The remainder when 7^ 2022 +3^ 2022 is divided by 5 is. - Vidyadip

Question

The remainder when $7^{2022}+3^{2022}$ is divided by 5 is.

✓

Answer

c
$7^{2022}+3^{2022}$

$=(49)^{1011}+(9)^{1011}$

$=(50-1)^{1011}+(10-1)^{1011}$

$=5 \lambda-1+5 K -1$

$=5\,m -2$

Remainder $=5-2=3$

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

Let $\int_0^x \sqrt{1-\left(y^{\prime}(t)\right)^2} d t=\int_0^x y(t) d t, 0 \leq x \leq 3, y \geq 0$, $\mathrm{y}(0)=0$. Then at $\mathrm{x}=2, \mathrm{y}^{\prime \prime}+\mathrm{y}+1$ is equal to :

Let $f$ be function such that $f(x + y) = f(x) + f(y)$ for all $x$ and $y$ and $f(x) = (2x^2 + 3x)g(x)$ for all $x$; where $g(x)$ is continuous and $g(0) = 3.$ Then $f '(x)$ is equal to :-

If the sum of the first ten terms of the series ${\left( {1\frac{3}{5}} \right)^2} + {\left( {2\frac{2}{5}} \right)^2} + {\left( {3\frac{1}{5}} \right)^2} + {4^2} + \;\;.\;.\;.\;.\;,$ is $\frac{{16}}{5}m$ then $m$ is equal to :

Let $a_1, a_2, a_3, \ldots, a_{11}$ be real numbers satisfying $a_1=15,27-2 a_2>0$ and $a_k=2 a_{k-1}-a_{k-2}$ for $k=3,4, \ldots$,

$11$. If $\frac{a_1^2+a_2^2+\ldots+a_{11}^2}{11}=90$, then the value of $\frac{a_1+a_2+\ldots+a_{11}}{11}$ is equal to

There are $4$ men and $5$ women in Group $A$, and $5$ men and $4$ women in Group $B.$ If $4$ persons are selected from each group, then the number of ways of selecting $4$ men and $4$ women is....................

In the expansion of ${({5^{1/2}} + {7^{1/8}})^{1024}}$, the number of integral terms is

The number of symmetric relations defined on the set $\{1,2,3,4\}$ which are not reflexive is

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 of $ea$, such that $f(a)=0$, is equal to.............

The foci of a hyperbola are $( \pm 2,0)$ and its eccentricity is $\frac{3}{2}$. A tangent, perpendicular to the line $2 x+3 y=6$, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the $x$ - and $y$-axes are $a$ and $b$ respectively, then $|6 a|+|5 b|$ is equal to $..........$.

Let $a \in R$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{\frac{1}{4}} x+a=0$. If $\alpha^4+\beta^4=-30$, then the product of all possible values of $a$ is $......$