Which one of the following can be considered as appropriate pair

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 Multiple Choice QuestionsMultiple Choice Questions

41.

Which one of the following graphs represents the function fx = xx,  0

 

  • None of the above


42.

Consider the following statements :

Statement I : x > sin(x) for all x > 0

Statement II : f (x) = x - sin(x) is an increasing function for all x > 0.

Which one of the following is correct in respect of the above statements ?

  • Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I

  • Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement I

  • Statement I is true but Statement II is false

  • Statement I is false but Statement II is true


43.

If fx = 4x + x41 + 4x3 and  gx = ln1 + x1 - x, then what is the value of f o ge - 1e + 1 = ?

  • 2

  • 1

  • 0

  • 12


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44.

Which one of the following can be considered as appropriate pair of values of regression coefficient of y on x and regression coefficient of x on y ?

  • (1, 1)

  • ( - 1, 1)

  •  - 12, 2

  • 13, 103


A.

(1, 1)

Regression coefficient of y on x

= regression coefficient of x on y

 (a, y) lies on (y = x) line


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45.

It is given that x = 10, y = 90, σx = 3, σy = 12 and rxy = 0.8

The regression equation of x and y is :

  • y = 3.2x + 58

  • x = 3.2y + 58

  • x = - 8 + 0.2y

  • y = - 8 + 0.2x


46.

The coefficient of correlation whenregression are 0.2 and 1.8 is :

  • 0.36

  • 0.2

  • 0.6

  • 0.9


47.

What is the range of the function y = x21 + x2

where, x  

  • [0, 1)

  • [0, 1]

  • (0, 1)

  • (0, 1]


48.

Consider the function

fθ = 4sin2θ + cos4θ

What is the maximum value of the function f(θ)?

  • 1

  • 2

  • 3

  • 4


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49.

Consider the function

fθ = 4sin2θ + cos4θ

What is the minimum value of the function f(θ)?

  • 0

  • 1

  • 2

  • 3


50.

Consider the function

fθ = 4sin2θ + cos4θ

Consider the following statements :

1. fθ = 2 has no solution2. fθ = 72 has a solutionWhich of the above statements is/are correct ?

  • 1 only

  • 2 only

  • Both 1 and 2

  • Neither 1 nor 2


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