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The coefficients of $x^{2} y^{2}, {yzt}^{2}$ and xyzt in the expansion of (r + y + z + t)⁴ are in the ratio

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4:2:1

1:2:4

2:4:1

1:4:2

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Correct option is B

Coefficient of x2y2 in (x+y+z+t)4=4!2!2!=6 and coefficient of yzt2 in⁡(x+y+z+t)4=4!1!1!1!2!=12AIso, coefficient of xyzt in (x+y+z+t)4=4!111!11!=24 .'. Required ratio is 6 :12:24 = 1:2:4

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The coefficients of x2y2, yzt2 and xyzt in the expansion of (r + y + z + t)4 are in the ratio

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Ready to Test Your Skills?

free study material

The coefficients of $x^{2} y^{2}, {yzt}^{2}$ and xyzt in the expansion of (r + y + z + t)⁴ are in the ratio