Higher Math 1st Paper CQ-Combined Board(Rajshahi, Cumilla, Chattogram, Barishal)-2018

Find the equation of the chord $\mathrm{AC}$.

Find the equation of the circle as mentioned in stem.

Find the equation of the tangent from the point $\mathrm{C}$ to the circle $x^{2}+y^{2}-6 x-8 y+9=0$.

Explain complementary combination.

Find the numbers of arrangement of the word as mentioned in stem in which the vowels do not remain together.

Show that the number of combinations of the letters of the word as mentioned in the stem taken 4 letters at a time is 11 .

Find the range of the function $f(x)=\frac{x^{2}-3}{x-\sqrt{3}}$.

Find $\mathbf{M}^{-1}$.

If $M^{\prime} X=\left[\begin{array}{r}-1 \\ 0 \\ 2\end{array}\right]$, then solve with the help of determinant method.

If $\sin ^{2} \alpha-\cos \alpha=0$, then prove that, $\tan ^{4} \alpha-\sec ^{2} \alpha=0$. 2

If $f(\theta)=\frac{5}{2}$ in the scenario-1, then show that, $\cos ^{n} \theta+\sec ^{n} \theta=2^{n}+2^{-n}$.

Draw the graph $\mathrm{g}(3 \mathrm{x})$, when $-\frac{\pi}{2} \leq \mathrm{x} \leq \frac{\pi}{2}$.

Prove that, $\tan 70^{\circ}=\tan 20^{\circ}+2 \tan 50^{\circ}$.

Show that the triangle is right angle triangle according to the scenario-1.

Prove that, $\operatorname{cosec}(A-B)= \pm 3$ according to the scenario- 2.