Question Bank - Permutation and Combination - IIT JEE - Toppr1

12/21/2015 Question Bank - Permutation and Combination - IIT JEE - Toppr.com

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Divisibility, factorial test andsummations

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restrictions/groupings

Permutation formula

Combination counting

Rules and theorems in combination

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Question Bank

1 #71952 Ask a doubt Solution

Exponent of 12 in 100! is

Submit

A 24

B 48

C 54

D 36


In an examination, the maximum marks for first three papers is , and for the fourth

paper is . The number of ways in which a student can secure marks is

Submit

*

* *

A* *

*

B* *

*

C* *

*

*

D* *

*


If the numbers be all different and each of them a prime number,

then the number of different factors (other than 1) of is

*

)

A)

*

B)

*

C)

*

D None of these

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11

12

Combination with restriction

Groupings and restrictions on

arrangements

Submit


Six colors of paint are available. Each face of a cube is to be painted a different color.

In how many different ways can this be done if two colorings are considered the

same when one can be obtained from the other by rotating the cube?

Submit

A

B

C

D


How many necklaces of 11 beads each can be made from 23 beads of various colours ?

Submit

A

B

C

D none of these

6 #71958 Ask a doubt Hint Solution

Number of natural numbers between 100 & 1000 such that at least one of their digits

is 6 is m, then which of the following digit occurs in m.

THIS QUESTION HAS MULTIPLE CORRECT OPTIONS

Submit

A 1

B 2

C 5

D 6




Let be a prime number & be a positive integer, then exponent of prime in is

denoted by & is given by

where is the largest positive integer such that and denotes the

greatest integer

Again every natural number can be expressed as the product of its prime factors

given by where are prime numbers &

are whole numbers.

The exponent of in is

Submit

, * , *

*

,

*

,

*

,

*

,

*

,

*

,

4

4 * ,

4

,

4

'

'

-

'

.

.

.

'

A

B

C

D None of these

8 #163156 Ask a doubt Hint Solution

Suppose a lot of n objects having objects of one kind, objects are of second kind,

objects of third kind, .... , objects of kind satisfying the condition

then the number of possible arrangements/permutation of m

objects out of this lot is the coefficient of in the expansion of

The number of ways in which an arrangement of 4 letters of the word PROPORTION

can be made is

Submit

*

*

*

*

'

'

0$

**

*

*

'

4

)

)

M

4

M

M

A 700

B 750

C 758

D 800


If then

THIS QUESTION HAS MULTIPLE CORRECT OPTIONS

g g g

A Number of even proper divisors of N are 215.

Number of divisors of N divisible by 15 are 150.



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Submit

B

C Number of ways in which the number N can be expressed as a product of two

divisors are 135.

D Number of ways in which the number N can be expressed as a product of two

divisors which are coprime are 8.


The different number of ways the letters of the word can be placed in

the 8 boxes of the given figure so that no row remains empty is

Submit

A g

B g

C g

D g

Question Bank - Permutation and Combination - IIT JEE - Toppr1

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