Simplify (212 * 212 + 312 * 312 )

Answer: Option D

Explanation:

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

Answer: Option B

Explanation:

A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself.
So from above options 2 is that number

Answer: Option C

Explanation:

3*6*9 = 162

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

Answer: Option D

Explanation:

Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944