Search any question & find its solution
Question:
Answered & Verified by Expert
$(102)^4=$ ?
Options:
Solution:
2288 Upvotes
Verified Answer
The correct answer is:
108243216
$$
\text { } \begin{aligned}
(102)^4= & (100+2)^4 \\
= & { }^4 C_0(100)^4 \cdot 1+{ }^4 C_1(100)^3 \cdot 2^1 \\
& \quad+{ }^4 C_2(100)^2 \cdot 2^2+{ }^4 C_3(100)^1 \cdot 2^3 \\
& \quad+4 C_4(100)^0 2^4 \\
= & (100)^4+4(100)^3 \cdot 2+6(100)^2 \cdot 4 \\
& \quad+4(100) 8+1 \cdot 1 \cdot 16 \\
= & 100000000+8000000+240000 \\
= & 108243216
\end{aligned}
$$
Hence, option (4) is correct.
\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.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.