Question Detail

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

1. 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}

2. 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

3. There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is:

Answer: Option B

Explanation:

\begin{aligned} \frac{abc}{bcd} = \frac{385}{1001} => \frac{a}{d} = \frac{5}{13} \end{aligned}So d = 13

4. 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