For the integer n, if n*n*n is odd, then what is true

Answer: Option A

Explanation:

Trick: Number is divisible by 9, if sum of all digits is divisible by 9, so (2+2+3+*+4+3+1) = 15+* should be divisible by 9,
15+3 will be divisible by 9,
so that least number is 3.

Answer: Option B

Answer: Option B

Explanation:

It is false, 2 is an even number

Answer: Option C

Explanation:

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

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