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In how many distinct ways can five guests be seated around a circular table?
a) 15
b) 24
c) 20
d) 35
e) 120
Option b – 24
Five guests are to be seated around a circular table, while six others remain standing. How many total seating arrangements are possible?
a) 65
b) 90
c) 110
d) 144
Option d – 144
A committee of five members is to be chosen from 4 men and 6 women, with the condition that at least one man must be included. How many possible committees can be formed?
a) 109
b) 147
c) 258
d) 246
e) 357
Option b – 147
Simran has 5 marigolds and 2 lotuses and wants to make a bouquet of 3 flowers. How many possible bouquets can be made if at least one lotus must be included?
a) 15
b) 30
c) 25
d) 40
e) 35
Option c – 25
From a group of 6 men and 5 women, in how many ways can a committee be formed with exactly 3 men and 2 women?
a) 100
b) 140
c) 150
d) 200
Option d – 200
A committee of five members must be formed from 4 women and 6 men, ensuring at least one woman is included. How many ways can this be done?
a) 119
b) 165
c) 218
d) 246
e) 352
Option d – 246
A line is to be formed using 5 boys and 4 girls, with boys positioned at both ends of the line. How many possible arrangements are there?
a) 4!7!/5!
b) 5!8!/2!
c) 5!7!/3!
d) 4!6!/3!
e) None of these
Option c – 5!7!/3!
In how many ways can the letters of the word MAHIMA be arranged so that all vowels are together and all consonants are together?
a) 14
b) 18
c) 35
d) 41
e) 39
Option b – 18
Four boys and four girls are to be arranged in a single row so that boys and girls alternate positions. How many such arrangements are possible?
a) 1082
b) 1152
c) 1354
d) 1624
e) 1764
Option b – 1152
Delhi, Panjab, and Shimla University each have four badminton players. How many ways can a team of nine players be selected with equal representation from each University?
a) 13
b) 14
c) 12
d) 10
e) 16
Option c – 12
Rana is a skilled shooter who hits the target once in every three shots. What is the probability that he hits the target at least once in four attempts?
a) 1/3
b) 1/9
c) 2/27
d) 65/81
e) 73/81
Option d – 65/81
Rana is a skilled shooter who hits the target once in every three shots. What is the probability that he will miss the target in his first three shots and only hit it on the fourth?
a) 1
b) 8/81
c) 17/81
d) 29/27
e) 71/81
Option b – 8/81
The letters of the word ALGEBRA are rearranged to form a new arrangement. What is the probability that the consonants will remain in their original positions?
a) 1/120
b) 1/35
c) 1/12
d) 1/35
Option d – 1/35
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