General Form of a Straight Line

Q. Which of the following correspondences can be called a function?

1. $f:\{-1,0,1\}\to \{0,1,2,3\}$ defined by $f\left(x\right)=x^3$
2. $f:\{0,1,4\}\to \{-2,-1,0,1,2\}$ defined by $f\left(x\right)=\pm \sqrt{x}$
3. $f:\{0,1,4\}\to \{-2,-1,0,1,2\}$ defined by $f\left(x\right)=\sqrt{x}$
4. $f:\{0,1,4\}\to \{-2,-1,0,1,2\}$ defined by $f\left(x\right)=-\sqrt{x}$

Q. For specifying a straight line how many geometrical parameters should be known

1. 1
2. 2
3. 4
4. 3

Q.

The equation of the straight line is perpendicular to $5x-2y=7$ and passing through the point of intersection of the lines $2x+3y=1$ and $3x+4y=6$, is

1. $2x+5y+17=0$

2. $2x+5y-17=0$

3. $2x-5y+17=0$

4. $2x–5y=17$

Q. If $m_1$ and $m_2$ are the roots of the equation $x^2+(\sqrt{3}+2)x+(\sqrt{3}-1)=0,$ then the area of the triangle formed by the lines $y=m_{1}x,$ $y=m_{2}x$ and $y=2,$ is

1. $\sqrt{33}-\sqrt{11}$ sq. units
2. $\sqrt{33}+\sqrt{11}$ sq. units
3. $\sqrt{33}+\sqrt{7}$ sq. units
4. $\sqrt{33}-\sqrt{7}$ sq. units

Q.

What is meant by orthogonal matrix?

Q.

What is $y=mx+b$?

Q.

For $a>b>c>0$, the distance between (1, 1) and the point of intersection of the lines $ax+by+c=0$ and $bx+ay+c=0$ is less than $2\sqrt{2}$. Then,

1. $a+b-c>0$

2. $a-b+c<0$

3. $a-b+c>0$

4. $a+b-c<0$

Q. The equation of the line parallel to $Y-$axis and $3$units to the right of it, is

1. $y=3$
2. $y=0$
3. $x=3$
4. $x=0$

Q. Let $a,b,c$ be real numbers with $a^2+b^2+c^2=1$ Show that the equation $\left|\begin{array}{ccc}ax-by-c& bx+ay& cx+a\\ bx+ay& -ax+by-c& cy+b\\ cx+a& cy+b& -ax-by+c\end{array}\right|$ = 0
represents a straight line.

Q.

find the equation of a straight line parallel to $X$-axis and passing through the point $(-2,7)$.

Q.

If $\left[\begin{array}{c}x-y-z\\ -y+z\\ z\end{array}\right]=\left[\begin{array}{c}0\\ 5\\ 3\end{array}\right]$ then $x,y,z$ are

1. $5,2,2$

2. $1,–2,3$

3. $0,–3,3$

4. $11,8,3$

5. $4,1,3$

Q.

Find the equation of straight line parallel to $Y$axis and passing through point $(1.8,0.9)$

Q. For $a>b>c>0$, the distance between (1, 1) and the point of intersection of the lines $ax+by+c=0$ and $bx+ay+c=0$ is less then $2\sqrt{2}$. Then

1. $a+b-c>0$
2. $a-b+c<0$
3. $a-b+c>0$
4. $a+b-c<0$

Q. If a variable straight line is drawn through the point of intersection of $\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{b}+\frac{y}{a}=1$ meets the co-ordinate axes at $A$ and $B$, then the locus of the mid-point of line segment $AB$ is

1. $(x+y)(a+b)=2xy\left(ab\right)$
2. $(x+y)(a-b)=2xy\left(ab\right)$
3. $(x+y)ab=2xy(a+b)$
4. $(x+y)ab=2xy(a-b)$

Q. If the point $(a,a^2)$ lies inside the triangle formed by the lines $2x+3y-1=0,x+2y-1=0$ and $-8x+8y+2=0$ then

1. $-1<a<\frac{1}{2}$
2. $a>1$
3. $a>\frac{1}{3}$
4. $\frac{1}{3}<a<\frac{1}{2}$

Q.

Find the value of p, if the lines $y=3x+7$and $y+px=3$are perpendicular to each other.

Q. The line $\frac{x}{a}+\frac{y}{b}=1$ cuts the axis at $A$ and $B$, another line perpendicular to $AB$ cuts the axes at$P,Q$respectively.Locus of points of intersection of $AQ$ and $BP$ is

1. $x^2+y^2+ax+by=0$
2. $x^2+y^2-ax-by=0$
3. $x^2+y^2-ax+by=0$
4. $x^2+y^2+ax-by=0$