Q71 / 160 · AP EAMCET 2020 (22 Sep Shift 2) · Mathematics

$(102)^4=$ ?

  • A
    108242316
  • B
    108423216
  • C
    102843216
  • Correct answer
    D
    108243216

Solution

$$ \text { } \begin{aligned} (102)^4= & (100+2)^4 \\ = & { }^4 C_0(100)^4 \cdot 1+{ }^4 C_1(100)^3 \cdot 2^1 \\ & \quad+{ }^4 C_2(100)^2 \cdot 2^2+{ }^4 C_3(100)^1 \cdot 2^3 \\ & \quad+4 C_4(100)^0 2^4 \\ = & (100)^4+4(100)^3 \cdot 2+6(100)^2 \cdot 4 \\ & \quad+4(100) 8+1 \cdot 1 \cdot 16 \\ = & 100000000+8000000+240000 \\ = & 108243216 \end{aligned} $$ Hence, option (4) is correct.

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

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