The coefficient of ${x^3}$ in ${\left( {\sqrt {{x^5}} + \frac{3}{{\sqrt {{x^3}} }}} \right)^6},$ is

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

1 of 1

Application +4 | -1

The coefficient of

{x^3}

{\left( {\sqrt {{x^5}} + \frac{3}{{\sqrt {{x^3}} }}} \right)^6},

View answer and explanation

Correct option: D

540

Option D (540) is correct because by finding the general term in the expansion and setting the power of x to 3, we can find the coefficient of

x^3

to be 540.

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\left({ }^{10} C_0\right)^2-\left({ }^{10} C_1\right)^2+\ldots-\left({ }^{10} C_9\right)^2+\left({ }^{10} C_{10}\right)^2

a

d

\left( {n + 1} \right)

a{C_0} - \left( {a + d} \right){C_1} + \left( {a + 2d} \right){C_2} - ... + ...

(1-x)^{201}\left(1+x+x^2\right)^{200}

\left(\frac{1}{x}+2 x\right)^n

{x^5}

\frac{{1 + {x^2}}}{{1 + x}},\left| x \right| < 1,

\left(\begin{array}{c}2 n+1 \\ 0\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 3\end{array}\right)+\left(\begin{array}{c}2 n+1 \\ 6\end{array}\right)+\ldots=170

n