8 Infomaths/Mca/Maths/Cw-1/Straight Lines

OLD QUESTIONS-CW1

8 INFOMATHS/MCA/MATHS/CW-1/STRAIGHT LINES

STRAIGHT LINES

1. Find the equation of the graph xy = 1 after a rotation of the axes by 45 degrees anti-clockwise in the new coordinate system (x', y').

HCU-2012

(a) x'2 – y'2 = 1 (b)

2. A point P on the line 3x + 5y = 15 is equidistant from the coordinate axes. Then P can lie in HCU-2012

(a) Quadrant I only

(b) Quadrant I or Quadrant III only

(d) any Quadrant

3. The orthocenter of the triangle formed by the lines xy = 0 and x + y = 1 is : PU CHD-2012

(A) (1/2, 1/2) (B) (1/3, 1/3)

4. The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5 is PU CHD-2012, NIT-2010

(A) (B) 1 (C) (D)

5. The medians of a triangle meet at (0, –3). While its two vertices are (–1, 4) and (5, 2), the third vertex is at PU CHD-2012

(A) (4, 5) (B) (–1, 2) (C) (7, 3) (D) (– 4, – 15)

6. The area of the triangle having the vertices (4, 6), (x, 4), (6, 2) is 10 sq units. The value of x is PU CHD-2012

(A) 0 (B) 1 (C) 2 (D) 3

7. The position of reflection of point (4, 1) w.r.to line y = x – 1 is

Pune-2012

(a) (-4, -1) (b) (1, 2) (c) (2, 3) (d) (3, 4)

8. If (4, - 3) and (-9, 7) are the two vertices of a triangle and (1, 4) is its centroid, then the area of triangle is NIMCET-2012

(a) (b) (c) (d)

9. The straight line passes through the point and makes an angle of 60° with the x-axis. The length of the intercept on it between the point P and the line is : BHU-2012

(a) 1.5 (b) 2.5 (c) 3.5 (d) 4.5

10. The equation of the straight line passing through the point of intersection of 4x + 3y – 8 = 0 and x + y – 1 = 0, and the point (-2, 5) is :

BHU-2012

(a) 9x + 7y – 17 = 0 (b) 4x + 5y + 6 = 0

11. The angle between the two straight line represented by the equation 6x2 + 5xy – 4y2 + 7x + 13y – 3 = 0 is:

BHU-2012

(a) (b)

12. The relation that represents the shaded region in the figure given below is

HCU-2011

(a) y £ x (b) |y| £ |x| (c) y £ |x| (d) |y| £ x

13. The area enclosed within the lines |x| + |y| = 1 is NIMCET-2011

(a) 1 (b) 2 (c) 3 (d) 4

14. Point A is a + 2b, P is a and P divides AB in the ratio of 2 : 3. The position vector of B is BHU-2011

(a) 2a – b (b) b – 2a (c) a – 3b (d) b

15. If the position vectors of A and B are a and b respectively, then the position vector of a point P which divides AB in the ratio 1 : 2 is BHU-2011

(a) (b) (c) (d)

16. Every homogeneous equation of second degree in x and y represent a pair of lines BHU-2011

(a) parallel to x-axis (b) perpendicular to y-axis

17. The equation represents a BHU-2011

(a) straight line (b) circle

18. The coordinates of the orthocenter of the triangle formed by the lines 2x2 – 2y2 + 3xy + 3x + y + 1 = 0 and 3x + 2y + 1 = 0 are

BHU-2011

(a) (b) (c) (d)

19. If a p, b  q, c  r and = 0, then the value of + is NIMCET-2010

(a) 0 (b) 1 (c) -1 (d) 2

20. The number of integral values of m for which the x coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer is KIITEE-2010

(a) 2 (b) 0 (c) 4 (d) 1

21. The medians of a triangle meet at (0, - 3) and two vertices are at (-1, 4) and (5, 2). Then the third vertex is at KIITEE-2010

(a) (4, 15) (b) (-4, -15) (c) (-4, 15) (d) (4, -15)

22. The length of the perpendicular drawn from the point (3, - 2) on the line 5x – 12y – 9 = 0 is PGCET-2010

(a) (b) (c) (d) None of these

23. If the lines x – 6y + a = 0, 2x + 3y + 4 = 0 and x + 4y + 1 = 0 are concurrent, then the value of ‘a’ is PGCET-2010

(a) 4 (b) 8 (c) 5 (d) 6

24. the angle between the lines represented by x2 + 3xy + 2y2 = 0 is

PGCET-2010

(a) tan-1(2/3) (b) tan-1(1/3)

25. The length of the perpendicular drawn from the point (1, 1) on the 15x + 8y + 45 = 0 is

(PGCET paper – 2009)

(a) 3 (b) 4 (c) 5 (d) 2

26. The equation of the line passing through the point of intersection 2x – y + 5 = 0 and x + y + 1 = 0 and the point (5, - 2) is

(PGCET paper – 2009)

(a) 3x + 7y – 1 = 0 (b) x + 2y + 1 = 0

27. The point of intersection of the lines represented by 2x2 – 9xy + 4y2 = 0 is

(PGCET paper – 2009)

(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)

28. If the distance of any point (x, y) from the origin is defined as d(x, y)= max (|x|, |y|), then the locus of the point (x, y) where d(x, y) = 1 is MCA : NIMCET – 2009, KIITEE-2010

(a) a square of area 1 sq. unit

(b) a circle of radius 1

(d) a square of area 4 sq. units

29. Let ABC be an isosceles triangle with AB = BC. If base BC is parallel to x-axis and m1, m2 are slopes of medians drawn through the angular points B and C, then (MCA : NIMCET – 2009)

