Higher Math 1st Paper CQ-Dinajpur Board-2019

Find the vector equation of the straight line passing through the points $(1,2,3)$ and $(3,2,1)$.

Determine the equation of the circle, taking diagonal of the aforementioned square in scenario-1 as diameter.

Determine the equation of the circle which touches all the aforementioned lines in scenario-2.

Find the slope of the tangent of $x^{2}-2 y^{2}=10$ at the point $(-4,3)$.

Evaluate $_{h\to0}^{\lim}$$\frac{f(x+h)-f(x)}{h}$.

Find the maximum and minimum value of $g(x)$ in the interval $(-1,2)$.

Without expansion prove that, $\left|\begin{array}{llc}2 & \mathrm{a} & 6-\mathrm{a} \\ 3 & \mathrm{~b} & 9-\mathrm{b} \\ 9 & \mathrm{c} & 27-\mathrm{c}\end{array}\right|=0$.

For $\mathrm{C}=\mathrm{A}-\mathrm{B}$, evaluate $\mathrm{C}^{2}+5 \mathrm{~B}+3 \mathrm{I}$.

By Cramer's rule find the solution of the system of equations mentioned at scenario-2.

If $\hat{i}-2 \hat{j}+\hat{k}$ and $2 \hat{i}+\mu \hat{j}-2 \hat{k}$ are perpendicular to each other then obtain the value of $\mu$.

From the scenario, find the equation of the straight line $\mathrm{AB}$.

From the stem find the equation of the diagonal PR.

Evaluate $\int \ln x^{4} d x$.

Evaluate the value of $\int_{0}^{\ln 2} \frac{u^{2}}{1+u^{2}} d x$.

By the method of integration obtain the area bounded by $f(x, y)=0$, above the axis of $x$.