(Mathematics-Part-2) NDA/NA Solved Paper 2017-I

Total Questions: 50

31. If f : R → R and g : R → R, then (f - g) is

Correct Answer: (d) one-one and on to
Solution:

 

32. What is the length of the longest interval in which the function f (x) = 3 sin x - 4 sin³ x is increasing?

Correct Answer: (a) π/3
Solution:

33. If xdy = y (dx + ydy); y(1) = 1 and y(x) > 0, then what is y(-3) equal to?

Correct Answer: (a) 3
Solution:

34. What is the maximum value of the function f (x) = 4 sin² x + 1?

Correct Answer: (a) 5
Solution:

We know, - 1≤ sinx ≤1
⇒ 0≤sin²x≤1
⇒ 0≤4sın²x ≤4
⇒ 1≤4sin²x + 1≤5

35. Let f (x) be an indefinite integral of sin² x. Consider the following statements:

Statement 1 : The function f(x) satisfies f(x + π)= f(x) for all real x.
Statement 2 : sin² (x + π) = sin² x for all real x.
Which one of the following is correct in respect of the above statements?

Correct Answer: (b) Both the statements are true but Statement 2 is not the correct explanation of Statement 1
Solution:


sin² (π+x)=sin²x
(-sinx)²=sin²x
⇒sin²x=sin²x
So, statement 2 is truе

36. What are the degree and order respectively of the difrantal equenion y = x (dy/dx)² + (dx/dy)² ?

Correct Answer: (d) 4,1
Solution:

37. What is the differential equation corresponding to y² - 2ay + x² = a² by eliminating a?

where p = dy/dx

Correct Answer: (a) (x²- 2y²)p² - 4 pxy - x²=0
Solution:


38. What is the general solution of the differential equation ydx - (x+ 2y²) dy=0?

Correct Answer: (c) x = 2y²+ cy
Solution:

39. Let ƒ (x + y) = ƒ (x) ƒ(y) for all x and y. Then what is ƒ '(5) equal to [where ƒ'(x) is the derivative of f (x)]?

Correct Answer: (a) ƒ(5) ƒ'0
Solution:

40. Solve the following equation?


Correct Answer: (b)
Solution: