MEDIUM

Earn 100

Which theory of decision-making emphasizes the role of utility in choices?

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Important Questions on Permutation and Combination

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

The Number of ways of choosing

10

objects out of

31

objects of which

10

are identical and the remaining

21

are distinct, is:

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

Amongst the following statements, that which was not proposed by Dalton was :

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

Suppose that

20

pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

The number of natural numbers less than

7000

which can be formed by using the digits

0, 1, 3, 7, 9

(repetition of digits allowed) is equal to:

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

Two cards are drawn at random and one-by-one without replacement from a well-shuffled pack of

52

playing cards. Find the probability that one card is red and the other is black.

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

The value of

\sum_{r = 1}^{10} r \cdot \frac{{}^{n}C_{r}}{{}^{n}C_{r - 1}}

is equal to

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

A committee of

11

member is to be formed from

8

males and

5

females. If

m

is the number of ways the committee is formed with at least

6

males and

n

is the number of ways the committee is formed with at least

3

females, then

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

Consider a class of

5

girls and

7

boys. The number of different teams consisting of

2

girls and

3

boys that can be formed from this class, if there are two specific boys

A

and

B,

who refuse to be the members of the same team, is:

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

{\sum_{i = 1}^{20} (\frac{^{20} C_{i - 1}}{^{20} C_{i} +^{20} C_{i - 1}})}^{3} = \frac{k}{21},

then

k

equals

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

There are

m

men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by

84

, then the value of

m

is :

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

If in a regular polygon the number of diagonals is

54

, then the number of sides of this polygon is:

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

A determinant of second order is made with the elements 0, 1. What is the probability that the determinant is positive?

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than

99 %

is:

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

In a class of

60

students,

40

opted for NCC,

30

opted for NSS and

20

opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is :

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

Identify the statement which is false regarding the postulates of Dalton's atomic theory.

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

What are the main postulates of Dalton’s Atomic Theory ? What were its limitations? How has the theory been modified ?

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

Give four important postulates of Dalton's atomic theory.

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

What are the limitations of Dalton's atomic theory?