Competishun Header
Competishun
Contact Us
Back

Report Issue

Jee Main 2024
29-01-2024 S2
Question
Remainder when $64^{32^{32}}$ is divided by 9 is equal to
Write Your Answer
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Let $32^{32}=\mathrm{t}$ $$ \begin{aligned} & 64^{32^{32}}=64^t=8^{2 t}=(9-1)^{2 t} \\ & =9 k+1 \end{aligned} $$ Hence remainder = 1
Question Tags
JEE Main
Mathematics
Medium
Start Preparing for JEE with Competishun
YouTube
Books
App
Tests
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
QJEE Main 20242024
The number of species from the following that have pyramidal geometry around the central atom is $\_\_\_\_$
$...
JEE MainChemistryEasy
View Solution→
QJEE Main 20242024
The number of unpaired d-electrons in $\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+}$ is $\_\_\_\_$
JEE MainChemistryEasy
View Solution→
QJEE Main 20242024
A first row transition metal in its +2 oxidation state has a spin-only magnetic moment value of 3.86 BM. The...
JEE MainChemistryEasy
View Solution→
QJEE Main 20242024
For a strong electrolyte, a plot of molar conductivity against (concentration) ${ }^{1 / 2}$ is a straight line, with...
JEE MainChemistryEasy
View Solution→
QJEE Main 20242024
Given below are two statements:
Statement I : The correct order of first ionization enthalpy values of Li, Na, F...
JEE MainChemistryEasy
View Solution→
QJEE Main 20242024
Choose the Incorrect Statement about Dalton's Atomic Theory
JEE MainChemistryEasy
View Solution→
QJee Main 20242024
Let the slope of the line $45 x+5 y+3=0$ be $27 r_1+\frac{9 r_2}{2}$ for some $r_1, r_2 \in R$. Then...
JEE MainMathematicsEasy
View Solution→
QJee Main 20242024
Let the set $C=\left\{(x, y) \mid x^2-2^y=2023, x, y \in \mathbb{N}\right\}$. Then $\sum_{(x, y) \in C}(x+y)$ is equal to
JEE MainMathematicsMedium
View Solution→
QJee Main 20242024
Remainder when $64^{32^{32}}$ is divided by 9 is equal to
JEE MainMathematicsMedium
View Solution→
QJee Main 20242024
Let $f(x)=\sqrt{\lim _{r \rightarrow x}\left\{\frac{2 r^2\left[(f(r))^2-f(x) f(r)\right]}{r^2-x^2}-r^3 e^{\frac{f(r)}{r}}\right\}}$ be differentiable in $(-\infty, 0) \cup(0, \infty)$ and $f(1)=1$. Then the value...
JEE MainMathematicsHard
View Solution→
Q JEE MAIN 20242024
The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is
JEE MainMathematicsEasy
View Solution→
QJee Main 20242024
Let $O$ be the origin, and $M$ and $N$ be the points on the lines $\frac{x-5}{4}=\frac{y-4}{1}=\frac{z-5}{3}$ and $\frac{x+8}{12}=\frac{y+2}{5}=\frac{z+11}{9}$ respectively such...
JEE MainMathematicsMedium
View Solution→
QJEE Main 20242024
Fuel cell, using hydrogen and oxygen as fuels,
A. has been used in spaceship
B. has as efficiency...
JEE MainChemistryEasy
View Solution→
QJEE Main 20242024
If an iron (III) complex with the formula $\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_{\mathrm{x}}(\mathrm{CN})_{\mathrm{y}}\right]^{-}$has no electron in its $\mathrm{e}_{\mathrm{g}}$ orbital, then the value of $\mathrm{x}+\mathrm{y}$...
JEE MainChemistryEasy
View Solution→
QJee Main 20242024
Let the area of the region $\left\{(x, y): 0 \leq x \leq 3,0 \leq y \leq \min \left\{\mathrm{x}^2+2,2 \mathrm{x}+2\right\}\right\}$ be...
JEE MainMathematicsMedium
View Solution→
QJEE Main 20242024
The correct order of the first ionization enthalpy is
JEE MainChemistryEasy
View Solution→
QJEE MAIN 20242024
The variance $\sigma^2$ of the data
JEE MainMathematicsEasy
View Solution→
QJee Main 20242024
If $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sqrt{1-\sin 2 x} d x=\alpha+\beta \sqrt{2}+\gamma \sqrt{3}$, where $\alpha, \beta$ and $\gamma$ are rational numbers, then $...
JEE MainMathematicsMedium
View Solution→
Check this project | Best Developer Portfolio