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Question: \(2^{4n - 2} + 2^{2n - 1}\)term in the expansion of \(2^{2n - 1} + ( - 1)^{n}2^{4n - 2}\)is....

24n−2+22n−12^{4n - 2} + 2^{2n - 1}term in the expansion of 22n−1+(−1)n24n−22^{2n - 1} + ( - 1)^{n}2^{4n - 2}is.

A

2152^{15}

B

2142^{14}

C

(1+x)n=C0+C1x+C2x2+....+Cnxn(1 + x)^{n} = C_{0} + C_{1}x + C_{2}x^{2} + .... + C_{n}x^{n}

D

None of these

Answer

2142^{14}

Explanation

Solution

=1024C16(51/2)1008(71/8)16=^{1024}C_{16}(5^{1/2})^{1008}(7^{1/8})^{16} term of =1024C1024(71/8)1024=7128=^{1024}C_{1024}\left( 7^{1/8} \right)^{1024} = 7^{128}is 1025=Tn=1+(n−1)8⇒n=1291025 = T_{n} = 1 + (n - 1)8 \Rightarrow n = 129

(y1/5+x1/10)55(y^{1/5} + x^{1/10})^{55}

Tr+1=55Cr(y1/5)55−r(x1/10)r=55Cr.y11−r/5xr/10T_{r + 1} =^{55}C_{r}(y^{1/5})^{55 - r}(x^{1/10})^{r} =^{55}C_{r}.y^{11 - r/5}x^{r/10}