If term independent of $x$ in the expansion of $\left(x^2-\frac{3}{x}\right)^6$ is $\lambda 3^5$, then find the value of $\lambda$.

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

1 of 1

Application +4 | -1

If term independent of

x

in the expansion of

\left(x^2-\frac{3}{x}\right)^6

\lambda 3^5

, then find the value of

\lambda

View answer and explanation

Correct option: A

Option A (5) is correct because the term independent of x is found by setting the power of x to zero and solving for the binomial coefficient.

Practice All Chapter MCQs →

\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