Binomial Theore...

If n is a rational number, which is not a whole number, then the number of terms in the expansion of (1+x)ⁿ,|x|<1, is

The term containing x3 in the expansion of (x−2y)7 is

In the expansion of (1 + x)^{2n + 1}, let the coefficients of x^r and x^{r + 1} be equal. Then, the value of r is

The exponent of  x occurring in the 7^th term of expansion of (3x/2−8/7x)⁹ is

The greatest coefficient in the expansion of (x₁ + x₂ + x₃ + x₄ + x₅)¹³ is

The largest term in the expansion of (1+x)19 when x=12 is

¹⁰C₁ + ¹⁰C₃ + ¹⁰C₅ + ¹⁰C₇ + ¹⁰C₉ is equal to

The term independent of x in is

If the first three terms in the expansion of (x+a)n are 729, 7290 and 30375 respectively, then the value of n is

The sum of the coefficients of the polynomial (1 + x - 3x²)²¹⁴³ is

The two consecutive terms in the expansion of (3+2x)74, which have equal coefficients, are

{ⁿC₁ + 2 ⁿC₂ + 3 ⁿC₃ + …….. + n ⁿC_n} is equal to 

How many middle terms are there in the expansion of (a + b)⁷?

The third, fourth and fifth terms in the expansion of (x + a)ⁿ are 84, 280 and 560, respectively. Find the value of n.

If A and B are the coefficients of x^r and x^{n – r}, respectively, in the expansion of (1 + x)ⁿ, then

The coefficient of x⁵ in the expansion of (1 + x)²¹ + (1 + x)²² + ……… + (1 + x)³⁰ is

What is the value of (1 + i)⁶ + (1 – i)⁶?

If n is a +ve integer, then the binomial coefficients equidistant from the beginning and the end in the expansion of (x+a)ⁿ are

The coefficient of  1/x¹⁷ in the expansion of (x⁴−1/x3)¹⁵ is

The middle term in the expansion of is

The number of dissimilar terms in the expansion of (a+b+c)¹² is

The total number of terms in the expansion of (x + k)¹⁰⁰ + (x – k)¹⁰⁰ after simplification is

If the third term in the binomial expansion of (1 + x)^m is x², then the rational value of m is

Using the binomial theorem, find the value of (99)⁴.