Question Detail

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}

1. A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is

22030
220030
23030
24030

Answer: Option B

Explanation:

(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030

2. What least number must be subtracted from 427398 so that remaining number is divisible by 15

Answer: Option A

Explanation:

On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted

3. Which is smallest prime number

Answer: Option B

4. 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

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