If $(2000)^{10}$=$1.024\times 10^{k}$., then the value of k is

If $(2000)^{10}$=$1.024\times 10^{k}$., then the value of k is
1). 33
2). 30
3). 34
4). 31

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1. If a= $\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and b = $\frac{\sqrt{5}-1}{\sqrt{5}+1}$ , the value of $\left(\frac{a^{2}+ab+b^{2}}{a^{2}-ab+b^{2}}\right)$ is

2. $\left(\frac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{1-\sqrt{2}}{\sqrt{5}-\sqrt{3}}\right)$ simplified to

3. If $\frac{(x-\sqrt{24})(\sqrt{75}+\sqrt{50})}{\sqrt{75}-\sqrt{50}}$ =1 , then the value of x is

4. $(64)^{-\frac{2}{3}}\times \left(\frac{1}{4}\right)^{-2}$ is equal to :

5. The greatest number among $2^{60}$,$3^{48}$,$4^{36}$, and $5^{24}$ is :

6. $8^{\frac{2}{3}}$ is equal to :

7. The value of $\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4\sqrt{2\sqrt[3]{4...........}}}}}}$ is :

8. The smallest among the numbers $2^{250}$ , $3^{150}$, $5^{100}$, and $4^{200}$

9. $\left(3+\frac{1}{\sqrt{3}}+\frac{1}{3+\sqrt{3}}+\frac{1}{\sqrt{3}-3}\right)$ is equal to

10. If $\sqrt{3}$ =1.732, then what is the value of $\frac{4+3\sqrt{3}}{\sqrt{7+4\sqrt{3}}}$ upto three places of decimal