Higher Math 1st Paper CQ-Cumilla Board-2022

1.

2. Stem-1: The straight line $\mathrm{AB}$ makes a triangle $\triangle \mathrm{OAB}$ with first quadrant whose area is $\frac{32}{\sqrt{3}}$ square units. Again $O P$ is a perpendicular on $A B$ which makes $60^{\circ}$ angle with positive direction of $x$-axis.

Stem-2: $x^{2}+y^{2}+4 x+4 y+1=0$ and $x^{2}+y^{2}+4 x+3 y+2=$ 0 are two equations of circle.

3. $\mathrm{h}(\mathrm{x})=\cos \mathrm{x} \text { and } \mathrm{p}(\mathrm{x})=\left(\mathrm{x}^{2}+1\right) \tan ^{-1} \mathrm{x}-\mathrm{x} \text {. }$

4.

5. $\begin{array}{l} \mathrm{A}=\left[\begin{array}{llr} 3 & 2 & 3 \\ 4 & 2 & 1 \\ 2 & 1 & -2 \end{array}\right], \mathrm{B}=\left[\begin{array}{rrr} 2 & 10 & 3 \\ 3 & 8 & 2 \\ 1 & 8 & 1 \end{array}\right], \mathrm{C}=\left[\begin{array}{rrr} \mathrm{a} & 12 & 6 \\ \mathrm{~b} & 10 & 3 \\ 3 & 9 & -1 \end{array}\right], \\ \mathrm{X}=\left[\begin{array}{l} \mathrm{x} \\ \mathrm{y} \\ \mathrm{z} \end{array}\right], \mathrm{D}=\left[\begin{array}{r} 5 \\ 10 \\ 15 \end{array}\right] \end{array}$