Permutations and Combinations · Mathematics · COMEDK

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MCQ (Single Correct Answer)

1
The number of words that can be formed with the letters of the word 'DEFINITE' if two vowels are together and the other two are also together but separated from the first two is
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2
How many natural numbers are there between 100 and 1000 such that at least one of their digits is $6 ?$
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3
If ${ }^{n+2} C_8:{ }^{n-2} P_4=57: 16$, then ' $n$ ' is
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4
On each working day of a school there are six periods. The number of ways in which five subjects are arranged if each subject is allotted at least one period and no period remains vacant is
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5
Codes used for vehicle identification consists of two distinct English alphabets followed by two distinct digits from 1 to 9 . How many of them end with an even number.
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6
A shopkeeper sells three varieties of fruit juice. He has a large number of bottles of same size of each variety. The number of different ways of displaying all the three varieties on the shelf with 5 places in a row and each display must have at least one bottle of each variety is
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7

For an examination a candidate has to select 7 questions from three different groups $$\mathrm{A}, \mathrm{B}$$ and C. The three groups contain 4, 5 and 6 questions respectively. In how many different ways can a candidate make his selection if he has to select atleast 2 questions from each group?

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8

The letters of the word "COCHIN" are permuted and all the permutations are arranged in alphabetical order as in an English dictionary. The number of words that appear before the word "COCHIN" is

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9

The number of four digit numbers strictly greater than 4321 formed using the digits $$0,1,2,3,4,5$$ with repetition of digit is

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10

A student has 3 library cards and 8 books of his interest in the library. Out of these 8 books he does not want to borrow Chemistry part 2 unless he can borrow Chemistry part 1 also. In how many ways can he choose the three books to be borrowed?

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11

In how many ways can the word "CHRISTMAS" be arranged so that the letters '$$\mathrm{C}$$' and '$$\mathrm{M}$$' are never adjacent?

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12

If $$\left[{ }^{n+1} C_{r+1}\right]:\left[{ }^n C_r\right]:\left[{ }^{n-1} C_{r-1}\right]=11: 6: 3$$ then $$n r=$$

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13

$$\text { Find }{ }^n C_{21} \text {, if }{ }^n C_{10}={ }^n C_{12}$$

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14

There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?

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15

The total number of numbers greater than 1000 but less than 4000 that can be formed using 0, 2, 3, 4 (using repetition allowed) are

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16

A polygon of n sides has 105 diagonals, then n is equal to

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17

How many factors of $$2^5 \times 3^6 \times 5^2$$ are perfect squares?

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18

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choose the 7 question is

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19

In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3 & 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey is

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20

$$(2^{3n}-1)$$ is divisible by

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21

$$\sum\limits_{n = 1}^m {n\,.\,n!} $$ is equal to

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22

If nC3 = 220, then n = ?

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23

There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?

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24

A regular polygon of n sides has 170 diagonals, then n is equal to

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25
How many 5-digit numbers greater than 50,000 can be formed using the digits 1, 2, 3, 4, 5 without repetition?
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26

The value of $$1\,.\,1! + 2\,.\,2! + 3\,.\,3! + \,...\, + \,n\,.\,n!$$ is

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27

The number of triangles which can be formed by using the vertices of a regular polygon of $$(n+3)$$ sides is 220. Then, $$n$$ is equal to

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28

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?

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29

How many numbers greater than 40000 can be formed from the digits 2, 4, 5, 5, 7?

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30

If a polygon of n sides has 275 diagonals, then n is equal to

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31

The number of positive divisors of 252 is

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32

The remainder obtained when 5124 is divided by 124 is

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