How many 5-digit numbers can be formed from the numbers 0, 2, 4, 5, 7 and 9 (without repetition), such that it is divisible by 4?

120

144

132

104

There are 6 train stops between Chennai and Assam. How many train tickets are to be printed, so that a person can travel between any of the two stations (irrespective of direction of travel)? 56 1 point

A man desires to throw a party for some of his friends. In how many ways can he select 5 friends from a group of 15 friends, if the two of his friends(say ’A’ and ’B’) will not attend the party together? 2717 1 point

Suman has 9 clothes of different types, say, C₁,C₂, ...,C₉ and she wants to wear all these clothes at different days, say, D₁,D₂,...,D₉. Due to some reason, C₁ must be used either at D₇ or at D₈ and C₂ can be used either at D₈ or at D₇ or at D₉. Every cloth is to be used at only one day, in how many ways can clothes be used? 20160 1 point

1 point How many 17-digit number can be formed such that they read the same way from either of the side (that is the number should be palindrome)?

10⁹ x 9

10⁸ x 9

10¹⁶ x 9

10¹⁷

In how many ways can a group of 7 players be formed from 12 state level players and 5 district level players such that the group contains exactly 1 district level player? 4620 1 point

1 point Choose the incorrect option/s for n>2 :

𝑛 𝐶 𝑟 + 𝑛 𝐶 𝑟 − 1

𝑛 + 1 𝐶 𝑟 n C r ​ + n C r−1 ​

n+1 C r ​

𝑛 𝐶 𝑟

1 n C r ​ =1 for 𝑟

0 r=0 and 𝑟

𝑛 r=n

𝑛 𝐶 𝑟

𝑛 − 1 𝐶 𝑟 − 1 + 𝑛 − 1 𝐶 𝑟 n C r ​

n−1 C r−1 ​ + n−1 C r ​

None of the above

Jimmi and Vishal are planning a dinner party. Vishal has 4 vegetarian friends and 3 non-vegetarian friends, while Jimmi has 3 vegetarian friends and 4 non-vegetarian friends. They decide to invite 4 friends in total and it was decided that both of them will invite two of their friends and also ensure that there are a total of 2 vegetarians and 2 non-vegetarians friends. How many ways can they invite their friends to the dinner party? 189 1 point If 𝑟 ! × ( 𝑛 − 1 𝐶 𝑟 − 1 + 𝑛 − 1 𝐶 𝑟 ) + ( 𝑟 + 1 ) ! × ( 𝑛 − 1 𝐶 𝑟 + 𝑛 − 1 𝐶 𝑟 + 1 )

𝑥 r!×( n−1 C r−1 ​ + n−1 C r ​ )+(r+1)!×( n−1 C r ​ + n−1 C r+1 ​ )=x, then for 𝑛

5 n=5 and 𝑟

2 r=2, calculate the value of 𝑥 x? 80 1 point A student is selecting books from a library shelf. There are 6 fiction books and 4 non-fiction books. If the student needs to choose 2 books, how many ways can it be done such that both of the selected books are either fiction or non-fiction? 21 1 point