The remainder when ((64)^ (64) )^ (64) is divided by 7 is equal t… - Vidyadip

MCQ

The remainder when $\left((64)^{(64)}\right)^{(64)}$ is divided by 7 is equal to

A
4
B
1
C
3
D
6

✓

Answer

B. 1
Let $\mathrm{N}=\left((64)^{64}\right)^{64}$
$\mathbf{N}=(64)^{64^{2}}$
$\mathbf{N}=(1+63)^{64^{2}}$, let $64^{2}=\mathrm{n}$
Expanding by binomial
$\mathrm{N}=(1+63)^{\mathrm{n}}=1+{ }^{\mathrm{n}} \mathrm{C}_{1} 63+{ }^{\mathrm{n}} \mathrm{C}_{2}(63)^{2}+\ldots .$.
$=1+63 \lambda=1+7(9 \lambda)$
Remainder when divided by 7 is 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

More "SECTION - A [MATHS - MCQ]" from JEE Main 7-April-2025 Paper - Shift 1→JEE Main 7-April-2025 Paper - Shift 1 — all question types→JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\mathop {\lim }\limits_{x \to \infty } {x^{\frac{1}{3}}}\left( {{{\left( {x + 1} \right)}^{\frac{2}{3}}} - {{\left( {x - 1} \right)}^{\frac{2}{3}}}} \right)$ is

Let $E ^{ C }$ denote the complement of an event $E$. Let $E _{1}, E _{2}$ and $E _{3}$ be any pairwise independent events with $P \left( E _{1}\right) > 0$ and $P \left( E _{1} \cap E _{2} \cap E _{3}\right)=0$ Then $P \left( E _{2}^{ C } \cap E _{3}^{ C } / E _{1}\right)$ is equal to

An ellipse is inscribed in a circle and a point within the circle is chosen at random. If the probability that this point lies outside the ellipse is $2/3 $ then the eccentricity of the ellipse is :

The equation $\sqrt {(x + 1)} - \sqrt {(x - 1)} = \sqrt {(4x - 1)} $, $x \in R$ has

Let $y=y(x), x>1$, be the solution of the differential equation $(x-1) \frac{d y}{d x}+2 x y=\frac{1}{x-1}$, with $y(2)=\frac{1+e^{4}}{2 e^{4}}$. If $y(3)=\frac{e^{\alpha}+1}{\beta e^{\alpha}}$. then the value of $\alpha+\beta$ is equal to

Let $A B$ be the la tusrectum of the parabola $y^2=4a x$ in the $X Y$-plane. Let $T$ be the region bounded by the finite arc $A B$ of the parabola and the line segment $A B$. A rectangle $P Q R S$ of maximum possible area is inscribed in $T$ with $P, Q$ on line $A B$, and $R, S$ on arc $A B$. Then, area $(P Q R S)$ area $(T)$ equals

If $a, b, c$ are digits, then the rotational number represeneted by $0.cababab ........ $is :-

A circle of radius $2$ unit passes through the vertex and the focus of the parabola $y^{2}=2 x$ and touches the parabola $y=\left(x-\frac{1}{4}\right)^{2}+\alpha$, where $\alpha>0$.

Then $(4 \alpha-8)^{2}$ is equal to

Let $3,6,9,12, \ldots$ upto $78$ terms and $5,9,13,17, \ldots$ upto $59$ terms be two series. Then, the sum of the terms common to both the series is equal to

The series of positive multiples of $3$ is divided into sets : $\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots$ Then the sum of the elements in the $11^{\text {th }}$ set is equal to $................$