Higher Math 2nd Paper CQ-Rajshahi Board-2022

Express $\frac{2-3 i}{4-4 i}$ in the form of $A+i B$.

Find the value of $\sqrt{a+b}$.

If $1=m=3$ and $n=\sqrt{18}$, then determine the sum of cube roots of $|2|$.

Find the modulus and principal argument Chopters \& $-4+4 \mathrm{i}$.

If one root of the equation $f_{2}(x)=0$ is the square of the other, then find the value of $a$, where $\alpha=9$, $\beta=2$ and $\gamma=-\frac{1}{3}(a+2)$.

If $\mathrm{p}, \mathrm{q}$ are the roots of the equation $f_{1}(\mathrm{x})=0$, then form the equation whose roots are $\frac{1}{p}$ and $\frac{1}{q^{3}} \quad 4$

Show that, the roots of the equation $2 x^{2}+6 x-8=$ 0 are rational.

If the equations $\varphi(x)=0$ and $\psi(x)=0$ have a common root, then express $m$ in terms of $l$ and $n$.

If the roots of the equation $f(x) \cdot g(x)=0$ are $p, q$, $r$, then find the value of symmetric expression $\Sigma p^{3} q$.

An object starts from the rest moves to the uniform acceleration $3 \mathrm{~m} / \mathrm{s}^{2}$. After how long time its velocity will be $60 \mathrm{~m} / \mathrm{s}$ ?

According to the secnario-1, if the speed of the swimmer $20 \mathrm{~cm} / \mathrm{s}$ and the current is $10 \mathrm{~cm} / \mathrm{s}$, then determine $t_{1}: t_{2}$.

According to the scenario-2, if $\mathrm{OA}=49$ meter, then find the distance of $O B$ the question no. 3

Find the magnitude of the resultant of two equal forces $P$ acting at a point inclined at angle $\alpha$ to each other.

If two like parallel forces as shown in scenario-1 interchange with each other, the action point of resultant is moved to a distance $d$ along $A B$. Prove that, $\mathrm{d}=\frac{10}{7}$ meter.

In scenario-2, if $P=6 \mathrm{~N}, \mathrm{Q}=9 \mathrm{~N}$ and $\mathrm{R}=5 \mathrm{~N}$, then find the magnitude and direction of the resultant of forces.