Inclination of a Line

Q.

The gradient of the line joining the points on the curve $y=x^2+2x$ whose abscissa are $1$ and $3$, is

1. $6$

2. $5$

3. $4$

4. $3$

Q. Match the given angles with the corresponding slopes.
$\begin{array}{cc}Positivex-direction& Slopeofline\\ 1.)0^o& p.)0\\ 2.){90}^o& q.)-\sqrt{3}\\ 3.){120}^o& r.)-\frac{1}{\sqrt{3}}\\ 4.){150}^o& s.)Notdefined\end{array}$

1. 1 - p 2 - s 3 - q 4 - r

2. 1 - p 2 - s 3 - r 4 - q

3. 1 - p 2 - q 3 - r 4 - s

4. 1 - s 2 - p 3 - q 4 - r

Q.

PQ is a double ordinate of the parabola $y^2=4ax$ . The locus of the points of trisection of PQ is

1. 

2. 

3. 

4. 

Q. Let $P=(-1,0),Q=(0,0),andR=(3,3\sqrt{3})$ be three points. Then the equation of the bisector of $\angle PQR$ is

1. $\left(\frac{\sqrt{3}}{2}\right)x+y=0$
2. $x=\sqrt{3}y=0$
3. $\sqrt{3}x+y=0$
4. $x+\left(\frac{\sqrt{3}}{2}\right)y=0$

Q. The gradient of the line joining the points on the curve $y=x^2+2x$ whose abscissa are 1 and 3, is

1. 4
2. 5
3. 3
4. 6

Q. When the angle of inclination of the line with the x axis is ${45}^{\circ }$, the slope is equal to .

1. \N
2. $\frac{1}{\sqrt{3}}$
3. $\sqrt{3}$
4. 1

Q.

Find the value of $\lambda$ if $\lambda$ $x^2$ + ( ${\lambda }^2$ - $\lambda$) x + 1 = 0 is an identity.

1. -1

2. 1

3. No value of λ

4. 0

Q. The gradient of the line joining the points on the curve $y=x^2+2x$ whose abscissa are 1 and 3, is

1. 6
2. 5
3. 4
4. 3