(a) m1m2 = - 1/2 (b) m1 + m2 = 0

30. The equation of the line segment AB is y = x, if A and B lie on the same side of the line mirror 2x – y = 1 the image of AB has the equation (MCA : KIITEE - 2009)

(a) 7x – y = 6 (b) x + y = 2

31. The point (-1, 1) and (1, -1) are symmetrical about the line

(MCA : KIITEE - 2009)

(a) y + x = 0 (b) y = x

32. The product of perpendiculars drawn from the point (1, 2) to the pair of lines x2 + 4xy + y2 = 0 is (MCA : KIITEE - 2009)

(a) 9/4 (b) 9/16 (c) 3/4 (d) None of these

33. The centroid of the triangle whose three sides are given by the combined equation (x2 + 7xy + 12y2) (y – 1) = 0 is

(MCA : KIITEE - 2009)

(a) (b)

34. If y = mx bisects the angle between the lines x2 (tan2q + cos2q) + 2xy tan q - y2 sin2q = 0 when q = p/3, then the value of is NIMCET - 2008

(a) 1 (b) (c) (d)

35. If a, b, c are the roots of the equation x3 – 3px2 + 3qx – 1 = 0, then the centroid of the triangle with vertices and is at the point NIMCET - 2008

(a) (p, q) (b)

36. The coordinates of a point on the line x + y = 3 such that the point is at equal distances from the lines |x| = |y| are KIITEE - 2008

(a) (3, 0) (b) (-3, 0) (c) (0, - 3) (d) None

37. The point of intersection of lines (i) x + 2y + 3 = 0 and (ii) 3x + 4y + 7 = 0 is KARNATAKA - 2007

(a) (1, 1) (b) (1, - 1) (c) (-1, 1) (d) (-1, -1)

38. The acute angle between the lines (i) 2x – y + 13 = 0 and (ii) 2x – 6y + 7 = 0 KARNATAKA - 2007

(a) 0° (b) 30° (c) 45° (d) 60°

39. If the points (k, - 3), (2, - 5) and (-1, -8) are collinear then K = ICET - 2007

(a) 0 (b) 4 (c) – 2 (d) – 3

40. The equation of the line with slope -3/4 and y – intercept 2 is ICET - 2007

(a) 3x + 4y = 8 (b) 3x + 4y + 8 = 0

41. If the lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and gx + 4y + 1 = 0 pass through a point then a + g = ICET - 2007

(a) b (b) 2b (c) 1/b (d) 1/2b

42. Equation of the line passing through the point (2, 3) and perpendicular to the segment joining the points (1, 2) and (-1, 5) is

ICET – 2005

(a) 2x – 3y – 13 = 0 (b) 2x – 3y – 9 = 0

43. The two sides forming the right angle of the triangle whose area is 24 sq. cm. are in the ratio 3:4. Then the length of the hypotenuse (in cm) is ICET – 2005

(a) 12 (b) 10 (c) 8 (d) 5

44. The equation of the straight line which cuts off equal intercepts from the axis and passes through the point (1, - 2) is ICET – 2005

(a) 2x + 2y + 1 = 0 (b) x + y + 1 = 0

45. If the lines 2x + 3y = 6, 8x – 9y + 4 = 0, ax + 6y = 13 are concurrent, then a = ICET – 2005

(a) 3 (b) – 3 (c) – 5 (d) 5

46. The points of concurrence of medians of a triangle is ICET – 2005

(a) incentre (b) orthocenter

47. If (0, 0), (2, 2) and (0, a) form a right angled isosceles triangle, then a = ICET – 2005

(a) 4 (b) – 4 (c) 3 (d) – 3

48. The orthocenter of the triangle determined by the lines 6x2 + 5xy – 6y2 – 29x + 2y + 28 = 0 and 11x – 2y – 7 = 0 is IP Univ.– 2006

(a) (-4, 5) (b) (4, 4) (c) (6, 7} (d) (2, 1) (e) (-1, 3)

49. a, b, c Î R. if 2a + 3b + 4c = 0, then the line ax + by + c = 0 passes through the point

(a) (b)

50. The distance of the point (x, y) form y-axis is

Karnataka PG-CET : Paper 2006

(a) x (b) y (c) |x| (d) |y|

51. If the lines 4x + 3y = 1, y = x + 5 and 5y + bx = 3 are concurrent, then the value of b is

Karnataka PG-CET : Paper 2006

(a) 1 (b) 3 (c) 6 (d) 0

52. The system of equations x + y = 2 and 2x + 2y = 3 has Karnataka PG-CET : Paper 2006

(a) No solution (b) a unique solution

53. The equation of line passing through the intersection of lines 5x – 6y – 1 = 0 and 3x + 2y + 5 = 0 and perpendicular to 3x – 5y + 27 = 0 is : UPMCAT :– 2002

(a) 5x + 3y + 10 = 0 (b) 5x + 3y + 21 = 0

54. The area of triangle formed by y = m1x + c, y = m2x + c2 and y axis is : UPMCAT : paper – 2002

(a) (b)

55. Reflection of the point P(1, 2) in x + 2y + 4 = 0 is

UPMCAT : paper – 2002

(a) (b)

56. If 2x2 – 5xy + 2y2 – 3x + 1 = 0, represents pairs of lines, then the angle between the lines is : UPMCAT : paper – 2002

(a) tan-1 (2/3) (b) tan-1 (4/3)

57. The condition that eqa. ax2 + by2 + 2gx + 2fy + 2hxy + c = 0 represents a pair of the line is