1. Scenario-1: φ(x)=xcosx1−cos(π2−x) \varphi(x)=\frac{x \cos x}{1-\cos \left(\frac{\pi}{2}-x\right)} φ(x)=1−cos(2π−x)xcosx
Scenario-2: f(x,y)=x3−2xy−y3−3 f(\mathrm{x}, \mathrm{y})=\mathrm{x}^{3}-2 \mathrm{xy}-\mathrm{y}^{3}-3 f(x,y)=x3−2xy−y3−3.
Evaluate ∫ln2xdx \int \ln 2 x d x ∫ln2xdx.
Differentiate φ(x) \varphi(x) φ(x) with respect to x x x from scenario-1.
Determine the equation of tangent and nommal on the curve f(x,y)=0 f(\mathrm{x}, \mathrm{y})=0 f(x,y)=0 at (1,1) (1,1) (1,1) from scenario-2.
2.
Determine the area and centroid of △OAB \triangle O A B △OAB.
Determine the equation of straight line AB \mathrm{AB} AB and find out the two trisect point on AB A B AB.
Determine the equation of circle taking AB A B AB ss diameter and the equation of tangent on B B B.
3. Scenario-1: 3x−4y+7=0,4x−3y+2=0 3 x-4 y+7=0,4 x-3 y+2=0 3x−4y+7=0,4x−3y+2=0.
Scenario-2:
Express the equation r=bsin2θ \mathrm{r}=\mathrm{b} \sin 2 \theta r=bsin2θ as Cartesian equation. 2
In scenario-1 the bisector of obtuse angle created by the two given line through intersecting made a triangle with the two axes. Determine the area of that triangle.
Determine the equation of the circle shown in scenario-2.
4. Scenario-1: f(x)=x+3(x−1)(x2+5) f(x)=\frac{x+3}{(x-1)\left(x^{2}+5\right)} f(x)=(x−1)(x2+5)x+3
Scenario-2: y2=8x,x−y=0 y^{2}=8 x, x-y=0 y2=8x,x−y=0
Evaluate ∫dx3−5x2 \int \frac{d x}{\sqrt{3-5 x^{2}}} ∫3−5x2dx
Determine ∫f(x)dx \int f(x) d x ∫f(x)dx from scenario-1.
Determine the area bounded by the parabola and the straight line given in scenario- 2 .
5. A=[201342213],f(x)=x2+3x−51 A=\left[\begin{array}{lll} 2 & 0 & 1 \\ 3 & 4 & 2 \\ 2 & 1 & 3 \end{array}\right], f(x)=x^{2}+3 x-51 A=232041123,f(x)=x2+3x−51
Without expanding prove that, ∣1aa−22 b b−43cc−6∣=0 \left|\begin{array}{lll}1 & \mathrm{a} & \mathrm{a}-2 \\ 2 & \mathrm{~b} & \mathrm{~b}-4 \\ 3 & \mathrm{c} & \mathrm{c}-6\end{array}\right|=0 123a bca−2 b−4c−6=0.
Evaluate f( A) f(\mathrm{~A}) f( A).
Determine A−1 \mathbf{A}^{-1} A−1.
