Question Detail

\begin{aligned}
46^2 - (?)^2 = 4398 - 3066
\end{aligned}

Answer: Option D

1. For the integer n, if nnn is odd, then what is true

n is odd and n*n is even
n*n is odd
n is even
n*n is odd

Answer: Option A

2. 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

3. A number when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 31

Answer: Option A

Explanation:

P ÷ 44 = 432

=> P = 432 * 44 = 19008

P / 31 = 19008 / 31 = 613, remainder = 5

4. Which of the following is a prime number

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

5. Find the unit digit in \begin{aligned}
(544)^{102} + (544)^{103}
\end{aligned}

Answer: Option C

Explanation:

Required digit is = \begin{aligned}
(4)^{102} + (4)^{103} \end{aligned}
as \begin{aligned} (4)^2 \end{aligned} gives unit digit 6 so \begin{aligned} (4)^{102} \end{aligned} unit digit is 6 and \begin{aligned} (4)^{103} \end{aligned} unit digit is, unit digit of \begin{aligned} 6 \times 4 \end{aligned}= 4, so answer will be unit digit of 6 + 4 = 0