MATHEMATICS (NDA/NA SOLVED PAPER 2022-I) (51 to 100)

Total Questions: 50

31. If the points with coordinates (-5, 0 ), (5p², 10p) and (5q², 10q) are collinear, then what value pq where p ≠ q?

Correct Answer: (c) 1
Solution:

32. What is the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from the axes?

Correct Answer: (c) x + y + 1 = 0
Solution:

33. What is the equation of the circle which touches both the axes in the first quadrant and the line y - 2 = 0?

Correct Answer: (c) x² + y² - 2x - 2y + 1 = 0
Solution:

34. What is the equation of the parabola with focus (-3, 0) and directrix x - 3 = 0?

Correct Answer: (d) y² = - 12x
Solution:

35. What is the distance between the foci of the ellipse x²+ 2y² = 1?

Correct Answer: (b) √2
Solution:

36. Let a, b, c be the lengths of sides BC, CA, AB respectively of a triangle ABC. If p is the perimeter and q is the area of the triangle, then what is p(p - 2a) tan(A/2) equal to?

Correct Answer: (d) 4q
Solution:

37. A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts in fourth quadrant. What is the sum of the absolute values of the intercepts?

Correct Answer: (a) 2
Solution:

38. Under which one of the following conditions are the lines ax + by + c = 0 and bx + ay + c = 0 parallel ( a ≠ 0, b ≠ 0)?

Correct Answer: (c) a² - b² = 0
Solution:

39. What is the equation of the locus of the mid-point of the line segment obtained by cutting the line x + y = p (where p is a real number) by the coordinate axes?

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

40. If the point (x, y) is equidistant from the points (2a, 0) and (0, 3a) where a > 0, then which one of the following is correct?

Correct Answer: (c) 4x - 6y + 5a = 0
Solution: