Q100 / 160 · AP EAMCET 2003 · Mathematics

The coefficient of $x^5$ in the expansion of $\left(1+x^2\right)^5(1+x)^4$, is :

  • Correct answer
    A
    60
  • B
    50
  • C
    40
  • D
    56

Solution

We have, $\left(1+x^2\right)^5(1+x)^4$ $=\left[1+{ }^5 C_1 x^2+{ }^5 C_2 x^4+\ldots+\left(x^2\right)^5\right]$ $\left[1+{ }^4 C_1 x+{ }^4 c_2 x^2+{ }^4 C_3 x^3+x^4\right]$ Coefficient of $x^5={ }^5 C_1 \cdot{ }^4 C_3+{ }^5 C_2 \cdot{ }^4 C_1$ $=5 \cdot 4+10 \cdot 4=20+40=60$

Hence, the correct answer is option: 'A'.

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