NDA/NA SOLVED PAPER 2015-II (MATHEMATICS)

Total Questions: 120

51. The line 3x + 4y - 24 = 0 intersects the x-axis at A and y-axis at B. Then the circumcentre of the triangle OAB where O is the origin is

Correct Answer: (c) (4, 3)
Solution:

52. The eccentricity of the hyperbola 16x² - 9y² = 1 is

Correct Answer: (b) 5/3
Solution:

53. The product of y the perpendiculars from the two points (± 4, 0) to the line 3x cos φ + 5y sin φ = 15 is

Correct Answer: (c) 9
Solution:


54. If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are

Correct Answer: If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are
Solution:

55. The lines 2x = 3y = - z and 6x = - y = - 4z

Correct Answer: (a) are perpendicular
Solution:

56. Two straight lines passing through the point A(3, 2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is

Correct Answer: (a) 7x + y - 21 = 0
Solution:

57. The radius of the sphere 3x² + 3y² + 3z² - 8x + 4y + 8z - 15 = 0 is

Correct Answer: (b) 3
Solution:

58. The direction ratios of the line perpendicular to the lines with direction ratios and are

Correct Answer: (a)
Solution:

59. What are the co-ordinates of the foot of the perpendicular drawn from the point (3, 5, 4) on the plane z = 0 ?

Correct Answer: (b) (3, 5, 0)
Solution:

60. The lengths of the intercepts on the co-ordinate axes made by the plane 5x + 2y + z - 13 = 0 are

Correct Answer: (b) 13/5, 13/2, 13 unit
Solution: