The remainder when 19^ 200 +23^ 200 is divided by 49 , is .......… - Vidyadip

MCQ

The remainder when $19^{200}+23^{200}$ is divided by $49$ , is $.........$.

A
$28$
B
$27$
✓
$29$
D
$26$

✓

Answer

Correct option: C.

$29$

c
$(21+2)^{200}+(21-2)^{200}$

$\Rightarrow 2\left[{ }^{100} C _0 21^{200}+200 C _2 21^{198} \cdot 2^2+\ldots . .+{ }^{200} C _{198} 21^2\right.$

$\left.2^{198}+2^{200}\right]$

$\Rightarrow 2\left[49 I _1+2^{200}\right]=49 I _1+2^{201}$

Now, $2^{201}=(8)^{67}=(1+7)^{67}=49 I _2+{ }^{67} C _0{ }^{67} C _1 \cdot 7=$ $49 I _2+470=49 I _2+49 \times 9+29$

$\therefore$ Remainder is $29$

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 "MCQ" from binomial theoram→binomial theoram — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the angle between the lines joining the end points of minor axis of an ellipse with its foci is $\pi\over2$, then the eccentricity of the ellipse is

If $P\,(A) = 0.4,\,\,P\,(B) = x,\,\,P\,(A \cup B) = 0.7$ and the events $A$ and $B$ are mutually exclusive, then $x = $

In a rectangle $A B C D$, points $X$ and $Y$ are the mid-points of $A D$ and $D C$, respectively. Lines $B X$ and $C D$ when extended intersect at $E$, lines $B Y$ and $A D$ when extended intersect at $F$. If the area of $A B C D$ is 60 , then the area of $B E F$ is

The roots of the equation $i{x^2} - 4x - 4i = 0$ are

Let $\alpha $ and $\beta $ be integers satisfying $0 < \beta < \alpha $ .Let $P\left( {\alpha ,\beta } \right),Q$ be the reflection of $P$ in the line $y = x, R$ be the reflection of $Q$ in the $y-$ axis, $S$ be the reflection of $R$ in the $x-$ axis and $T$ be the reflection of $S$ in the $y-$ axis. If the area of convex pentagon $PQRST$ is $187\ sq. units$ , then value of $\alpha + {\beta ^2}$ is

Let $l_1, l_2, \ldots, l_{100}$ be consecutive terms of an arithmetic progression with common difference $d_1$, and let $w_1, w_2, \ldots, w_{100}$ be consecutive terms of another arithmetic progression with common difference $d_2$, where $d_1 d_2=10$. For each $i=1,2, \ldots, 100$, let $R_i$ be a rectangle with length $l_i$, width $w_i$ and area $A_i$. If $A_{51}-A_{50}=1000$, then the value of $A_{100}-A_{90}$ is. . . . .

The solution of ${\log _{\sqrt 3 }}x + {\log _{\sqrt[4]{3}}}x + {\log _{\sqrt[6]{3}}}x + ......... + {\log _{\sqrt[{16}]{3}}}x = 36$ is

If $a$ and $d$ are two complex numbers, then the sum to $(n + 1)$ terms of the following series $a{C_0} - (a + d){C_1} + (a + 2d){C_2} - ........$ is

If ${\log _{10}}x = y,$ then ${\log _{1000}}{x^2} $ is equal to

If $y = x - {x^2} + {x^3} - {x^4} + ......\infty $, then value of $x$ will be