The value of ( 5 + 1)^5 - ( 5 - 1)^5 is - Vidyadip

MCQ

The value of ${(\sqrt 5 + 1)^5} - {(\sqrt 5 - 1)^5}$ is

A
$252$
✓
$352$
C
$452$
D
$532$

✓

Answer

Correct option: B.

$352$

b
(b) ${(\sqrt 5 + 1)^5} - {(\sqrt 5 - 1)^5}$

$ = 2\left\{ {^5{C_1}{{(\sqrt 5 )}^4}{ + ^5}{C_3}{{(\sqrt 5 )}^2}{ + ^5}{C_5}.1} \right\}$

$= 352$

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

The range of $f(x) = \cos x - \sin x$ is

The area of the parallelogram whose diagonals are $\frac{3}{2}i + \frac{1}{2}j - k$ and $2i - 6j + 8k$ is

If $\mathrm{R}$ is the smallest equivalence relation on the set $\{1,2,3,4\}$ such that $\{(1,2),(1,3)\} \subset R$, then the number of elements in $\mathrm{R}$ is

If $y=y(x)$ is solution of the differential equation $x\frac{{dy}}{{dx}} + 2y = {x^2}$ satisfying $y(1)=1$ then $y\left( {\frac{1}{2}} \right)$ is equal to

Let $y=m x+c, m>0$ be the focal chord of $y^{2}=-64 x$, which is tangent to $(x+10)^{2}+y^{2}=4$ Then, the value of $4 \sqrt{2}(\mathrm{~m}+\mathrm{c})$ is equal to $.....$

The equations of the common tangents to the ellipse, $ x^2 + 4y^2 = 8 $ $\&$ the parabola $y^2 = 4x$ can be

If one side of a square be represented by the vector $3i + 4j + 5k,$ then the area of the square is

For what values of $k$ will the equation ${x^2} - 2(1 + 3k)x + $$7(3 + 2k) = 0$ have equal roots

Solution of the differential equation $\frac{{dy}}{{dx}} + y{\sec ^2}x = \tan x{\sec ^2}x$ is

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$ then the probability of both of them occur together is