Binomial Theorem 1 Question 6

7. If the fourth term in the binomial expansion of x11+log10x+x112 is equal to 200 , and x>1, then the

value of x is

(a) 100

(b) 104

(c) 10

(d) 103

Show Answer

Answer:

Correct Answer: 7. (a)

Solution:

  1. Given binomial is x11+log10x+x112

Since, the fourth term in the given expansion is 200.

6C3xx1+log10x32x1123=200

20×x32(1+log10x)+14=200x32(1+log10x)+14=1032(1+log10x)+14log10x=1

[applying log10 both sides]

[6+(1+log10x)]log10x=4(1+log10x)(7+log10x)log10x=4+4log10xt2+7t=4+4t[ let log10x=t]t2+3t4=0t=1,4=log10xx=10,104 Since, x>1x=10



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