1

JEE Main 2023 (Online) 31st January Morning Shift

Numerical

+4

-1

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

Your input ____

2

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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3

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 ____________.

Your input ____

4

JEE Main 2023 (Online) 29th January Morning Shift

Numerical

+4

-1

Let the coefficients of three consecutive terms in the binomial expansion of $$(1+2x)^n$$ be in the ratio 2 : 5 : 8. Then the coefficient of the term, which is in the middle of those three terms, is __________.

Your input ____

Questions Asked from Mathematical Induction and Binomial Theorem (Numerical)

Number in Brackets after Paper Indicates No. of Questions

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