JEE MAIN - Mathematics Hindi (2016 - 9th April Morning Slot - No. 1)
$$x \in \mathbf{R}, x \neq-1$$ के लिए, यदि $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}}\, + \,.....\, + \,{x^{2016}} = \sum\limits_{i = 0}^{2016} {{a_i}\,{x^i}} $$, है, तो $$a_{17}$$ बराबर है :
$$\frac{2017 !}{17 ! ~2000 !}$$
$$\frac{2016 !}{17 ! ~1999 !}$$
$$\frac{2017 !}{2000 !}$$
$$\frac{2016 !}{16 !}$$
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