Consider the functionfx = x - 12x &thins

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

11.

Let fx = x + 1x, where x  (0, 1). Then which one of the following is correct ?

  • f(x) fluctuates in the interval

  • f(x) increases in the interval

  • f(x) decreases in the interval

  • None of the above


12.

Which one of the following is correct in respect of the function f(x) = x(x - 1)(x + 1) ?

  • The local maximum value is larger than local minimum value

  • The local maximum value is smaller than localminimum value

  • The function has no local maximum

  • The function has no local minimum


13.

Consider the function

fx = x - 1 + x2

where, x  

Which one of the following statements is correct ?

  • f(X) has local minima at more than one point in  - , 

  • f(x) has local maxima at more than one point in  - , 

  • f(x) has local minimum at one point only in  - , 

  • (x) has neither maxima nor minima in  - , 


14.

Consider the function

fx = x - 12x + 1x  - 23

What is the number of points of local minima of the function f(x) ?

  • None

  • One

  • Two

  • Three


Advertisement
Advertisement

15.

Consider the function

fx = x - 12x + 1x  - 23

What is the number of points of local maxima of the function f(x) ?

  • None

  • one

  • Two

  • Three


C.

Two

fx = x - 12x + 1x - 23f'x = 2x - 1x + 1x - 23 + x - 12x - 23 + 3x - 12x + 1x - 22= x - 1x - 222x + 1x - 2 + x - 1x - 2 + 3x - 1x + 1= x - 1x  - 226x2 - 5x - 5When, f'(x) = 0 x = 1, 2, - 712, 1712f''x = 2x - 2x - 16x2 - 5x - 5 + x - 22= 6x2 - 5x - 5 + x - 1x - 22= 12x - 5at x = 1, f''1 < 0 fx has local maximum at x = 1x =  - 712, f'' - 712 > 0, fx has local minimum at x =  - 712x =  1712, f''1712 > 0, fx has local maximum at x =  1712

Number of points of local maxima x = 1 and 1712


Advertisement
16.

Consider the function

f(x) = x3sinxcosx6 - 10pp2p3

where, p is a constant

What is the value of f'(0) ?

  • P3

  • 3P3

  • 6P3

  •  - 6P3


17.

Consider the function

f(x) = x3sinxcosx6 - 10pp2p3

where, p is a constant

What is the value of P for which f''(0) = 0 ?

  •  - 16 or 0

  •  - 1 or 0

  • - 16 or 1

  •  - 1 or 1


18.

Which one of the following statements is correct irespect of the function

f(x) = x3sin(x) ?

  • It has local maximum at x = 0

  • It has local minimum at x = 0

  • It has neither maximum nor minimum at x = 0

  • It has maximum value 1


Advertisement
19.

fx = 3x2 + 12x - 1, - 1  x  237 - x,                  2 < x  3 

Which of the following statements is/are correc

  1. f(x) is increasing in the interval [1, 2].
  2. f(x) is decreasing in the interval [2, 3]

Select the correct answer using the code given below :

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


20.

What is the value of k for which the sum of the squares of the roots of 2x2 – 2(k 2)x – (k + 1) = 0 is minimum ?

  • - 1

  • 1

  • 32

  • 2


Advertisement