Method of Difference

Q. A boy was asked to write $2^5\ast 9^2$, but he wrote 2592. What is the numerical difference between the two?

1. 0
2. 1
3. 2
4. 3

Q. Sum of n terms of series $16+24+40+........$ will be.

1. $8(2^n-1)+8n$
2. $4(2^n-1)+8n$
3. $6(2^n-1)+6n$
4. $3(2^n-1)+8n$

Q.

$2^{\frac{1}{4}}$. $4^{\frac{1}{8}}$. $8^{\frac{1}{16}}$. ${16}^{\frac{1}{32}}$................ is equal to

1. 

2. 

3. 1

4. 2

Q. Find the sum of the following series to $n$ terms: $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\dots$

Q. The sum of the series $\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}\cdots$ up to $\infty$ is equal to

1. $2lo{g}_{e}2$
2. $lo{g}_{e}2-1$
3. $lo{g}_e\left(\frac{4}{e}\right)$
4. $lo{g}_{e}2$

Q. If $\sqrt{5+2\sqrt{6}}=A+\sqrt{3}$ then $A=$ .