The coefficients of ${x^2}{y^2},\;yz{t^2}$ and ${\rm{\;}}xyzt$ in the expansion of ${\left( {x + y + z + t} \right)^4}$ are in the ratio

JEE MATHEMATICS MCQ: BINOMIAL THEOREM

1 Easy

1 of 1

Application +4 | -1

The coefficients of

{x^2}{y^2},\;yz{t^2}

and

\mathrm{\;}xyzt

in the expansion of

{\left( {x + y + z + t} \right)^4}

are in the ratio

View answer and explanation

Correct option: B

1:2:4

Option B (

1:2:4

) is correct because the coefficients can be calculated using the multinomial theorem, and their ratio is

6:12:24

which simplifies to

1:2:4

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