Q167 / 270 · NDA 2017 (Phase 2) · Mathematics

The number of terms in the expansion of $(x+a)^{100}+(x-a)^{100}$ after simplification is

  • A
    $202$
  • B
    $101$
  • Correct answer
    C
    $51$
  • D
    $50$

Solution

$(x+a)^{100}+(x-a)^{100}$ Simple logic is we get ${ }^n c_0,{ }^n c_2,{ }^n c_4 \ldots .{ }^n c_{100}$ in this expansion. The number of terms from $\mathrm{n}_{\mathrm{c}_0}$ to $\mathrm{n}_{\mathrm{c}_{100}}$ are 51 $\therefore$ There are 51 terms.

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

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