Higher Math 2nd Paper CQ-Dhaka Board-2019

If $\sin ^{-1} m+\cos ^{-1} n=\frac{\pi}{2}$, then prove that, $m^{2}+n^{2}=1$.

If $\operatorname{cosec}^{-1} \frac{1}{f(a)}-\sec ^{-1} \frac{1}{g(b)}=2 \tan ^{-1} x$, then show that, $x=$ $\frac{a-b}{1+a b}$.

Solve the equation, $2 h(\theta) \cdot h(3 \theta)=1$ in the interval $0 \leq \theta \leq$ $2 \pi$.

A car starts from rest with uniform acceleration and moved a distance of 1 kilometre by 2 minutes time, what will be its velocity?

From the scenario-1, prove that, $\frac{1}{m}+\frac{1}{n}=8$.

Show that, the height of the tower is $\frac{(x+y)^{2}}{4 x}$ metres.

Rewrite the inequality -7<x<-1 using absolute sign.

Show the solution set of the inequality $\frac{1}{f(x)} \geq 2$ on real line.

Find the minimum value of z with the help of graph.

Find the eccentricity of $3 x^{2}+5 y^{2}=1$.

If S is the focus and A is the vertex in the scenario-1, then find the equation of the parabola.

From scenario-2, find the equation of an ellipse of which eccentricity is $\frac{1}{\sqrt{2}}, S$ is the focus and MZM' is directrix.

Make a Pascal's triangle of expansion $(3-y)^{5}$.

If the co-efficient of $\mathrm{x}^{7}$ and $\mathrm{x}^{8}$ are equal in the expansion of $\{f(x)\}^{n}$, where $n \in N$, determine the value of $n$.

Show that, the co-efficient of $(\mathrm{n}+1)$ th term of $\{\mathrm{g}(4 \mathrm{x})\}^{-\frac{1}{2}}$ is $\frac{(2 n) !}{(n !)^{2} \cdot 2^{n}}$