Remainder when 64^ 32^ 32 is divided by 9 is equal to ...........… - Vidyadip

Question

Remainder when $ 64^{32^{32}}$ is divided by $9$ is equal to .........................

✓

Answer

d
Let $32^{32}=\mathrm{t}$

$ 64^{32^{32}}=64^t=8^{2 t}=(9-1)^{2 \mathrm{t}} $

$ =9 \mathrm{k}+1$

Hence remainder $=1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Consider a line $L$ passing through the points $P(1,2,1)$ and $Q(2,1,–1)$. If the mirror image of the point $A(2,2,2)$ in the line $L$ is $(\alpha, \beta, \gamma),$ then $\alpha+\beta+6 \gamma$ is equal to …..

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

The sum of all natural numbers $‘n’$ such that $100 < n < 200$ and $H.C. F\, (91, n) > 1$ is

The product of all the roots of ${\left( {\cos \frac{\pi }{3} + i\sin \frac{\pi }{3}} \right)^{3/4}}$ is

A line drawn through the point $P(4, 7)$ cuts the circle $x^2 + y^2\, = 9$ at the points $A$ and $B$. Then $PA· PB$ is equal to

Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x ^2- px +\frac{5}{4} p =0$ are rational. Then the area of the region $\{(x, y): 0 \leq y$ $\left.\leq(x-q)^2, 0 \leq x \leq q\right\}$ is

If the sum of the series

$\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{2^2}-\frac{1}{2.3}+\frac{1}{3^2}\right)+$

$\left(\frac{1}{2^3}-\frac{1}{2^2 \cdot 3}+\frac{1}{2.3^2}-\frac{1}{3^3}\right)+$

$\left(\frac{1}{2^4}-\frac{1}{2^3 \cdot 3}+\frac{1}{2^2 \cdot 3^2}-\frac{1}{2 \cdot 3^3}+\frac{1}{3^4}\right)+\ldots$ is $\frac{\alpha}{\beta}$, where $\alpha$ and $\beta$ are co-prime, then $\alpha+3 \beta$ is equal to....

If the area of the bounded region

$R=\left\{(x, y): \max \left\{0, \log _{e} x\right\} \leq y \leq 2^{x}, \frac{1}{2} \leq x \leq 2\right\}$

is, $\alpha\left(\log _{e} 2\right)^{-1}+\beta\left(\log _{e} 2\right)+\gamma$, then the value of $(\alpha+\beta-2 \gamma)^{2}$ is equal to:

Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6: 15$ the difference between these two angles is $....^{\circ}$

Suppose $f ( x )$ is a polynomial of degree four, having critical points at $-1,0,1$ . If $T =\{ x \in R \mid f ( x )= f (0)\},$ then the sum of squares of all the elements of $T$ is