Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 22

EASY

CAT

IMPORTANT

Earn 100

For $x \in R$ , et $[x]$ denote the largest integer less than or equal to $x,$ then the value of $E = [\frac{1}{3}] + [\frac{1}{3} + \frac{1}{100}] + [\frac{1}{3} + \frac{2}{100}] + \dots + [\frac{1}{3} + \frac{99}{100}]$ is :

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Important Questions on Permutations & Combinations

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 23

The number of positive integers from

1

to

10^{6}

(both inclusive) which are neither perfect squares, nor cubes, nor perfect fourth powers is :

MEDIUM

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 24

A family consists of a grandfather, m sons and daughters and

2 n

grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the n seats at each end and the grandfather refuses to have a grandchildren on either side of him. In how many ways can the family be made to sit.

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 25

Six $Ps$ have to be placed in the squares of the diagram given below such that each column contains at least one $P .$ In how many ways this can be done?

Question Image

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 26

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 27

Ajay has

7

relatives,

3

men and

4

women. His wife Kajol also has

7

relatives,

3

women and

4

men. In how many ways can they invite

3

men and

3

women so that

3

of them are the Ajay's relatives and

3

his wife Kajol's?

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 28

Serena and Venus were only two women participating in a chess tournament. Every participant played two games with every other participant. The number of games that men played between themselves proved to exceed by

66,

compared to the number of games the men played with women. How many participants were there?

EASY

CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 29

In the previous questions (no.

28

) how many games were played?

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CAT

IMPORTANT

Quantum CAT Also Useful for XAT>Chapter 19 - SNAP>CMAT>Q 30

Six Burfis and six rasgullas are to be distributed among ten girls so that each girl receives at least one piece of sweets out of burfis and rasgullas. Find the number of ways in which the sweets can be distributed.