Higher Math 2nd Paper CQ-Dinajpur Board-2017

What do you mean by Range according to the stem?

Determine standard Deviation according the grouped data of the stem.

In light of the stem find out Mean Deviation.

Solve the equation $2 x^{2}+5 x-9=0$ with the help of factor

There is a common root of the two equations in the stem, then show that $\mathrm{m}+l= \pm \mathrm{n}$.

If two roots of the 1st equation in the stem are $\alpha$ and $\beta$ then express the roots of the equation $m l\left(x^{2}+1\right)-\left(n^{2}-2 m l\right) x=0 \text { as } \alpha \text { and } \beta \text {. }$

What do you mean by linear programming?

Formulate a linear program for this problem.

Solve the linear program by graphically.

Taking the axes of the ellipse as the $x$ and $y$ axes, find the equation of the ellipse passing through the points $(0,2 \sqrt{2})$ and $(-3,0)$

Find out the vertexes, foci, eccentricity, length of its latus rectum.

Sketching the conic determine the equations of the lateral recta and equation of the directrices.

To find the resultant and its direction of two forces $100 \mathrm{~N}$ and $70 \mathrm{~N}$ act at a point at an angle $62^{\circ}$.

When $P$ is increased by $(\mathrm{R}+3)$ and $\mathrm{Q}$ is increased by $(\mathrm{S}+2)$, the resultant again pass through the point $C$. Also when $Q$ and $(R+3)$ replaced by $P$ and $Q$ respectively the resultant passes through $\mathrm{C}$.

Then prove that $\mathrm{R}=\mathrm{S}+\frac{(\mathrm{Q}-\mathrm{R}-3)^{2}}{\mathrm{P}-\mathrm{Q}}+1$.

In the stem the two equal and opposite forces $\mathrm{R}$ along any two parallel lines at a distance $x$ apart in the same plane of $\mathrm{P}$ and $\mathrm{Q}$. Then show that the resultant is displaced by a distance $\frac{\mathrm{xR}}{\mathrm{P}+\mathrm{Q}}$.

[N. B. $\mathrm{R}=\mathrm{S}+\frac{(\mathrm{Q}-\mathrm{R}-3)^{2}}{\mathrm{P}-\mathrm{Q}}+1$ Replace

$\mathrm{R}=\mathrm{S}+\frac{(\mathrm{Q}-\mathrm{R}-3)^{2}}{\mathrm{P}-\mathrm{Q}}-1$]