Name the plant whose leaves are economically important and earn foreign exchange.

To remove the second term of the equation $x^4-8x^3+x^2-x+3=0$,diminish the roots of the equation by

At a given instant of time,two particles have position vectors $4 \hat{i} + 4 \hat{j} + 57 \hat{k} \text{ m}$ and $2 \hat{i} + 2 \hat{j} + 5 \hat{k} \text{ m}$ respectively. If the velocity of the first particle is $0.4 \hat{i} \text{ ms}^{-1}$,what is the velocity of the second particle in $\text{ms}^{-1}$ if they collide after $10 \text{ s}$?

The maximum value of the function $f(x) = x^3 - 12x^2 + 36x + 17$ in the interval $[1, 10]$ is:

If a line makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the $X$-axis and $Y$-axis respectively,then the angle made by the line with the $Z$-axis is

If $\overrightarrow{a}=\hat{i}-\hat{j}-\hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}-3 \hat{j}+\hat{k}$ and the orthogonal projection of $\overrightarrow{b}$ on $\overrightarrow{a}$ is $\frac{4}{3}(\hat{i}-\hat{j}-\hat{k})$,then $\lambda$ is equal to