Tiêu đề 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

(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