1
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1
Change Language

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

Your input ____
2
JEE Main 2023 (Online) 31st January Morning Shift
Numerical
+4
-1
Change Language

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 ___________.

Your input ____
3
JEE Main 2023 (Online) 30th January Evening Shift
Numerical
+4
-1
Change Language
$50^{\text {th }}$ 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
Change Language

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 ____
JEE Main Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12