List of top Mathematics Questions on Binomial theorem asked in AIEEE

The middle term in the expansion of $\left(1-\frac{1}{x}\right)^{n} \left(1-x^{n}\right)$ in powers of x is

For each natural number $n, (n + 1)^7 - n^7 -1$ is divisible by 7. For each natural number $n, n^7 - n$ is divisible by 7.

The coefficient of $x^7$ in the expansion of $(1- x - x^2 + x^3 )^6$ is

In the binomial expansion of $(a - b)^n, n \geq 5,$ a the sum of $5^{th}$ and $6^{th}$ terms is zero, then $\frac{a}{b}$ equals

The sum of the series ${^{20}C_0} - {^{20}C_1} + {^{20}C_2} - {^{20}C_3} + ..... - .... + {^{20}C_{10}}$ is

If the coefficient of $x^7$ in $\left[ ax^2 + (\frac{1}{bx} ) \right]^{11}$ equals the coefficient of $x^{-7}$ in $\left[ax - \left(\frac{1}{bx^{2}}\right)\right]^{11}$ , then a and b satisfy the relation

If $x$ is so small that $x^3$ and higher powers of $x$ may be neglected, then $\frac{\left(1+x\right)^{\frac{3}{2}} - \left(1+ \frac{1}{2}x\right)^{3}}{\left(1-x\right)^{\frac{1}{2}}} $ may be approximated as

The coefficient of the middle term in the binomial expansion in powers of x of $(1+ \alpha x)^4$ and of $ (1 - \alpha x)^6$ is the same if $\alpha$ equals

The coefficient of $x^n$ in expansion of $(1+ x)(1- x)^n$ is

The positive integer just greater than $(1 + 0.0001)^{10000}$ is

If the sum of the coefficients in the expansion of $(a + b)^n$ is 4096, then the greatest coefficient in the expansion is

r and n are positive integers $r > 1, n > 2$ and coefficient of $(r+2)^{th}$ term and $3r^{th}$ term in the expansion of $(1 + x)^{2n }$ are equal, then n equals

The coefficients of $x^p$ and $x^q$ (p and q are positive integers) in the expansion of $(1+ x )^{p+q}$ are