Binomial Theorem
4 Board Maths previous year questions on Binomial Theorem — options free on every question; 1 include the answer & explanation free, the rest unlock with PYQ Pass.
The remainder when 32022 is divided by 5 is:
[JEE Main 2022, 24 Jun (Shift 1)]
4
\((3\times 3\times 3\times \ldots .2022\text{ times })\div 5\\ \text{ Remainder }=((-1)(-1)(-1)\ldots .1011\text{ times })\\ \Rightarrow \text{ Remainder }=-1+5=4\)
The coefficient of the term independent of \(\ x \) in the expansion of \(\ \left(\sqrt{\frac{x}{3}}+\frac{3}{2 x^2}\right)^{10} \) is
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The coefficient of \(x^{301}\) in \((1+x)^{500}+x(1+x)^{499}\) \(+x^2(1+x)^{498}+\ldots+x^{500}\) is:
[JEE Main 2023, 30 Jan (Shift 1)]
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If the greatest value of the term independent of '\( x \)' in the expansion of \( \left(x \sin \alpha+a \frac{\cos \alpha}{x}\right)^{10} \) is \( \frac{10 \text { ! }}{(5 !)^{2}} \), then the value of '\( a \)' is equal to
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