List of top Mathematics Questions on Binomial Expansion asked in JEE Main

Let $ \alpha_1 $ and $ \beta_1 $ be the distinct roots of $ 2x^2 + (\cos\theta)x - 1 = 0, \ \theta \in (0, 2\pi) $. If $ m $ and $ M $ are the minimum and the maximum values of $ \alpha_1 + \beta_1 $, then $ 16(M + m) $ equals:

If \[ \sum_{r=0}^{10} \left( \frac{10^{r+1} - 1}{10^r} \right) \cdot {^{11}C_{r+1}} = \frac{\alpha^{11} - 11^{11}}{10^{10}}, \] then $ \alpha $ is equal to:

The number of integral terms in the expansion of $ \left( 5^{\frac{1}{2}} + 7^{\frac{1}{8}} \right)^{1016} $ is:

The number of rational terms in the binomial expansion of $ \left( 5^{1/2} + 7^{1/8} \right)^{1016} $ is:

If $ (1 + x + x^2)^{10} = 1 + a_1 x + a_2 x^2 + \dots $, then $ (a_1 + a_3 + a_5 + \dots + a_{19}) - 11a_2 $ equals to:

Let $ \alpha, \beta, \gamma $ and $ \delta $ be the coefficients of $ x^7, x^5, x^3, x $ respectively in the expansion of $ (x + \sqrt{x^3 - 1})^5 + (x - \sqrt{x^3 - 1})^5, \, x > 1 $. If $ \alpha u + \beta v = 18 $, $ \gamma u + \delta v = 20 $, then $ u + v $ equals:

The minimum value of $ n $ for which the number of integer terms in the binomial expansion $\left(7^{\frac{1}{3}} + 11^{\frac{1}{12}}\right)^n$ is 183, is

If in the expansion of $ (1 + x)^p (1 - x)^q $, the coefficients of $ x $ and $ x^2 $ are 1 and -2, respectively, then $ p^2 + q^2 $ is equal to:

The sum of all rational terms in the expansion of $ \left( 1 + 2^{1/3} + 3^{1/2} \right)^6 $ is equal to