Angle between Pair of Straight Lines

Q. If the lines 2x + 3y = 5 and kx – 6y = 7 are parallel, then what is the value of k?

1. -4

Q. If two lines are perpendicular with respect to each other, then the product of their slopes is equal to .

1. 1
2. \N
3. -1
4. 2

Q.

The equation of the straight line passing through the point of intersection of lines 3x – 4y – 7 = 0 and 12x – 5y – 13 = 0 and perpendicular to the line 2x – 3y + 5 = 0 is

1. 33x + 22y – 13 = 0

2. 33x – 22y + 13 = 0

3. None of these

4. 33x + 22y + 13 = 0

Q.

One of the equation of the lines which passes through the point (-2, 3) and equally inclined to the co-ordinate axes is .

1. $y=x+5$
2. $y=x+4$
3. $y=-x-1$

Q. In triangle ABC cosa/a=cosb/b=cosc/c the value of r1+r2+r3/r is equal to

Q. Find the slope of equation of the straight line passing through origin and the point of intersection of the lines $x+2y=7andx–y=4$.

1. 0.2

Q.

Find the equation of the line through the intersection of $2x+y=8,3x–7=y$ and parallel to $4x+y=11$.

1. 4x + y =14

2. x + 4y -10 = 0

3. 3x + 4y -14 = 0

4. 3x + y -11 = 0

Q. How many number of straight lines are equally inclined to both the axes?

1. 2

Q. Find the equation to the straight line which passes through point of intersection of line $2x+y+1=0$ & $3x-y+4=0$ and is parallel to line $3x-2y=0$.

1. $3x-2y=-5$.
2. $3x-2y=-8$.
3. $3x-2y=1$.
4. $x-y=-5$.

Q. One of the equation of the lines which passes through the point (-2, 3) and equally inclined to the co-ordinate axes is .

1. 
   $y=x+5$
2. $y=x+4$
3. $y=-x-1$
4. 
   None of the above

Q. The equation of the straight line passing through the point of intersection of $5x-6y-1=0,3x+2y+5=0$ and perpendicular to the line $3x-5y+11=0$

1. $5x+3y+18=0$
2. $-5x-3y+18=0$
3. $5x+3y+8=0$
4. $5x+3y-8=0$

Q. Solve each of the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the $x-$axis:
$x-y+3=0,2x+3y-4=0$

Q. Consider the following linear programming problem:

Maximize	$12X+10Y$
Subject to:	$4X+3Y\le 480$
	$2X+3Y\le 360$
	all variables $\ge 0$

Which of the following points $(X,Y)$ could be a feasible corner point?

1. $(40,48)$
2. $(120,0)$
3. None of these
4. $(30,36)$
5. $(180,120)$

Q. Suppose $ABCD$ (in order) is a quadrilateral inscribed in a circle. Which of the following is/are always true?

1. $\tan B+\tan D=0$
2. $\text{cosec A}=\text{cosec C}$
3. $\sec B=\sec D$
4. $\cot A+\cot C=0$

Q. Let a, b, c and d be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$ and $5bx+2by+d=0$ lies in the fourth quadrant and is equidistant from the two axes then

1. $2bc+3ad=0$
2. $3bc-2ad=0$
3. $3bc+2ad=0$
4. $2bc-3ad=0$