Q 1. The number of integral values of {tex} m , {/tex} for which the {tex} x {/tex} -coordinate of the point of intersection of the lines {tex} 3 x + 4 y = 9 {/tex} and {tex} y = m x + 1 {/tex} is also an integer is

Q 2. If the coordinates of the middle point of the portion of a line intercepted between coordinate axes {tex} ( 3,2 ) , {/tex} then the equation of the line will be

Q 3. A line through point {tex} A ( - 5 , - 4 ) {/tex} meets the lines {tex} x + 3 y + 2 = 0, {/tex} {tex} 2 x + y + 4 = 0 {/tex} and {tex} x - y - 5 = 0 {/tex} at points {tex} B , C {/tex} and {tex} D , {/tex} respectively. If {tex} \left( \frac { 15 } { \mathrm { AB } } \right) ^ { 2 } + \left( \frac { 10 } { \mathrm { AC } } \right) ^ { 2 } = \left( \frac { 6 } { \mathrm { AD } } \right) ^ { 2 } , {/tex} then the equation of the line is

Q 4. The equation of perpendicular bisectors of sides {tex} A B {/tex} and {tex} A C {/tex} of a triangle {tex} A B C {/tex} are {tex} x - y + 5 = 0 {/tex} and {tex} x + 2 y = 0 {/tex} , respectively. If point {tex} A {/tex} is {tex} ( 1 , - 2 ) , {/tex} then the equation of line {tex} B C {/tex} is

Q 5. The medians {tex} A D {/tex} and {tex} B E {/tex} of a triangle with vertices {tex} A ( 0 , b ) , B ( 0,0 ) {/tex} and {tex} C ( a , 0 ) {/tex} are perpendicular to each other if

Q 6. Let {tex} P S {/tex} be the median of the triangle with vertices {tex} P ( 2,2 ) , Q ( 6 , - 1 ) {/tex} and {tex} R ( 7,3 ) . {/tex} Then the equation of the line passing through {tex} ( 1 , - 1 ) {/tex} and parallel to {tex} P S {/tex} is

Q 7. The equation of straight line passing through {tex} ( - a , 0 ) {/tex} and making the triangle with axes of area {tex} T {/tex} is

Q 8. The equations of two equal sides of an isosceles triangle are {tex} 7 x - y + 3 = 0 {/tex} and {tex} x + y - 3 = 0 {/tex} and the third side passes through the point {tex} ( 1 , - 10 ) {/tex} . The equation of the third side is

Q 9. If the equation of base of an equilateral triangle is {tex} 2 x - y = 1 {/tex} and the vertex is {tex} ( - 1,2 ) , {/tex} then the length of the side of the triangle is

Q 10. If {tex} x _ { 1 } , x _ { 2 } , x _ { 3 } {/tex} and {tex} y _ { 1 } , y _ { 2 } , y _ { 3 } {/tex} are both in GP, with the same common ratio, then the points {tex} \left( x _ { 1 } , y _ { 1 } \right) , \left( x _ { 2 } , y _ { 2 } \right) {/tex} and {tex} \left( x _ { 3 } , y _ { 3 } \right) {/tex}

Q 11. In what direction a line be drawn through the point {tex} ( 1,2 ) {/tex} so that its points of intersection with the line {tex} x + y = 4 {/tex} is at a distance {tex} \sqrt { 6 } / 3 {/tex} from the given point

Q 12. If straight lines {tex} a x + b y + p = 0 {/tex} and {tex} x \cos \alpha + y \sin \alpha - p = 0 {/tex} include an angle {tex} \pi / 4 {/tex} between them and meet the straight line {tex} x \sin \alpha - y \cos \alpha = 0 {/tex} in the same point, then the value of {tex} a ^ { 2 } + b ^ { 2 } {/tex} is equal to

Q 13. Given vertices {tex} A ( 1,1 ) , B ( 4 , - 2 ) {/tex} and {tex} C ( 5,5 ) {/tex} of a triangle, then the equation of the perpendicular dropped from {tex} C {/tex} to the the the interior bisector of the angle {tex} A {/tex} is

Q 14. The equation of the line joining the point {tex} ( 3,5 ) {/tex} to the point of intersection of the lines {tex} 4 x + y - 1 = 0 {/tex} and {tex} 7 x - 3 y - 35 = 0 {/tex} is equidistant from the points {tex} ( 0,0 ) {/tex} and {tex} ( 8,34 ) {/tex}

Q 15. The line {tex} 3 x + 2 y = 24 {/tex} meets {tex} y {/tex} -axis at point {tex} A {/tex} and {tex} x {/tex} -axis at point {tex} B {/tex} . The perpendicular bisector of {tex} A B {/tex} meets the line through {tex} ( 0 , - 1 ) {/tex} parallel to {tex} x {/tex} -axis at point {tex} C . {/tex} The area of the triangle {tex} A B C {/tex} is

Q 16. The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point {tex} ( a , b ) {/tex} is

Q 17. The orthocentre of the triangle formed by the lines {tex} x y = 0 {/tex} and {tex} x + y = 1 {/tex} is

Q 18. The lines joining the origin to the points of intersection of the line {tex} y = m x + c {/tex} and the circle {tex} x ^ { 2 } + y ^ { 2 } = a ^ { 2 } {/tex} will be mutually perpendicular if

Q 19. Two of the lines represented by the equation {tex} a y ^ { 4 } + b x y ^ { 3 } + c x ^ { 2 } {/tex} {tex} y ^ { 2 } + d x ^ { 3 } y + e x ^ { 4 } = 0 {/tex} will be perpendicular when

Q 20. The equations of the lines which are parallel to the line common to the pair of the lines given by and and at a distance of 7 units from it are

Q 21. If and are two fixed points, then the locus of a point which moves in such a way that the angle is a right angle is

Q 22. The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at is

Q 23. Two of the lines represented by the equation will be perpendicular, then

Q 24. The line for different values of p and q passes through the fixed point

Q 25. If 3, 4 are intercepts of a line then the distance of from the origin is