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7.Binomial Theorem
hard
${({x^2} - x - 2)^5}$ ના વિસ્તરણમાં ${x^5}$ નો સહગુણક મેળવો.
A
$-83$
B
$-82$
C
$-81$
D
$0$
Solution
(c) ${({x^2} – x – 2)^5} = {(x – 2)^5}{(1 + x)^5}$
= $[\,{}^5{C_0}{x^5} – {}^5{C_1}{x^4} \times 2 + …\,]$ $[\,{}^5{C_0} + {}^5{C_1}x + …\,]$
Collecting the coefficient of $x^5$:
=$1 – 5.5.2 + 10.10.4 – 10.10.8 + 5.5.16 – 32$
= $1 – 50 + 400 – 800 + 400 – 32 = – 81$.
Standard 11
Mathematics
