Using binomial theorem, evaluate: (99)^5 - Vidyadip

Question

Using binomial theorem, evaluate: $(99)^5$

✓

Answer

$(99)^5 = (100 - 1)^5$
Using binomial theorem, we have
$(100 - 1){ = ^5}{C_0}{(100)^5}{ + ^5}{C_1}{(100)^4}( - 1)$${ + ^5}{C_2}{(100)^3}{( - 1)^2}{ + ^5}{C_3}{(100)^2}{( - 1)^3}$
${ + ^5}{C_4}(100){(1)^4}{ + ^5}{C_5}{( - 1)^5}$
$= (100)^5 + 5(100)^4(-1) + 10(100)^3 + 10(100)^2(-1)^3 + 5(100) + (-1)^5$
$= 10000000000 - 500000000 + 10000000 - 100000 + 500 - 1$
$= 10010000500 - 500100001$
$= 9509900499$

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 "2 Marks Questions" from Binomial Theorem→Binomial Theorem — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the equation of the line whose perpendicular distance from the origin is $4$ units and the angle which the normal makes with positive direction of $x-$axis is $15^\circ .$

Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}
Verify that $\text{L}-(\text{M}\cup\text{N})=(\text{L}-\text{M})\cap(\text{L}-\text{N})$

Find the domain of $f(x)=\frac{1}{x+2}$.

Using section formula, prove that the three points (– 4, 6, 10), (2, 4, 6) and (14, 0, –2) are collinear.

Evaluate:
$\lim\limits_{\text{x} \rightarrow 0}\frac{1-\cos2\text{x}}{\text{x}^{2}}$

Evaluate the following:
$\text{i}^{30}+\text{i}^{40}+\text{i}^{60}$

Express the following complex numbers in the standard form a + ib:
$\frac{5+\sqrt{2}\text{i}}{1-\sqrt{2}\text{i}}$

Find the derivative of function $\frac{a}{{{x^4}}} - \frac{b}{{{x^2}}} + \cos x$ (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers).

Prove that: $\frac{\cos 9 x-\cos 5 x}{\sin 17 x-\sin 3 x}=-\frac{\sin 2 x}{\cos 10 x}$.

Prove that : sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x