Find the term independent of x in  

a)

b)

c)

d)

Find the 13^th term of  

a) 17984

b) 18012

c) 18564

d) 18712

Find the term independent of x in  

a)

b)

c)

d) None of the above

If x^r occurs in the expansion of  , prove that its coefficient is 

If (1 + x)ⁿ = C₀ + C₁x + C₂x² + .  .  . + C_nxⁿ. Find the value of
C₀ + 2C₁ + 3C₂ + .  .  . + (n + 1)C_n

a) n . 2^{n – 1}

b) (n + 1) 2^{n – 1}

c) (n + 2) 2^{n – 1}

d) n . 2ⁿ

If (1 + x)ⁿ = C₀ + C₁x + C₂x² + .  .  . + C_nxⁿ. Find the value of
 

a)

b)

c)

d)

Show that the coefficient of the middle term of (1 + x)²ⁿ  is equal to the sum of the coefficients of the two middle terms of (1 + x)^{2n – 1}

If A be the sum of odd terms and B the sum of even terms in the expansion of (x + a)ⁿ, prove that A² – B² =

If second, third and fourth term in the expansion of (x + y)ⁿ are 240, 720, 1080 respectively; find x, y, n.

a) n = 5, x = 2, y = 3

b) n = 5, x = 3, y = 2

c) n = 5, x = 3, y = 3

d) n = 5, x = y = 3

Find the (p + 2)^th term from the end in

a)

b)

c)

d)

In the expansion of (1 + x)⁴³ the coefficient of the (2r+1)^th and (r+2)^th terms are equal. Find r.

a) r = 13

b) r = 14

c) r = 15

d) r = 16

Find the relation between r and n in order that the coefficient of the 3r^th and (r + 2)^th terms of (1 + x)²ⁿ be equal if n is an even integer.

a) n = r

b) n = 2r

c) n = 3r

d) n = 4r

Show that the middle term in the expansion of (1 + x)²ⁿ is

Prove that C₁ + 2C₂ + .  .  . +nC_n = n . 2^{n – 1}

Prove  

Prove that  

Prove that  

Prove that  

Prove that  

Prove that  

Find the seventh term of (3⁸ + 6⁴ x)^11/4

a) 1000x⁶

b) 2000x⁶

c)

d)

When x is so small that its square and higher powers may be neglected, find the value of   

a)

b)

c)

d)

Prove that the coefficient of x^r in the expansion of (1 – 4x)^{− 1/2}  is