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What is the first step in the decision-making process?

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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:

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

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:

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

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

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

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:

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

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 :

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

A person throws two fair dice. He wins Rs.

15

for throwing a doublet (same numbers on the two dice), wins Rs

12

when the throw results in the sum of

9

, and loses Rs.

6

for any other outcome on the throw. Then the expected gain/loss (in Rs.) of the person is:

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

Does the point

(- 2.5, 3.5)

lie inside, outside or on the circle

x^{2} + y^{2} = 25 ?

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

Find the equation of a circle with centre

(2, 2)

and passes through the point

(4, 5) .

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

Find the equation of the circle passing through the points

(4, 1)

and

(6, 5)

and whose centre is on the line

4 x + y = 16 .

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

The radius of the circle

x^{2} + y^{2} + 4 x + 6 y + 13 = 0

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

Let

P (x_{1}, y_{1})

and

Q (x_{2}, y_{2})

are two points such that their abscissas

x_{1}

and

x_{2}

are the roots of the equation

x^{2} + 2 x - 3 = 0

while the ordinates

y_{1}

and

y_{2}

are the roots of the equation

y^{2} + 4 y - 12 = 0

.Then the centre of the circle with

P Q

as diameter is

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

Find the centre and radius of the circle

x^{2} + y^{2} - 4 x - 8 y - 45 = 0

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

The equation of circle which touches the

x

-axis and

y

-axis at the points

(1, 0)

and

(0, 1)

respectively, is

HARD

Mathematics>Algebra>Permutation and Combination>Permutations

Find the equation of the circle whose center is

(2, - 1)

and which passes through

(3, 6)

MEDIUM

Mathematics>Algebra>Permutation and Combination>Permutations

Let

A (1, 2), B (3, 4)

be two points and

C (x, y)

be a point such that

(x - 1) (x - 3) + (y - 2) (y - 4) = 0

. If area of

∆ A B C

is 1 sq. unit. Then maximum number of positions of C in

x y

plane is

EASY

Mathematics>Algebra>Permutation and Combination>Permutations

Find the equation of the circle with centre

(- 2, 3)

and radius

4

What is the first step in the decision-making process?

Important Questions on Permutation and Combination

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