JEE Main 2023 (Online) 31st January Evening Shift | Binomial Theorem Question 53 | Mathematics | JEE Main - ExamSIDE.com

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JEE Main 2023 (Online) 31st January Evening Shift

Numerical

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-1

If the constant term in the binomial expansion of $\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{l}}\right)^{9}$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^{\alpha} \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to ________.

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2

JEE Main 2023 (Online) 31st January Morning Shift

Numerical

+4

-1

The remainder on dividing $$5^{99}$$ by 11 is ____________.

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3

JEE Main 2023 (Online) 31st January Morning Shift

Numerical

+4

-1

Let $$\alpha>0$$, be the smallest number such that the expansion of $$\left(x^{\frac{2}{3}}+\frac{2}{x^{3}}\right)^{30}$$ has a term $$\beta x^{-\alpha}, \beta \in \mathbb{N}$$. Then $$\alpha$$ is equal to ___________.

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4

JEE Main 2023 (Online) 30th January Evening Shift

Numerical

+4

-1

$50^{\text {th }}$ root of a number $x$ is 12 and $50^{\text {th }}$ root of another number $y$ is 18 . Then the remainder obtained on dividing $(x+y)$ by 25 is ____________.

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