Higher Math 1st Paper CQ-Rajshahi Board-2019

Determine the $(3,2)$ th entry of $|\mathrm{A}|$.

Find out $5, A^{2}-3 I$, where $I$ is an identity matrix.

If $B C=D$, then solve the system of linear equation by Crammer's rule.

Find the value of $\cos 75^{\circ}$. (without calculator)

If $A=20^{\circ}, B=2 A, C=3 A, D=4 A$, then show that, $p q=$ 3.

If $\alpha+\beta+\gamma=0$ then prove that, $\cos \alpha+\cos \beta-\cos \gamma=r+2$.

If ${ }^{n} C_{5}={ }^{n} C_{7}$ then find the value of ${ }^{n} C_{11}$ .

Find the length of intercept from $x$-axis by the circle with centre $\mathbf{C}$ in the stem.

If $f^{1}(-2)=\mathrm{n}$ ! from the equation of $f(\mathrm{x})$ of $A B$, then find the value of $n$.

Determine the ratio that the $x$-axis divides the line $P Q$.

Find the intercept from $x$-axis by the line which is perpendicular bisector of the line $P Q$.

How many words can be formed by taking two vowels and one consonant from the given word in the stem which, is written with block letters so that the order of vowels can not be changed?

Show that, $\lim _{x \rightarrow 0} \frac{x}{1-\sqrt{1+x}}=-2$.

Find out $\frac{d y}{d x}$ with respect to $x$.

Show that, $f(x)=0$, when $\sin ^{-1} x=\frac{\ln y}{\alpha}$