Mathematics (NDA/NA SOLVED PAPER 2019 (I) (51 to 100)

Total Questions: 50

41. What is the general solution of the differential equation dy/dx + x/y = 0?

Correct Answer: (a) x² + y² = C
Solution:

42. Simplify the equation?

Correct Answer: (d) 0
Solution:

43. What is the minimum value of a²x + b²y where xy = c²?

Correct Answer: (b) 2abc
Solution:

44. Find the answer of given equation?

Correct Answer: (a)
Solution:

45. What is the area of one of the loops between the curve y = c sin x and X -axis?

Correct Answer: (d) 4c
Solution:

46. If sinθ + cosθ = √2 cosθ, then what is (cosθ - sinθ) equal to?

Correct Answer: (c) -√2sinθ
Solution:

47. In a circle of diameter 44 cm, the length of a chord is 22 cm. What is the length of minor arc of the chord?

Correct Answer: (a) 484/21 cm
Solution:

48. If sinθ = − 1/2 and tanθ = 1√3, then in which quadrant does θ lie?

Correct Answer: (c) Third
Solution:

We know that, if θ lies in third quadrant then, sinθ < 0 and tanθ > 0.

49. How many three digit even numbers can be formed using the digits 1, 2, 3, 4 and 5 when repetition of digits is not allowed?

Correct Answer: (c) 24
Solution:

Here, unit digit can be filled by 2 or 4. So number of ways is 2. Since repetition is not allowed therefore hundred place and ten place can be fill in ⁴C₂ × 2 ways.
∴ Total number of three-digit even number = 4 × 3 × 2 = 24

50. The angle of elevation of a tower of height h from a point A due South of it is x and from a point B due East of A is y. If AB = z, then which one of the following is correct?

Correct Answer: (a) h²(cot² y - cot² x) = z²
Solution: