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Question: If \(x^{16}\), then \[\left( \frac{x}{2} - \frac{3}{x^{2}} \right)^{10}\]...

If x16x^{16}, then

(x2−3x2)10\left( \frac{x}{2} - \frac{3}{x^{2}} \right)^{10}

A

504259\frac{504}{259}

B

450263\frac{450}{263}

C

(1+x)n(1 + x)^{n}

D

(x22−2x)8\left( \frac{x^{2}}{2} - \frac{2}{x} \right)^{8}

Answer

(1+x)n(1 + x)^{n}

Explanation

Solution

2n−12^{n} - 1

2n−12^{n - 1}

(x2+x−3)319(x^{2} + x - 3)^{319}

Trick : Put (x−2y+3z)n(x - 2y + 3z)^{n}....., then

(1+x)n(1 + x)^{n},

(1+x−2x2)6=1+a1x+a2x2+....+a12x12(1 + x - 2x^{2})^{6} = 1 + a_{1}x + a_{2}x^{2} + .... + a_{12}x^{12}

By option, (put n=1,2......) (1) and (2) does not hold condition, but (3) a2+a4+a6+....+a12a_{2} + a_{4} + a_{6} + .... + a_{12}, put n =1, 2......

a−nC1(a−1)+nC2(a−2)+....+(−1)n(a−n)=a -^{n}C_{1}(a - 1) +^{n}C_{2}(a - 2) + .... + ( - 1)^{n}(a - n) = which is correct.