Checking Whether nth Root of a Combination of Numbers is a Surd or Not

Q.

$\int \frac{dx}{x^2\left(\sqrt{4-x^2}\right)}=$

1. $\left(\frac{1}{4}\right)\left(\frac{\sqrt{4–x^2}}{x}\right)+c$

2. $\left(\frac{1}{2}\right)\left(\frac{\sqrt{4–x^2}}{x}\right)+c$

3. $\left(\frac{-1}{4}\right)\left(\frac{\sqrt{4–x^2}}{x}\right)+c$

4. $\left(\frac{-1}{2}\right)\left(\frac{\sqrt{4–x^2}}{x}\right)+c$

Q.

If ${\log }_{\sqrt{3}}\left(5\right)=a$ and ${\log }_{\sqrt{3}}\left(2\right)=b$ then ${\log }_{\sqrt{3}}\left(300\right)=$

1. $2(a+b)$

2. $2(a+b+1)$

3. $2(a+b+2)$

4. $(a+b+4)$

5. $(a+b+1)$

Q.

If ${\int }_a^b{x}^{3}dx=0$ and ${\int }_a^b{x}^{2}dx=\frac{2}{3}$, then the values of $a$ and $b$ are respectively,

1. $1,1$

2. $-1,-1$

3. $1,-1$

4. $-1,1$

Q.

Differentiate the following w.r.t. $x$: $\cos e{c}^{-1}\left(e^{-x}\right)$

Q.

How do you simplify $\sqrt{10}$?

Q. Which among the following is a surd?

1. $\sqrt{11\times 11\times 27\times 27}$
2. $\sqrt{12\times 16\times 24}$
3. $\sqrt{11\times 22\times 27\times 6}$
4. $\sqrt{3\times 7\times 8\times 42}$

Q.

$\int \left\{\frac{\sqrt{\left(5+x^2\right)}}{x^4}\right\}dx=$

1. $\left(\frac{1}{15}\right){\left[1+\left(\frac{5}{x^2}\right)\right]}^{\frac{3}{2}}+c$

2. $\left(-\frac{1}{15}\right){\left[1+\left(\frac{1}{x^2}\right)\right]}^{\frac{3}{2}}+c$

3. $\left(-\frac{1}{15}\right){\left[1+\left(\frac{5}{x^2}\right)\right]}^{\frac{3}{2}}+c$

4. $\left(\frac{1}{15}\right){\left[1+\left(\frac{1}{x^2}\right)\right]}^{\frac{3}{2}}+c$

5. $\left(-\frac{1}{10}\right){\left[1+\left(\frac{1}{x^2}\right)\right]}^{\frac{3}{2}}+c$

Q.

For any integer $n$, $arg\left[\frac{{(\sqrt{3}+i)}^{4n+1}}{{(1-i\sqrt{3})}^{4n}}\right]$ equals

1. $\frac{\mathrm{\pi }}{3}$

2. $\frac{\mathrm{\pi }}{6}$

3. $\frac{2\mathrm{\pi }}{3}$

4. $\frac{5\mathrm{\pi }}{6}$

Q.

$\frac{d}{dx}{\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)}^2=$

1. $1-\frac{1}{x^2}$

2. $1+\frac{1}{x^2}$

3. $1-\frac{1}{2x}$

4. none of these

Q. Is the expression $\sqrt[3]{325\times 40}$ a surd?

1. yes
2. no

Q.

Solution of $1+3^{\frac{x}{2}}=2^x$ is

1. $x=1$

2. $x=2$

3. $x=0$

4. None of these

Q.

The integral given equals to

$\int \left(\sqrt[3]{x}\right)\left(\sqrt[5]{1+\sqrt[3]{x^4}}\right)dx=$

1. ${\left(1+x^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\right)}^{\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}+C$

2. ${\left(1+x^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^{\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}+C$

3. $\frac{5}{8}{\left(1+x^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^{\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}+C$

4. $\frac{1}{6}{\left(1+x^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^6+C$

5. $\frac{15}{7}{\left(1+x^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^{\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}+C$

Q.

On simplification$x^3=27$then x is equal to

Q. Is the expression $\sqrt{24\times 25}$ a surd?

1. yes
2. no

Q. Identify wheather $\sqrt[4]{481\times 49}$ is a surd.

1. It is a surd. Its simplified value is $7\sqrt{3}.$
2. It is a surd. Its simplified value is $3\sqrt{7}.$
3. It is not a surd.

Q.

If $0<y<x,$ which statements must be true?

1. a) $\sqrt{x}-\sqrt{y}=\sqrt{x-y}$

2. b) $x\sqrt{y}=y\sqrt{x}$

3. c) $\sqrt{x}+\sqrt{x}=\sqrt{2x}$

4. d) $\sqrt{xy}=\sqrt{x}\sqrt{y}$.

Q. Is the expression $\sqrt{12\times 27}$ a surd?

1. yes
2. no

Q. Simplify the expression $1÷{(5+\frac{8}{\sqrt{2}}-\sqrt[3]{3125})}^{\frac{1}{3}}\times \sqrt{4}$ and comment whether it is a surd or not.

1. It is a surd.
2. It is a quadratic surd.
3. It is not a surd.

Q.

How do you simplify $\sqrt{-32}$?

Q. A cuboid has dimentions of $\sqrt{7}\text{unit}\times \sqrt[3]{34}\text{unit}\times \sqrt[4]{49}\text{unit}.$ Find the volume of the cuboid.

1. $\sqrt[3]{34}\times \sqrt{21}$
2. $\sqrt[3]{34}\times \sqrt{12}$
3. $\sqrt[3]{34}\times \sqrt{21}{\text{unit}}^3$
4. $\sqrt[3]{34}\times \sqrt{21}{\text{unit}}^2$

Q. A rectangle has a side of $\sqrt[3]{33}\text{unit}$ and $\sqrt[3]{39}\text{unit}.$ Find the area of the rectangle and comment whether it is a surd or not.

1. It is a surd.
2. Area is $\sqrt[3]{327}{\text{unit}}^2.$
3. It is not a surd.
4. Area is $3{\text{unit}}^2.$

Q. Is the expression $\sqrt[3]{364\times 13}$ a surd?

1. yes
2. no