Algebraic Expression

If $\mathrm{X}=2+\sqrt[3]{2}+{\left(\sqrt[3]{2}\right)}^2$, then find the value of ${\mathrm{X}}^3-6{\mathrm{X}}^2+6\mathrm{X}$.

Given$t=2+\sqrt[3]{4}+\sqrt[3]{2},$find the value of$t^3-6t^2+6t-2.$

If ${\left(x+\frac{1}{x}\right)}^2=3,$ then the value of $x^{206}{+x}^{200}+x^{90}+x^{84}{+x}^{18}+x^{12}{+x}^6+1$ is _____.

The number of oxygen atoms in $4.4$ gram of $\text{C}{\text{O}}_2$ is
(Given that atomic mass $\text{C}$ and $\text{O}$ are $\text{12}$ and $\text{16}$ $\text{g/mol}$ )

In the process of extraction of gold,
$\left[\mathrm{X}\right]+\mathrm{Zn}\stackrel{}{\to }\left[\mathrm{Y}\right]+\mathrm{Au}$

How many of the following given in the box are included under downstream processing?

If a pair of linear equations given by $a_{1}x+b_{1}y+c_1=0 \text{and} a_{2}x+b_{2}y+c_2=0$ has a unique solution, then which of the following is true$?$

 The radius of a cylindrical wire is measured by screw gauge is $1.25 \mathrm{mm}$. The length of wire is $25.0 \mathrm{cm}$ and the mass of wire is $12 \mathrm{g}$. The density of wire is  

The maximum horizontal range of a projectile is $400 \mathrm{m}$. The maximum height attained by it will be

400 gram 20% weight/weight solution on cooling gives 30 gram precipitate then find out percentage weight/weight of remaining solution.

Which of the following answers indicate the dominant carbon fixation enzyme in each of the two cells?

If $a^2=by+cz; b^2=cz+ax; c^2=ax+by;$ the the value of $\frac{x}{a+x}+\frac{y}{b+y}+\frac{z}{c+z}$

Solving equation $m+\sqrt{m}=6/25$ the value of '$m$' works out to

If $x=\sqrt{3}+\frac{1}{\sqrt{3}}$ then $\left(x-\frac{\sqrt{126}}{\sqrt{42}}\right)\left(x-\frac{1}{x-\frac{2\sqrt{3}}{3}}\right)=$

The free fall of an object is possible only in

Assume that there is a tunnel in the shape of a circular arc through the earth. Wall of the tunnel is smooth. A ball of mass ' $m$ ' is projected into the tunnel at A with speed ' $v$ '. The ball comes out of the tunnel at $B$ and escapes out of the gravity of earth. Mass and radius of earth are $M$ and $R$ respectively and radius of circular shaped tunnel is also $R$.

An electron moves around another charge in closed orbit. The de-Broglie wavelength of electron varies cyclically between two values ${\lambda }_1$ and ${\lambda }_2$ with ${\lambda }_1>{\lambda }_2$. Which of the following statements are true :-

Match the following columns.

The correct pairing sequence is:

The springs are identical and initially relaxed. The block is pushed to left and released.