Tiêu đề STRAIGHT LINES.pdf ✅

4. The equation to the perpendicular bisector of the line segment joining (1, b), (3, d) is a) 2x − y + 5 = 0 b) x + y − 5 = 0 c) 3x − 2y + 5 = 0 d) x + y − 4 = 0 5. The perpendicular bisector of the line seg- ment joining P(1, d) and Q(K, c) has Y In- tercept ' 4 ', then the possible value of K is a) -4 b) 1 c) 2 d) -2 6. The normal form of the line 4x − 3y + 12 = 0 is a) −4x 5 + 3y 5 = 12 5 b) 4x 5 − 3y 5 = 12 5 c) 4x 5 + 3y 5 = − 12 5 d) 3x 5 + 4y 5 = − 12 5 MULTIPLE CORRECT CHOICE TYPE 7. The equation 2x + 3y = 6 is converted into normal form then which of the following is true. a) Cos α = 2 √13 b) Sin α = 3 √13 c) p = 6 √13 d) Cos α = 13 √13 SINGLE CORRECT CHOICE TYPE: 8. The perpendicular form of the line √3x + y − 4 = 0 is a) xCos 5π 6 + yCos 5π 6 = 2 b) xCos 5π 6 + ySin 5π 6 = 4 c) xCos π 6 + ySin π 6 = 2 d) xCos 11π 6 + ySin 11π 6 = 2 9. The equation of the straight line in the sym- metric form having the given slope −1 √3 and passing through the point (−2,0) is a) x+2 −1 2 = y−0 √3 2 b) x−2 1 2 = y−0 1 √3 c) x+2 1 2 = 0−y 1 √2 d) x+2 −√3 2 = y−0 1 2 10. The slope of a straight line through A(3, b) is 3 4 then the coordinates of the two points on the line that are 5 units away from A are a) (−7,5), (1, −a) b) (7,5), (−1, −a) c) (6,9), (−2, d) d) (7, c), (−2, a) JEE MAIN LEVEL - 2 11. Equation of the straight line joining the points [am1 2 , 2am1 ] and [am2 2 , 2am2 ] is a) 2x + (m1 + m2 )y − 2am1m2 = 0 b) 2x − (m1 + m2 )y + 2am1m2 = 0 c) 2x − (m1 + m2 )y − 2am1m2 = 0 d) 2x − (m1 − m2 )y + 2am1 m2 = 0 12. The area of the triangle formed by the line 2x − 4y − 5 = 0 with the coordinate axes is sq. units. a) 25 16 b) 49 8 c) 12 d) 49 12 13. The equation of the line passing through (−2, c) and having intercepts equal in mag- nitude but opposite in sign is a) x − y − 5 = 0 b) x − y + 5 = 0 c) x + y − 1 = 0 d) x − y + 7 = 0 INTEGER ANSWER TYPE: 14. If the straight line (x + y + a) + K(2x − y − a) = 0 is perpendicular to 2x + 3y − 8 = 0 then |K| = JEE MAIN LEVEL - 3 15. The equation of the line xcos α + ysin α − p = 0 in intercepts form is a) x ( p Sin α ) + y ( p Cos α ) = 1 b) x ( p Cos α ) + y ( p Sin α ) = 1

lines a1x + b1y + c1 = 0, a2x + b2y + c2 = 0 are perpendicular then a1a2 + b1 b2 = 0 26. If 2x + 3y + 5 = 0, kx + 6y + 7 = 0 are parallel, then the value of K is a) 2 b) 4 c) 6 d) -9 27. If 3x − ky − 2 = 0,2x + y + 2 = 0 are per- pendicular, then K = a) 4 3 b) 4 5 c) 5 3 d) 6 28. If 5x + 3y + 7 = 0, kx − 7y + 8 = 0 are perpendicular then K = a) 21 5 b) 1 3 c) 5 3 d) -5 MATRIX MATCH TYPE: Column-I Col- umn-II a) The slope of the line joining the points (3, d) and (4, a) is p) 0 b) The slope of the line parallel to 2x + 3y + 4 = 0 is q) − 2 3 c) The slope of the line perpendicular to x − 2y + 5 = 0 is r) -3 Z s) -1 t) -2 30. Match the slopes of the corresponding lines Column-I Column-II a) 2x − 3y + 5 = 0 p) −3 2 b) 3x + 2y − 6 = 0 q) −2 3 c) 3x − 2y − 5 = 0 r) 2 3 d) 2x + 3y − 7 = 0 s) 3 2 INTEGER ANSWER TYPE: 31. If 3x + ky + 5 = 0,2x + 2y + 5 = 0 are parallel then k = 32. The slope of horizontal line is JEE ADVANCED LEVEL-2&3 MULTIPLE CORRECT CHOICE TYPE 33. The perpendicular form of the line 3x + 4y − 5 = 0 is a) xcos α + ysin α = 1 where cos α = 3 5 , sin α = 4 5 b) xcos α − ysin α = 1 where cos α = 3 5 sin α = −4 5 c) xsin α + ycos α = 1 where cos α = 3 5 , sin α = 4 5 d) xcos α + ysin α where cos α = −3 5 , sin α = 4 5 JEE ADVANCED LEVEL-4&5 MATRIX MATCH TYPE: Column - I Column - II a) Line passing through (−4, c) and having intercepts in the ratio 5: 3 p) 2x − 5y + 4 = 0 b) Line passing through P(2, −5) such that P bisects the part inter- cepted between the axes q) 5x − 2y − 20 = 0 c) Line parallel to 2x − 3y + 5 = 0 with x-intercept 2 5 is r) 3x + 5y = 3 d) Line perpendicular to 5x + 2y + 7 = 0 with y-intercept 4 5 is s) 10x − 15y = 4 WORKSHEET 02 CUQ 1. The angle between the lines x + y + 1 = 0 and x = 5 is a) 30∘ b) 90∘ c) 45∘ d) 1 0 2. If the angle between the straight lines 4x − y + 7 = 0 and kx − 5y − 9 = 0 is 45∘ , then the value of ' k ' is a) 1 b) 3 c) 5 d) 4