Title 8.STRAIGHT LINES.pdf ✅

8. STRAIGHT LINES-MCQS TYPE (1.) The lines ( ) 2 p p x y q + − + = 1 0 and ( ) 2 2 p x + + 1 ( ) 2 p y q + + = 1 2 0 are perpendicular to a common line for [AIEEE-2009] (a.) Exactly one value of p (b.) Exactly two values of p (c.) More than two values of p (d.) No value of p (2.) Three distinct points AB, and C are given in the 2 - dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1,0) to the distance from the point (−1,0) is equal to 1 3 . Then the circumcentre of the triangle ABC is at the point [AIEEE-2009] (a.) 5 ,0 4       (b.) 5 ,0 2       (c.) 5 ,0 3       (d.) (0,0) (3.) The line L given by 1 5 + = x y b passes through the point (13,32) . The line K is parallel to L and has the equation 1 3 + = x y c . Then the distance between L and K is [AIEEE-2010] (a.) 23 15 (b.) 17 (c.) 17 15 (d.) 23 17 (4.) The lines x y a + = and ax y − =1 intersect each other in the first quadrant. Then the set of all possible values of a is the interval [AIEEE-2011] (a.) (−1, ) (b.) (−1,1 (c.) (0, ) (d.) 1, ) (5.) If A(2, 3− ) and B(−2,1) are two vertices of a triangle and third vertex moves on the line 2 3 x y + = 9 , then the locus of the centroid of the triangle is: [AIEEE-2011] (a.) 2 3 3 x y + = (b.) 2 3 1 x y − = (c.) x y − =1 (d.) 2 3 1 x y + = (6.) If the line 2x y k + = passes through the point which divides the line segment joining the points (1,1) and (2, 4) in the ratio 3: 2 , then k equals [AIEEE-2012] (a.) 5 (b.) 6 (c.) 11/ 5 (d.) 29 / 5 (7.) A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it form a triangle OPQ where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is [AIEEE-2012] (a.) -4 (b.) -2 (c.) −1/ 2 (d.) −1/ 4
(8.) A ray of light along x y + = 3 3 gets reflected upon reaching x -axis, the equation of the reflected ray is [JEE (Main)-2013] (a.) y x = + 3 (b.) 3 3 y x = − (c.) y x = − 3 3 (d.) 3 1 y x = − (9.) The x -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0,1 , 1,1 ) ( ) and (1,0) is [JEE (Main)-2013] (a.) 2 2 + (b.) 2 2 − (c.) 1 2 + (d.) 1 2 − (10.) Let PS be the median of the triangle with vertices P Q (2, 2 , 6, 1 ) ( − ) and R(7,3) . The equation of the line passing through (1, 1− ) and parallel to PS is [JEE (Main)- 2014] (a.) 4 7 3 0 x y + + = (b.) 2 9 11 0 x y − − = (c.) 4 7 11 0 x y − − = (d.) 2 9 7 0 x y + + = (11.) Let abc , , and d be non-zero numbers. If the point of intersection of the lines 4 2 0 ax ay c + + = and 5 2 0 bx by d + + = lies in the fourth quadrant and is equidistant from the two axes then [JEE (Main)-2014] (a.) 3 2 0 bc ad − = (b.) 3 2 0 bc ad + = (c.) 2 3 0 bc ad − = (d.) 2 3 0 bc ad + = (12.) The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0,0 , 0, 41 ) ( ) and (41,0) , is [JEE (Main)-2015] (a.) 901 (b.) 861 (c.) 820 (d.) 780 (13.) Locus of the image of the point (2,3) in the line (2 3 4 2 3 0, x y k x y k R − + + − + =  ) ( ) , is a [JEE (Main)-2015] (a.) Straight line parallel to x -axis (b.) Straight line parallel to y -axis (c.) Circle of radius 2 (d.) Circle of radius 3 (14.) Two sides of a rhombus are along the lines, x y − + =1 0 and 7 5 0 x y − − = . If its diagonals intersect at (− − 1, 2) , then which one of the following is a vertex of this rhombus? [JEE (Main)-2016] (a.) (− − 3, 8) (b.) 1 8 , 3 3     −   (c.) 10 7 , 3 3     − −   (d.) (− − 3, 9) (15.) Let k be an integer such that the triangle with vertices (k k k , 3 , 5, − ) ( ) and (−k,2) has area 28sq . units. Then the orthocentre of this triangle is at the point [JEE (Main)-2017] (a.) 3 1, 4       (b.) 3 1, 4     −   (c.) 1 2, 2       (d.) 1 2, 2     −  
