Higher Math 2nd Paper CQ-Jessore Board-2021

Find the nature of the roots of equation $x^{2}+x+1$ $=0$.

Construct the equation whose roots are $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ from scenario-1.

If the equations $x^{2}+g x+h=0$ and $x^{2}+h x+g=0$ have a common root of scenario-2, construct the equation with the other two roots.

Find the resultant of the two forces $4 \mathrm{~N}$ and $3 \mathrm{~N}$ which acting at a point with angle $90^{\circ}$.

If the stick is equilibrium, then show that, $\mathrm{F}_{1}: \mathrm{F}_{2}$ : $F_{3}=1: 2: 3$ from scenario-1.

From scenario-2, show that the resultant of the two forces, $F=\frac{F_{1}^{2}-F_{2}^{2}}{F_{2}}\left(F_{1}>F_{2}\right)$.

Find out the equation of directrix of parabola $x^{2}=$ $-16 \mathrm{y}$.

Find the focus, length of latus rectum, equation of directrix of ellipse from scenario-1.

From scenario-2, find out the equation of ellipse with figure and find its length of major axis.

Find out the value of $\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}$.

Draw the graphs $q=\cos ^{-1} p$ with interval $-1 \leq p \leq$ 1 from scenario-1.

Solve the equation $2\{f(x)\}^{2}+5 f(x)-3=0$ from scenario-2.

The maximum resultant of the forces $P$ and $Q$ is equal to their double of minimum resultant. Find out their ratio.

Find the resultant of the forces from scenario-1.

If the forces be interchanged in position, find the distance through which their resultant is displaced along line LM.