Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 11

MEDIUM

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IMPORTANT

Earn 100

Words of length $10$ are formed using the letters $A, B, C, D, E, F, G, H, I, J .$ Let $x$ be the number of such words where no letter is repeated; and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated, then $\frac{y}{9 x} =$

Important Questions on Permutation and Combination

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 12

Let

S = {1, 2, 3, \dots \dots, 9} .

For

k = 1, 2, \dots \dots 5,

let

N_{k}

be the number of subsets of

S

, each containing five elements out of which exactly

k

are odd. Then

N_{1} + N_{2} + N_{3} + N_{4} + N_{5} =

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 13

The number of

5

digit numbers which are divisible by

4

with digits from the set

{1, 2, 3, 4, 5}

and the repetition of digits is allowed, is.........

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 15

From

6

different novels and

3

different dictionaries,

4

novels and

1

dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 17

There are

10

points in a plane, out of these

6

are collinear. If

N

is the number of triangles formed by joining these points, then

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 18

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from

10

white,

9

green and

7

black balls is

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 19

Let

T_{n}

be the number of all possible triangles formed by joining vertices of an

n

-sided regular polygon. If

T_{n + 1} - T_{n} = 10,

then the value of

n

is

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 20

The number of integers greater than

6000

that can be formed using the digits

3, 5, 6, 7

and

8

without repetition is

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 8 - Permutation and Combination>Exercise-3>Q 21

If all the words (with or without meaning) having five letters, formed using the letters of the word

SMALL

and arranged as in a dictionary; then the position of the word

SMALL

is