SATHEE: Binomial Theorem 1 Question 18

Binomial Theorem 1 Question 18

19.

Coefficient of $x^{11}$ in the expansion of ${(1 + x^{2})}^{4} {(1 + x^{3})}^{7} {(1 + x^{4})}^{12}$ is

(2014 Adv.)

(a) 1051

(b) 1106

(d) 1120

Show Answer

Answer:

Correct Answer: 19. (c)

Solution:

Coefficient of $x^{r}$ in $(1 + x)^{n}$ is $^{n} C_{r}$ .

In this type of questions, we find different composition of terms where product will give us $x^{11}$ .

Now, consider the following cases for $x^{11}$ in

${(1 + x^{2})}^{4} {(1 + x^{3})}^{7} {(1 + x^{4})}^{12}$ .

Coefficient of $x^{0} x^{3} x^{8}$ ; Coefficient of $x^{2} x^{9} x^{0}$

Coefficient of $x^{4} x^{3} x^{4}$ ; Coefficient of $x^{8} x^{3} x^{0}$

$=^{4} C_{0} \times^{7} C_{1} \times^{12} C_{2} +^{4} C_{1} \times^{7} C_{3} \times^{12} C_{0} +^{4} C_{2} \times^{7} C_{1}$ $\times^{12} C_{1} +^{4} C_{4} \times^{7} C_{1} \times^{12} C_{0}$

$= 462 + 140 + 504 + 7 = 1113$

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Binomial Theorem 1 Question 18

19.

Answer:

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