Higher Math 1st Paper CQ-Jessore Board-2023

Find the length of the tangent drawn from the point $(3,2)$ to the circle $2 x^{2}+2 y^{2}-6 x-7=0$.

Obtain the equation of the circle which touch the three straight lines of scenario-1.

Find the equation of the circle whose diameter is the common chord of two circles of scenario-2.

Find the co-ordinates of the trisection points of the intercept of the line $\mathrm{AB}$ made by the axis of coordinate.

Obtain the equation of the straight line which passes through the point $(7,9)$ and makes an angle $45^{\circ}$ with the line $\mathrm{AB}$.

Find the co-ordinates of the point $\mathrm{D}$.

If $3\left(\begin{array}{rr}1 & -1 \\ 2 & 4\end{array}\right)+E=I_{2}$, then find $E$.

Solve the system of equation $B X^{T}=A^{T}$.

Show that, $|C|=2 \operatorname{lmn}(1+m+n)^{3}$.

Determine $\int \sin 9 x . \sin 11 x d x$.

Using scenario-1, determine $\int_{0}^{4} f(x) d x$.

Find the area of the smaller part bounded by the circle and the line of scenario-2.

Prove that, $2 \cos x=\sqrt{2+\sqrt{2+2 \cos 4 x}}$.

From the stem, prove that, $1+4 \sin \frac{\mathrm{Q}+\mathrm{R}}{4} \cdot \sin \frac{\mathrm{R}+\mathrm{P}}{4} \cdot \sin \frac{\mathrm{P}+\mathrm{Q}}{4}=\sin \frac{\mathrm{P}}{2}+\sin$ $\frac{\mathrm{Q}}{2}+\sin \frac{\mathrm{R}}{2}$.

From the stem, prove that, $\mathrm{p}^{3} \cos (\mathrm{Q}-\mathrm{R})+\mathrm{q}^{3} \cos (\mathrm{R}-\mathrm{P})+\mathrm{r}^{3} \cos (\mathrm{P}-\mathrm{Q})=3$ pqr.