NDA/NA SOLVED PAPER 2015-I (MATHEMATICS)

Total Questions: 120

31. The point on the parabola y² = 4ax nearest to the focus has its abscissa

Correct Answer: (a) x = 0
Solution:

32. A line passes through (2, 2) and is perpendicular to the line 3x + y = 3 Its y-intercept is

Correct Answer: (b) 4/3
Solution:

33. The hyperbola (x² / a²) - (y² / b²) = 1 passes through the point (3√5, 1) and the length of its latus rectum is 4/3 units. The length of the conjugate axis is

Correct Answer: (c) 4 units
Solution:


34. The Perpendicular distance between the straight lines 6x + 8y + 15 = 0 and 3x + 4y + 9 = 0 is

Correct Answer: (b) 3/10 unit
Solution:

35. The area of a triangle, whose vertices are (3, 4), (5, 2) and the point of intersection of the lines x = a and y = 5 is 3 square units. What is the value of a?

Correct Answer: (d) 5
Solution:


36. The length of perpendicular from the origin to a line is 5 units and the line makes an angle 120° with the positive direction of x-axis. The equation of the line is

Correct Answer: (b) √3 x + y = 10
Solution:


37. The equation of the line joining the origin to the point of interesection of the lines x/a + y/b = 1 and x/b + y/a = 1 is

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


38. What is the length of the line segment?

The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively.

Correct Answer: (d) 13 units
Solution:

39. What are the direction cosines of the line segment?

The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively.

Correct Answer: (a) ⟨12/13, 4/13, 3/13⟩
Solution:

40. What are the direction ratios of the line segment PQ?

From the point P(3, - 1, 11) a perpendicular is drawn on the line L given by the equation x/2 = (y - 2)/3 = (z - 3)/4. Let Q be the foot of the perpendicular.

Correct Answer: (b) ⟨- 1, 6, - 4⟩
Solution: