The total number of terms in the expansion of $(2 x - y + 4 z)^{12}$ , is

90

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91

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13

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None of these

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Solution

The correct option is A $91$
${(2 x - y + 4 z)}^{12} = {((2 x - y) + 4 z)}^{12}$
$=^{12} C_{0} {(z)}^{0} {(2 x - y)}^{12} +^{12} C_{1} {(z)}^{1} {(2 x - y)}^{11} + . . . . +^{12} C_{12} {(z)}^{12} {(2 x - y)}^{0}$
Terms $= 13 + 12 + 11.... + 1$
$= \frac{14 \times 13}{2} = 91$

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