Question Detail

Simplify (212 * 212 + 312 * 312 )

132288
142088
142188
142288

Answer: Option D

Explanation:

Trick: Above equation can be solved by using following formula
\begin{aligned}
(a^2 + b^2) = \frac{1}{2}((a+b)^2 + (a-b)^2)
\end{aligned}

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

Answer: Option D

2. Which is smallest prime number

Answer: Option B

3. 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

4. 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

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

Question Detail

Simplify (212 * 212 + 312 * 312 )

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

2. Which is smallest prime number

3. Which of the following is a prime number

4. 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:

5. How many terms are there in 2,4,8,16,....,1024

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