Let cos (α + β) = 4/5 and let sin (α - β) = 5/13, where 0

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 Multiple Choice QuestionsMultiple Choice Questions

1. limit as straight x space rightwards arrow 0 of space fraction numerator sin begin display style left parenthesis end style begin display style straight pi end style begin display style space end style begin display style begin display style cos end style squared end style begin display style straight x end style begin display style right parenthesis end style over denominator straight x squared end fraction space is space equal space to
  • π/2

  • 1

301 Views

2. limit as straight x space rightwards arrow 0 of fraction numerator left parenthesis 1 minus cos space 2 straight x right parenthesis left parenthesis 3 plus cos space straight x right parenthesis over denominator straight x space tan space 4 straight x end fraction space is space equal space to space
  • -1/4

  • 1/2

  • 1

  • 1

188 Views

3.

The equation of the tangent to the curve y = x +4/x2, that is parallel to the x-axis, is

  • y= 0

  • y= 1

  • y= 2 

  • y= 2 

162 Views

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4.

Let cos (α + β) = 4/5 and let sin (α - β) = 5/13, where 0 ≤α,β ≤ π/4. Then tan 2α is equal to

  • 25/16

  • 56/33

  • 19/12

  • 19/12


B.

56/33

Cos (α + β) = 4/5 
⇒  (α + β) ∈ 1st quadrant
and sin (α - β) = 5/13
⇒  (α - β) ∈ 1st quadrant
⇒ 2α =(α + β) +  (α - β)
space tan space 2 straight alpha space equals space fraction numerator tan space left parenthesis straight alpha space space plus space straight beta right parenthesis space plus space tan space left parenthesis straight alpha space minus straight beta right parenthesis over denominator 1 minus tan space left parenthesis straight alpha space plus straight beta right parenthesis space tan left parenthesis straight alpha minus straight beta right parenthesis end fraction
space equals space fraction numerator begin display style 3 over 4 end style plus begin display style 5 over 12 end style over denominator 1 minus begin display style 3 over 4 end style. begin display style 5 over 12 end style end fraction space equals space 56 over 33

145 Views

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5. stack lim space with straight x space rightwards arrow straight pi over 2 below space fraction numerator cot space straight x space minus cos space straight x over denominator left parenthesis straight pi minus 2 straight x right parenthesis cubed end fraction space equals
  • 1/4

  • 1/24

  • 1/16

  • 1/16

396 Views

6.

If 5(tan2x – cos2x) = 2cos 2x + 9, then the value of cos4x is

  • -7/9

  • -3/5

  • 1/3

  • 1/3

542 Views

7.

The differential equation which represents the family of curves y=c1ec2xe, where c1 and c2 are arbitrary constants, is

  • y' =y2

  •  y″ = y′ y

  • yy″ = y′

  • yy″ = y′

120 Views

8.

The solution of the differential equation dy over dx space equals space fraction numerator straight x plus straight y over denominator straight x end fraction   satisfying the condition y (1) = 1 is  

  • y = ln x + x

  • y = x ln x + x2

  •  y = xe(x−1)

  •  y = xe(x−1)

128 Views

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9.

If limit as straight x space rightwards arrow infinity of space open parentheses 1 plus straight a over straight x plus straight b over straight x squared close parentheses to the power of 2 straight x end exponent space equals space straight e squared then the values of a and b, are

  • straight a element of space straight R with equals below space straight b element of space straight R with equals below
  • straight a space equals 1 comma space straight b element of space straight R with equals below
  • straight a element of space straight R with equals below space comma space straight b space equals 2
  • straight a element of space straight R with equals below space comma space straight b space equals 2
117 Views

10.

For each t ∈R, let [t] be the greatest integer less than or equal to t. Then

limx0+ x1x+2x+......+15x

  • does not exist (in R)

  • is equal to 0

  • is equal to 15

  • is equal to 120


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