The last digit in 7^ 300 is - Vidyadip

MCQ

The last digit in ${7^{300}}$ is

A
$7$
B
$9$
✓
$1$
D
$3$

✓

Answer

Correct option: C.

$1$

c
(c) We have ${7^2} = 49 = 50 - 1$

Now, ${7^{300}} = {({7^2})^{150}} = {(50 - 1)^{150}}$

= $^{150}{C_0}{(50)^{150}}{( - 1)^0} + {\,^{150}}{C_1}{(50)^{149}}{( - 1)^1} + ...... + {\,^{150}}{C_{150}}{(50)^0}{( - 1)^{150}}$

Thus the last digits of ${7^{300}}$ are $^{150}{C_{150}}.1.1$ $i.e., 1$.

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 "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 ${{\log x} \over {b - c}} = {{\log y} \over {c - a}} = {{\log z} \over {a - b}},$ then which of the following is true

Let $A B C D$ be a square and $E$ be a point outside $A B C D$ such that $E, A, C$ are collinear in that order. Suppose $E B=E D=\sqrt{130}$ and the areas to $\triangle E A B$ and square $A B C D$ are equal. Then, the area of square $A B C D$ is

$x = 1 + a + {a^2} + ....\infty \,(a < 1)$ $y = 1 + b + {b^2}.......\infty \,(b < 1)$ Then the value of $1 + ab + {a^2}{b^2} + ..........\infty $ is

There are two candles of same length and same size. Both of them burn at uniform rate. The first one burns in $5\,hr$ and the second one burns in $3\,h$. Both the candles are lit together. After how many minutes the length of the first candle is $3$ times that of the other?

The centre of the circle $x = 2 + 3\cos \theta $, $y = 3\sin \theta - 1$ is

The product of the lengths of perpendiculars drawn from any point on the hyperbola ${x^2} - 2{y^2} - 2 = 0$ to its asymptotes is

If $^{43}{C_{r - 6}} = {\,^{43}}{C_{3r + 1}},$ then the value of $r$ is

Find the equation perpendicular to 2x - y = 4 and pass through (2, 4):

The points of intersection of the line $4x - 3y - 10 = 0$ and the circle ${x^2} + {y^2} - 2x + 4y - 20 = 0$ are

The mean of the data set comprising of $16$ observations is $16.$ If one of the observation valued $16$ is deleted and three new observations valued $3, 4$ and $5$ are added to the data, then the mean of the resultant data, is: