Question Detail

217 * 217 + 183 * 183

70578
82578
80578
80568

Answer: Option C

Explanation:

\begin{aligned}
\frac {1}{2}\times 2(a^2 + b^2) = \frac {1}{2} \times [(a + b)^2 + (a - b)^2]
\end{aligned}
\begin{aligned}
= \frac {1}{2} \times [(217 + 183)^2 + (217 - 183)^2] = 80578
\end{aligned}

1. Simplify 586645 * 9999

5865863355
5665863355
4865863355
4665863355

Answer: Option A

Explanation:

Although it is a simple question, but the trick is to save time in solving this.
Rather than multiplying it we can do as follows:
586645 * (10000 - 1) = 5866450000 - 586645 = 5865863355

2. What is the unit digit in
\begin{aligned}
(6324)^{1797} \times (615)^{316} \times (341)^{476}
\end{aligned}

Answer: Option D

3. 1307 * 1307 = ?

1608249
1508249
1408249
1708249

Answer: Option D

Explanation:

\begin{aligned}
(a + b)^{2} = (a^2 + b^2 + 2ab)
\end{aligned}
\begin{aligned}
1307^{2} = (1300 + 7)^2 = (1690000 + 49 + 18200)
\end{aligned}

4. 587 * 999 = ?

586411
586413
486411
486413

Answer: Option B

Explanation:

Trick: 587 * (1000 - 1) = 587000 - 587 = 586413

5. How many terms are there in 2,4,8,16,....,1024

Answer: Option D

Explanation:

It is a GP. with r = 2, ie \begin{aligned} 2^1, 2^2, 2^3... \end{aligned}
If number of terms is n. Then,
\begin{aligned} 2 \times 2^{n-1} = 1024 \end{aligned} =>
\begin{aligned} 2^{n-1} = 512 \end{aligned}
or \begin{aligned} 2 \times 2^{n-1} = 2^9 \end{aligned}
so n-1 = 9 => n = 10