If nC₃ = nC₂, then the value of nC₄ is _______.

(a)

2

(b)

3

(c)

4

(d)

5

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 term containing x³ in the expansion of (x - 2y)⁷ is _________.

(a)

3^rd

(b)

4^th

(c)

5^th

(d)

6^th

The middle term in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 10 }\) is _______.

(a)

10C₄\(\left( \frac { 1 }{ x } \right) \)

(b)

10C₅

(c)

10C₆

(d)

10C₇x⁴

The constant term in the expansion of \({ \left( x+\frac { 2 }{ x } \right) }^{ 6 }\) is _______

(a)

156

(b)

165

(c)

162

(d)

160

The last term in the expansion of (3 +\(\sqrt{2}\) )⁸ is ________

(a)

81

(b)

16

(c)

8\(\sqrt{2}\)

(d)

27\(\sqrt{3}\)

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to _______.

(a)

9

(b)

11

(c)

5

(d)

7

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 total number of 9 digit number which have all different digit is ________.

(a)

10!

(b)

9!

(c)

9\(\times\)9!

(d)

10\(\times\)10!

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

(a)

120

(b)

240

(c)

720

(d)

6