Higher Math 1st Paper CQ-Dhaka Board-2017

If $y=\sec x$, then prove that $y_{2}=y\left(2 y^{2}-1\right)$.

From Scenario-I, find the equations of the tangent and normal a the point on the curve, where it meets the $x$-axis.

From Scenario-II, find the extreme values of this function.

Determine $\mathrm{A} \times \mathrm{C}$, also find its order.

Determine $\mathrm{A}^{-1}$

If $\mathbf{A} \times \mathbf{B}=\mathbf{C}$ then solve the system of equations by Cramer's rule.

If ${ }^{n} P_{r}=54$ and ${ }^{n} C_{r}=9$, then find the value of $r$.

How many different arrangements can be made from the letters of 'user ID' taken 4 at a time?

How many odd numbers of five significant digits can be formed with the digits of password, using each digit only once in a number?

a. If $r=6 \cos \theta+4 \sin \theta$, then find its centre and radius.

Determine the equation of a circle from Scenario-1.

Find the equation of two such tangents of the circle which are both perpendicular to the given Scenario-II.

Find $\int \ln x \mathrm{dx}$.

From scenario-1 determine $\int f(x) d x$.

Find the area of the region enclosed by the scenario-II in the first quadrant.