NDA/NA SOLVED PAPER 2016-II (MATHEMATICS)

Total Questions: 120

51. An equilateral triangle has one vertex at (0, 0) and another at (3, √3) . What are the coordinates of the third vertex?

Correct Answer: (c) (0, 2√3) or (3, - √3)
Solution:

52. What is the equation of the right bisector of the line segment joining (1, 1) and (2, 3)?

Correct Answer: (a) 2x + 4y - 11 = 0
Solution:

53. What is the radius of the circle passing through the point (2, 4) and having centre at the intersection of the lines x - y = 4 and 2x + 3y + 7 = 0 ?

Correct Answer: (d) 5√2 units
Solution:

54. What is the equation of the hyperbola having latus rectum and eccentricity 8 and 3/√5 respectively?

Correct Answer: (a)
Solution:

55. If the point (a, a) lies between the lines |x + y| = 2 then which one of the following is correct?

Correct Answer: (c) |a| < 1
Solution:

56. What is the equation of the straight line which passes through the point of intersection of the straight lines x + 2y = 5 and 3x + 7y = 17 and is perpendicular to the straight line 3x + 4y = 10?

Correct Answer: (d) 4x - 3y + 2 = 0
Solution:

57. If (a, b) is at unit distance from the line 8x + 6y + 1 = 0 then which of the following conditions are correct?

1. 3a - 4b - 4 = 0
2. 8a + 6b + 11 = 0
3. 8a + 6b - 9 = 0

Select the correct answer using the code given below:

Correct Answer: (b) 2 and 3 only
Solution:

58. If the ellipse 9x² + 16y² = 144 intercepts the line 3x + 4y = 12 then what is the length of the chord so formed?

Correct Answer: (a) 5 units
Solution:

59. A straight line cuts off an intercept of 2 units on the positive direction of x-axis and passes through the point (-3, 5). What is the foot of the perpendicular drawn from the point (3, 3) on this line?

Correct Answer: (d) (1, 1)
Solution:


60. What is the eccentricity of rectangular hyperbola?

Correct Answer: (a) √2
Solution: