NDA/NA SOLVED PAPER 2016-II (MATHEMATICS)

Total Questions: 120

31. Under what condition does the above equation have real roots ?

Let alpha and beta be the roots of the equation
x² - (1 - 2a²) x + (1 - 2a²) = 0

Correct Answer: (d)
Solution:

32. Under what condition is 1/α² + 1/β² < 1 ?

Let alpha and beta be the roots of the equation
x² - (1 - 2a²) x + (1 - 2a²) = 0

Correct Answer: (a)
Solution:

33. Solve the following equation

Correct Answer: (b) ω
Solution:

34. In an examination, 70% students passed in Physics, 80% students passed in Chemistry, 75% students passed in Mathematics and 85% students passed in Biology, and X% students failed in all the four subjects. What is the minimum value of x ?

Correct Answer: (c) 15
Solution:Here, maximum number of students failed in all the four subject = 15% But, minimum number of students failed in all the four subject varies from 0 to 15%. So, correct option is (d).

35. Under what condition does the above system of equations have infinitely many solutions?

For the system of linear equations 2x + 3y + 5z = 9 7x + 3y -2z = 8 and 2x + 3y + ʎz = mμ

Correct Answer: (b) ʎ = 5 and mμ = 9
Solution:

36. Under what condition does the above system of equations have unique solutions?

For the system of linear equations 2x + 3y + 5z = 9 7x + 3y -2z = 8 and 2x + 3y + ʎz = mμ

Correct Answer: (c) ʎ ≠ 5 and µ has any real value
Solution:

37. What is the number of odd integers between 1000 and 9999 with no digit repeated?

Correct Answer: (c) 2240
Solution:

38. What is the greatest value of the positive integer n satisfying the condition

Correct Answer: (c) 10
Solution:

39. What is the value of alpha ?

2x² + 3x - α - 0 has roots -2 and β while the equation x² -3mx + 2m² = 0 has both roots positive, where α > 0 and β > 0.

Correct Answer: (c) 2
Solution:

40. If β, 2, 2m are in GP, then what is the value of β√m ?

2x² + 3x - α - 0 has roots -2 and β while the equation x² -3mx + 2m² = 0 has both roots positive, where α > 0 and β > 0.

Correct Answer: (a) 1
Solution: