Given thatan = ∫0πsinn + 1xsin2xdxCons

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 Multiple Choice QuestionsMultiple Choice Questions

21.

What is the solution of the differential equation

logdydx - a = 0

  • y = xea + c

  • x = yea + c

  • y = lnx + c

  • x = lny + c


22.

e - 1e - 2logxxdx = ?

  • 32

  • 52

  • 3

  • 4


23.

What is tan-1secx + tanxdx = ?

  • πx4 +x24 +c

  • πx2 + x24 + c

  • πx4 +πx24 + c

  • πx4 - x24 + c


24.

What is 02π1 + sinx2dx = ?

  • 8

  • 4

  • 2

  • 0


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25.

lnx - 1dx - lnx - 2dx = ?

  • xlnx  - 1 + c

  • xlnx - 2 = c

  • xlnx + c

  • xlnx2 + c


26.

The value of 0π4tanxdx + 0π4cotxdx = ?

  • π4

  • π2

  • π22

  • π2


27.

Consider the functions

f(x) = xg(x) and g(x) = 1x

where [ . ] is the greatest integer function

  • 16

  • 13

  • 518

  • 536


28.

Consider the functions

f(x) = xg(x) and g(x) = 1x

where [ . ] is the greatest integer function

What is 131fxdx

  • 3772

  • 23

  • 1772

  • 37144


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29.

Given that

an = 0πsinn + 1xsin2xdx

Consider the following statements :

  1. The sequence {a2n } is in AP with common difference zero.
  2. The sequence {a2n + 1} is in AP with common difference zero.

Which of the above statements is/are correct ?

  • 1 only

  • 2 only

  • both 1 and 2

  • neither 1 nor 2


C.

both 1 and 2

a0 = 0πsin2xsin2xdx = 120πtanxdx = 12logsecx0π = 0a1 =  0πsin22xsin2xdx =  0πsin2xdx = - cos2x20π = 0a3 =   0πsin24xsin2xdx =   0π2sin4x . cos2xdx     = 0πsin6x + sin2xdx     = - cos6x6 + cos2x20π = 0Thus, an is in A.P. with C.d = 0

 


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30.

Given that

an = 0πsinn + 1xsin2xdx

What is an - 1 - an - 4 = ?

 

  •  - 1

  • 0

  • 1

  • 2


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