The value of n, when nP₂ = 20 is _______.

(a)

3

(b)

6

(c)

5

(d)

4

The number of ways selecting 4 players out of 5 is _______.

(a)

4!

(b)

20

(c)

25

(d)

5

The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n \(\in\) N is ________.

(a)

2

(b)

6

(c)

20

(d)

24

If n is a positive integer, then the number of terms in the expansion (x + a)ⁿ is _______.

(a)

n

(b)

n + 1

(c)

n-1

(d)

2n

For all n > 0, nC₁ + nC₂ + nC₃ + ... +nC_n is equal to _______

(a)

2n

(b)

2ⁿ- 1

(c)

n²

(d)

n² - 1

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is _________.

(a)

18

(b)

12

(c)

9

(d)

6

There are 10 true or false questions in an examination. Then these questions can be answered in ______.

(a)

240 ways 

(b)

120 ways 

(c)

1024 ways 

(d)

100 ways 

The value of (5C₀ + 5C₁) + (5C₁ + 5C₂) + (5C₂ + 5C₃) + (5C₃ + 5C₄) + (5C₄ + 5C₅ ) is ________.

(a)

2⁶-2

(b)

2⁵-1

(c)

2⁸

(d)

2⁷

The number of ways to arrange the letters of the word "CHEESE" is ______.

(a)

120

(b)

240

(c)

720

(d)

6

Thirteen guests has participated in a dinner. The number of handshakes happened in the dinner is __________.

(a)

715

(b)

78

(c)

286

(d)

13

Resolve into partial fractions for the following : \(\frac{x^2-3}{(x+2)\left(x^2+1\right)}\)

Resolve into partial fractions for the following : \(\frac{x^2-6 x+2}{x^2(x+2)}\)

Resolve into partial fractions for the following : \(\frac{x+2}{(x-1)(x+3)^2}\)

Show that 10P₃ = 9 P₃ + 3. 9P₂

How many permutations can be made out of the letters of the word "TRIANGLE" beginning with T?

In how many ways can 10 beads of different colours form a necklace?

Resolve into partial factors:\(\frac { x+4 }{ ({ x }^{ 2 }-4)(x+1) } \)

Solve : \(\frac { (2x+1)! }{ (x+2)! } .\frac { (x-1)! }{ (2x-1)! } =\frac { 3 }{ 5 } \)

It the letters of the word are arranged as in dictionary, find the rank of the word "AGAIN".

In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

If p(n) is the statement "12n + 3" is a multiple of 5, then show that P (3) is false, whereas P(6) is true.

Let p(n) be the statement "n² + n is even". If P(k) is true, then show that P(k+1) is true.

Expand the following by using binomial theorem.\(\left( x+\frac { 1 }{ y } \right) ^{ 7 }\)

Expand the following by using binomial theorem.\({ \left( x+\frac { 1 }{ { x }^{ 2 } } \right) }^{ 6 }\)