The area enclosed between the curves y2 = x and y = |x| is from

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21.

The solution for x of the equation integral subscript square root of 2 end subscript superscript straight x fraction numerator dt over denominator straight t square root of straight t squared minus 1 end root end fraction space equals straight pi over 2 space is

  • 2

  • π

  • square root of 3 divided by 2
  • square root of 3 divided by 2
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22. integral fraction numerator dx over denominator cos space straight x space plus space square root of 3 space sin space straight x end fraction equals
  • 1 half space log space tan space open parentheses straight x over 2 plus straight pi over 12 close parentheses space plus straight C
  • 1 half space log space tan space open parentheses straight x over 2 minus straight pi over 12 close parentheses plus straight c
  • log space tan space open parentheses straight x over 2 minus straight pi over 12 close parentheses plus straight c
  • log space tan space open parentheses straight x over 2 minus straight pi over 12 close parentheses plus straight c
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23.

The area enclosed between the curves y2 = x and y = |x| is

  • 2/3

  • 1/3

  • 1/6

  • 1/6


C.

1/6



straight A space equals space integral subscript 0 superscript 1 left parenthesis square root of straight x minus straight x right parenthesis dx
space equals space open square brackets 2 over 3 straight x to the power of 3 divided by 2 end exponent minus straight x squared over 2 close square brackets subscript 0 superscript 1
space equals space 2 over 3 space minus 1 half space equals space 1 over 6
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24.

The area enclosed between the curve y = loge (x + e) and the coordinate axes is

  • 1

  • 2

  • 3

  • 3

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25.

The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to bottom; then S1 : S2: S3 is

  • 1 : 2 : 1

  • 1 : 2 : 3

  • 2 : 1 : 2

  • 2 : 1 : 2

243 Views

26. limit as straight n rightwards arrow infinity of space sum from straight r equals 1 to straight n of space 1 over straight n straight e to the power of straight r over straight n end exponent space is space
  • e

  • e+1

  • e-1
  • e-1
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27.

The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is

  • 1

  • 2

  • 3

  • 3

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28.

Let g(x) = cos x2, f(x) = x and α, β (α <β) be the roots of the quadrtic equation 18x2 - 9πx + π2 = 0. Then the area (in sq. units) bounded by the curve y = (gof)(x) and the lines x = α, x = β and y = 0 is

  • 12(2-1)

  • 12(3-1)

  • 12(3+1)

  • 12(3-2)


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29.

If sum of all the solutions of the equation 8 cos x. cos π6+x.cosπ6-x-12 = 1 in [0,π] is kπ, then k is equal to:

  • 20/9

  • 2/3

  • 13/9

  • 8/9


30.

The area enclosed by y = 5 - x2 and y = x - 1 is

  • 5π4 - 2 sq. units

  • 5π - 22 sq. units

  • 5π4 - 12 sq. units

  • π2 - 5 sq. units


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