NDA/NA SOLVED PAPER 2016-I (MATHEMATICS)

Total Questions: 120

51. Which one of the following is correct?

Correct Answer: (c) in both AP and GP
Solution:Similarly xy, yz, zx are also in A.P. and G.P. both.

52. What is |z| equal to?

Correct Answer: (a) 6
Solution:

53. Solve the following equation

Correct Answer: (d) 0
Solution:

54. Consider the following statements:


1. The function f(x) is continuous at x = 0.
2. The function f(x) is continuous at x = π/2.

Which of the above statements is/are correct?

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


55. Consider the following statements:


1. The function f(x) is differentiable at x = 0 .
2. The function f(x) is differentiable at x = π/2

Which of the above statements is/are correct ?

Correct Answer: (d) Neither 1 nor 2
Solution:




56. Consider the following:

Let α and ẞ beta(α < β) be the roots of the equation x² + bx + c = 0 where b > 0 and c < 0 .

1. ẞ < -α
2. ẞ < |α|

Which of the above is/are correct?

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

57. Consider the following

Let α and ẞ beta(α < β) be the roots of the equation x² + bx + c = 0 where b > 0 and c < 0 .

1. α + β + α β > 0
2. α² β + β² α > 0

Which of the above is/are correct?

Correct Answer: (b) 2 only
Solution:

58. What is the value of AC² - BD² ?

Consider a parallelogram whose vertices are A(1, 2) B (4, y), C(x,6) and D (3, 5) taken in order.

Correct Answer: (c) 36
Solution:

59. What is the point of intersection of the diagonals?

Consider a parallelogram whose vertices are A(1, 2) B (4, y), C(x,6) and D (3, 5) taken in order.

Correct Answer: (a) (7/2, 4)
Solution:Point of intersection (a, b) is (7/2, 4) .

60. What is the area of the parallelogram ?

Consider a parallelogram whose vertices are A(1, 2) B (4, y), C(x,6) and D (3, 5) taken in order.

Correct Answer: (d) 7 square units
Solution: