List of top Mathematics Questions on Binomial theorem asked in JEE Advanced

Let \[ \left(1 + \frac{2}{5}x\right)^{23} = \sum_{i=0}^{23} a_i x^i \] If the maximum value of \(a_i\) occurs at \(i = r\), find the value of \(r\).

Let a and b be two nonzero real numbers. If the coefficient of x⁵ in the expansion of (\(ax^2+(\frac{70}{27bx})^4\) is equal to the coefficient of x^-5 in the expansion of \((ax-\frac{1}{bx^2})^7\). then the value of 2b is

Let a and b be two nonzero real numbers. If the coefficient of x⁵ in the expansion of (\(ax^2+(\frac{70}{27bx})^4\) is equal to the coefficient of x^-5 in the expansion of \((ax-\frac{1}{bx^2})^7\). then the value of 2b is

Coefficient of $ x^{11}$ in the expansion of $(1 + x^2)^4 (1 + x^3)^7 (1 + x^4)^{12} $

If $^{n-1}C_r =(k^2 -3) \, ^nC_{r+1}$then k belongs to

Coefficient of $t^{24} $ in $ (1+t^2)^{12}) (1+t^{12}(1+t^{24})$ is

In the binomial expansion of $(a - b)^n , n \ge 5 $ the sum of the 5th and 6th terms is zero. Then, a /b equals

For $2 \le \, r \, \le \, n,\binom{n}{r}+2 \binom{n}{r-1}+\binom{n+2}{r}$ is equal to

If in the expansion of $(1 + x)^m (1 - x)^n$, the coefficients of $x$ and $x^2$ are 3 and - 6 respectively, then m is euqal to

The expression $[x+(x^3-1)^{1/2}]^5 +[x-(x^3-1)^{1/2}]^5$ is a polynomial of degree

Given positive integers $r >1, n > 2$ and the coefficient of $(3r)th$ and $ (r + 2)th $ terms in the binomial expansion of $(1 + x)^2n$ are equal. Then,