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Arjuna JEE 2023

1. There are 15 players in a cricket team, out of which 7. Suppose that 20 pillars of the same height have been
6 are bowlers, 7 are batsman and 2 are wicket- erected along the boundary of a circular stadium.
keepers. The number of ways, a team of 11 players be If the top of each pillar has been connected by beams
selected from them so as to include at least 4 bowlers, with the top of all its non-adjacent pillars, then the
5 batsman and 1 wicketkeeper, is total number of beams is
(1) 139 (2) 777 (1) 180 (2) 210
(3) 349 (4) 201 (3) 170 (4) 190

2. An automobile dealer provides motor cycles and 8. The number of ways that a volley ball team of 6 can
scooters in three body patterns and 4 different colours be selected out of 10 players so that 2 particular
each. The number of choices open to a customer is players are included is
(1) 4C3 (2) 4C3 (1) 72 (2) 70
(3) 4 × 3 (4) 4×3×2 (3) 68 (4) 66

3. In a class there are 10 boys and 8 girls. The teacher 9. If a man and his wife enter in a bus, in which five
wants to select either a boy or a girl to represent the seats are vacant, then the number of different ways in
class in a function. The number of ways the teacher which they can be seated is
can make this selection. (1) 2 (2) 5
(1) 18 (2) 80 (3) 20 (4) 40
10
(3) P8 (4) 10C8
10. There are 5 students in class 10, 6 students in class 11
4. The number of selecting at least 4 candidates from 8 and 8 students in class 12. If the number of ways,
candidates is in which 10 students can be selected from them so as
(1) 270 (2) 70 to include at least 2 students from each class and at
(3) 163 (4) None of these most 5 students from the total 11 students of class 10
and 11 is 100 k, then k is equal to
(1) 238 (2) 17
5. In a Mathematics paper there are three sections
containing 4, 5 and 6 questions respectively. From (3) 15 (4) 14
each section 3 questions are to be answered. In how
many ways can the selection of questions be made? 11. A polygon has 90 diagonals. Number of its sides is
(1) 34 (2) 800 (1) 25 (2) 17
(3) 1600 (4) 9600 (3) 15 (4) 14

6. A student is allowed to select at most n books from a 12. Out of 7 men and 4 ladies a committee of 5 is to be
collection of (2n + 1) books. If the total number of formed. In how many ways can this be done so as to
ways in which he can select at least one book is 63, include at least 3 ladies
then n is (1) 90 (2) 120
(1) 6 (2) 3 (3) 91 (4) 360
(3) 4 (4) 5
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13. From 5 apples, 4 oranges and 3 mangoes, how many 15. Let Tn denote the number of triangles which can be
selections of fruits can be made formed using the vertices of a regular polygon of n
(1) 119 (2) 120 sides. If Tn+1 – Tn = 21, then n equals
(3) 59 (4) 60 (1) 5 (2) 7
(3) 6 (4) 4
14. The maximum number of points of intersection of 8
circles, is 16. The number of diagonals that can be drawn by joining
(1) 16 (2) 24 the vertices of an octagon, is
(3) 28 (4) 56 (1) 20 (2) 28
(3) 48 (4) None of these
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Answer Key
1. (2) 9. (3)
2. (4) 10. (1)
3. (1) 11. (3)
4. (3) 12. (3)
5. (2) 13. (1)
6. (2) 14. (4)
7. (3) 15. (2)
8. (2) 16. (1)

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