(16.) A straight line through a fixed point (2,3) intersects the coordinate axes at distinct points P and Q . If O is the origin and the rectangle OPRQ is completed, then the locus of R is [JEE (Main)-2018] (a.) 3 2 6 x y + = (b.) 2 3 x y xy + = (c.) 3 2 x y xy + = (d.) 3 2 6 x y xy + = (17.) Consider the set of all lines px qy r + + = 0 such that 3 2 4 0 pqr + + = . Which one of the following statements is true? [JEE (Main)-2019] (a.) The lines are all parallel (b.) The lines are notconcurrent (c.) The lines are concurrent at the point 3 1 , 4 2       (d.) Each line passes through theorigin (18.) Let S be the set of all triangles in the xy -plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50sq . units, then the number of elements in the set S is: [JEE (Main)-2019] (a.) 9 (b.) 32 (c.) 36 (d.) 18 (19.) Let the equations of two sides of a triangle be 3 2 6 0 x y − + = and 4 5 20 0 x y +−= . If the orthocentre of this triangle is at (1,1) , then the equation of its third side is [JEE (Main)-2019] (a.) 26 122 1675 0 x y − − = (b.) 122 26 1675 0 y x − − = (c.) 122 26 1675 0 y x + + = (d.) 26 61 1675 0 x y + + = (20.) If the line 3 4 24 0 x y + − = intersects the x -axis at the point A and the y -axis at the point B , then the incentre of the triangle OAB , where O is the origin is [JEE (Main)-2019] (a.) (4,3) (b.) (3, 4) (c.) (4, 4) (d.) (2, 2) (21.) A point P moves on the line 2 3 4 0 x y − + = . If Q(1, 4) and R(3, 2− ) are fixed points, then the locus of the centroid of PQR is a line [JEE (Main)-2019] (a.) Parallel to y -axis (b.) With slope 3 2 (c.) With slope 2 3 (d.) Parallel to x -axis (22.) Two vertices of a triangle are (0, 2) and (4,3) . If its orthocentre is at the origin, then its third vertex lies in which quadrant? [JEE (Main)-2019] (a.) Fourth (b.) Third (c.) First (d.) Second
(23.) The straight line x y + = 2 1 meets the coordinate axes at A and B . A circle is drawn through AB, and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is [JEE (Main)-2019] (a.) 5 4 (b.) 5 2 (c.) 4 5 (d.) 2 5 (24.) In a triangle, the sum of lengths of two sides is x and the product of the lengths of the same two sides is y . If 2 2 x c y − = , where c is the length of the third side of the triangle, then the circumradius of the triangle is [JEE (Main)-2019] (a.) 3 c (b.) 3 2 y (c.) 3 c (d.) 3 y (25.) If in a parallelogram ABDC , the coordinates of A , B and C are respectively (1, 2 , 3, 4 ) ( ) and (2,5) , then the equation of the diagonal AD is [JEE (Main)-2019] (a.) 5 3 11 0 x y + − = (b.) 3 5 13 0 x y + − = (c.) 3 5 7 0 x y − + = (d.) 5 3 1 0 x y − + = (26.) If the straight line, 2 3 17 0 x y − + = is perpendicular to the line passing through the points (7,17) and (15,  ) , then  equals [JEE (Main)-2019] (a.) 35 3 − (b.) -5 (c.) 5 (d.) 35 3 (27.) A point on the straight line, 3 5 15 x y + = which is equidistant from the coordinate axes will lie only in [JEE (Main)-2019] (a.) th 4 quadrant (b.) st 1 quadrant (c.) st nd 1 , 2 and th 4 quadrants (d.) st 1 and nd 2 quadrants (28.) Suppose that the points (h k, , 1, 2 ) ( ) and (−3, 4) lie on the line L1 . If a line L2 passing through the points (h k, ) and (4,3) is perpendicular to L1 , then k h equals [JEE (Main)-2019] (a.) 3 (b.) 1 7 − (c.) 0 (d.) 1 3 (29.) Slope of a line passing through P(2,3) and intersecting the line, x y + = 7 at a distance of 4 units from P , is [JEE (Main)-2019] (a.) 7 1 7 1 − + (b.) 1 7 1 7 − + (c.) 5 1 5 1 − + (d.) 1 5 1 5 − +