at a circular table. The
number of ways, this can be done if A must have either B or C on his
right and B must have either C or D on his right is
(a) 36
(b) 12
(c) 24
(d) 18
14. If m
1
 and m
2
 satisfy the relation
 ,
then  m
1
 + m
2
 is equal to
(a) 10
(b) 9
(c) 13
(d) 17
15. A teaparty is arranged for 16 people along two sides of a large table
with 8 chairs on each side. Four men want to sit on one particular side
and two on the other side. The number of ways in which they can be
seated is
(a)
(b)
(c)
(d) None of these
16. Assuming the balls to be identical except for difference in colours, the
number of ways in which one or more balls can be selected from 10
white, 9 green and 7 black balls is :
(a) 880
(b) 629
(c) 630
(d) 879
17. The number of numbers greater than a million that can be formed with
the digits 2, 3, 0, 3, 4, 2 and 3 is
(a) 360
(b) 340
(c) 370
(d) None of these
18. There are 4 letters and 4 directed envelopes. The number of ways in
which all the letters can be put in wrong envelope is
(a) 9
(b) 4
(c) 5
(d) 12
19. The number of values of r satisfying the equation 
 is
(a) 1
(b) 2
(c) 3
(d) 4
20. A committee of 4 persons is to be formed from 2 ladies, 2 old men and