Higher Math 2nd Paper CQ-Cumilla Board-2023

Find the eccentricity of the ellipse $4 x^{2}+5 y^{2}=1$.

If $S$ is the focus and $S P=6$ unit in the scenario-1, then find the co-ordinates of the point $P$.

Find the equation and length of the latus rectum of the conic given in scenario-2.

Determine the value of $\mathrm { ( 1-i)^{-2} - ( 1 + i)^{-2}}$ .

If in the scenario $\mathrm{ \theta = 45^{\circ} and r = 1 }$ , then find the value of $\mathrm{ z^8 + z^6 + z^4 + 1}$ .

From the scenario prove that , $\mathrm{ Arg ( z²) = 2Arg(z)}$ .

Prove that, $\mathrm{ \sin ^ { -1} \frac{ 2x}{ 1 + x²} = \cos ^ { -1} \frac{ 1-x²}{1+x²}}$

Find the general solution of $f\mathrm{(\alpha) = \sin 4 \alpha}$

If $\mathrm{ g ( \pi g ( \frac{\pi}{2})) = g (\frac{\pi}{2} - \pi g (x))}$ , then show that $\mathrm{ x =\pm \frac{\pi}{4} + \cos ^{-1} \frac{1}{2 \sqrt2}}$ .

Find the resultant of the forces $4 \mathrm{~N}$ and $3 \mathrm{~N}$ acting at a point at an angle of $120^{\circ}$.

From scenario-1, Prove that, $\theta=\cos ^{-1}(2 \cos \varphi)$.

In scenario-2, if both forces are increased by a, then show that the resultant will move by a distance of $\frac{\mathrm{a}}{\mathrm{P}-\mathrm{Q}} \mathrm{AB}$.

Express $\mathrm{ 3 + 4i}$ in polar form.

Show that $\mathrm{ \sum( \alpha - \beta)² = \frac{ 18(b²-ac)}{a²}}$

Determine the value of $^6\sqrt{-q}.$