Higher Math 2nd Paper CQ-Mymensingh Board-2022

If $\tan ^{-1} x+\tan ^{-1} y=\frac{\pi}{2}$, then show that, $x=\frac{1}{y}$, [where \( x>0, y>0,0 ]

If $f^{-1}(2 x)+f^{-1}(2 y)=\frac{3 \pi}{2}$, then show that, $x^{2}+y^{2}=$ $\frac{1}{4}$

If $f(x)+\sqrt{3} f\left(\frac{\pi}{2}-x\right)=\sqrt{2}$, then solve the equation.

Find the eccentricity of the conic $\frac{x^{2}}{4}-\frac{y^{2}}{9}+1=0.2$

If the equation of the conic given in stem is $y^{2}=$ $6 x$ and $S P=6$, then find the coordinate of point P.

Find the equation of the stem mentioned conic whose focus is $(-1,1)$ and vertex $(2,-3)$.

If $P=Q, R=3 \sqrt{3} N$ and $\alpha=60^{\circ}$, then find two forces.

In scenario-1, if $\alpha=3 \theta$, then prove that, $R=$$\frac{P^{2}-Q^{2}}{Q} ;(P>Q) \text {. }$

In scenario-2, if the forces are interchanged, then find the distance through which resultant is shifted along $\mathrm{AB}$.

Find the length of the latus rectum of the conic $5 x^{2}+4 y^{2}=1$.

Express the equation described in stemstandard form then find the equation of of the conic.

Determine the equation of the conic described in stem-2.

Find an equation having roots $2-\sqrt{-3}$.

If one root of first equation is equal to 2 another, then find the value of $b$.

If $\alpha$ and $\beta$ ind the value of show the roots of second equation, then show that, $\alpha^{2}=\beta$ and $\beta^{2}=\alpha$.