NDA/NA SOLVED PAPER 2016-I (MATHEMATICS)

Total Questions: 120

41. If the circles intersect at two distinct points, then which one of the following is correct?

Consider the two circles (x - 1)² + (y - 3)² = r² and x²+ y² - 8x + 2y + 8 = 0

Correct Answer: (d) 2 < r < 8
Solution:

42. What is the equation of the line passing through the point of intersection of the given lines and parallel to x-axis?

Consider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0

Correct Answer: (d) y + 2 = 0
Solution:


43. What is the equation of the line passing through the point of intersection of the given lines and parallel to y-axis ?

Consider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0

Correct Answer: (b) x - 1 = 0
Solution:


44. If the equation possesses solution, then what is the minimum value of k?

Consider the equation k sin x + cos 2x = 2k - 7

Correct Answer: (b) 2
Solution:

45. If the equation possesses solution, then what is the maximum value of k ?

Consider the equation k sin x + cos 2x = 2k - 7

Correct Answer: (d) 6
Solution:

 

46. Solve the following equation

Correct Answer: (b) In a
Solution:

47. Solve the following equation

Correct Answer: (c) 1 - a⁻¹
Solution:

48. What is z₁ + z₂ + z₃ equal to?

Correct Answer: (c) 0
Solution:



49. Consider the following statements:

1. z₁  z₂  z₃ is purely imaginary.
2. z₁ z₂ + z₂ z₃ + z₃ z₁ is purely real.

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:


50. Which one of the following is correct?

Correct Answer: (c) in both AP and GP
Solution: