If ⁽ⁿ⁺⁵⁾P_(n+1)=\((\frac { 11(n-1) }{ 2 } )\).⁽ⁿ⁺³⁾P_n, then the value of n are

(a)

7 and 11

(b)

6 and 7

(c)

2 and 11

(d)

2 and 6

The product of r consecutive positive integers is divisible by

(a)

r!

(b)

(r-1)!

(c)

(r+1)!

(d)

r^r

The number of five digit telephone numbers having at least one of their digits repeated is

(a)

90000

(b)

10000

(c)

30240

(d)

69760

If ^a2-a \(C_2 = ^{a^2-a}\) C₄ then the value of 'a' is

(a)

2

(b)

3

(c)

4

(d)

5

Number of sides of a polygon having 44 diagonals is

(a)

4

(b)

4!

(c)

11

(d)

22

If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are

(a)

45

(b)

40

(c)

10!

(d)

2¹⁰

In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is

(a)

110

(b)

¹⁰C₃

(c)

120

(d)

116

In ²ⁿC₃ : ⁿC₃ = 11 : 1 then n is

(a)

5

(b)

6

(c)

11

(d)

7

If ⁿC₄,ⁿC₅,ⁿC₆ are in AP the value of n can be

(a)

14

(b)

11

(c)

9

(d)

5

1+3+5+7+........+17 is equal to

(a)

101

(b)

81

(c)

71

(d)

61

Count the number of three-digit numbers which can be formed from the digits 2, 4, 6, 8 if
(i) repetitions of digits is allowed.
(ii) repetitions of digits is not allowed

How many three-digit numbers are there with 3 in the unit place?
(i) with repetition
(ii) without repetition.

How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5 ? if
(i) repetition of digits allowed
(ii) the repetition of digits is not allowed.

How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even Places?

8 women and 6 men are standing in a line.
(i) How many arrangements are possible if any individual can stand in any position?
(ii) In how many arrangements will all 6 men be standing next to one another?
(iii) In how many arrangements will no two men be standing next to one another?

A Kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court?

There are 15 persons in a party and if each 2 of them shakes hands with each other, how many handshakes happen in the party?

How many chords can be drawn through 20 points on a circle?

In a parking lot one hundred, one year old cars, are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars can be chosen?

How many ways can a team of 3 boys,2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgenders?