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 Multiple Choice QuestionsMultiple Choice Questions

1.

The integral integral fraction numerator 2 straight x to the power of 12 space plus space 5 straight x to the power of 9 over denominator left parenthesis straight x to the power of 5 space plus space straight x cubed space plus space 1 right parenthesis cubed end fraction space dx is equal to 

  • fraction numerator negative straight x to the power of 5 over denominator left parenthesis straight x to the power of 5 space plus straight x cubed plus 1 right parenthesis squared end fraction space plus straight C
  • fraction numerator straight x to the power of 10 over denominator 2 left parenthesis straight x to the power of 5 space plus straight x cubed plus 1 right parenthesis squared end fraction space plus straight C
  • fraction numerator straight x to the power of 5 over denominator 2 left parenthesis straight x to the power of 5 space plus straight x cubed plus 1 right parenthesis squared end fraction space plus straight C
  • fraction numerator straight x to the power of 5 over denominator 2 left parenthesis straight x to the power of 5 space plus straight x cubed plus 1 right parenthesis squared end fraction space plus straight C
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2.

Two sides of a rhombus are along the lines, x−y+1=0 and 7x−y−5=0. If its diagonals intersect at (−1, −2), then which one of the following is a vertex of this rhombus?

  • (−3, −9)

  • (−3, −8)

  • (1/3, -8/3)

  • (1/3, -8/3)

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3.

The centres of those circles which touch the circle, x2+y2−8x−8y−4=0, externally and also touch the x-axis, lie on:

  • a circle

  • an ellipse which is not a circle

  • a hyperbola.

  • a hyperbola.

245 Views

4.

The integral integral fraction numerator dx over denominator straight x squared space left parenthesis straight x to the power of 4 plus 1 right parenthesis to the power of begin display style 3 over 4 end style end exponent end fraction space equals

  • open parentheses fraction numerator straight x to the power of 4 plus 1 over denominator straight x to the power of 4 end fraction close parentheses to the power of 1 fourth end exponent space plus straight C
  • left parenthesis straight x to the power of 4 plus 1 right parenthesis to the power of 1 fourth end exponent space plus straight C
  • negative left parenthesis straight x to the power of 4 plus 1 right parenthesis to the power of 1 fourth end exponent space plus straight C
  • negative left parenthesis straight x to the power of 4 plus 1 right parenthesis to the power of 1 fourth end exponent space plus straight C
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5.

The integral integral subscript 2 superscript 4 fraction numerator log space straight x squared over denominator log space straight x squared space plus space log space left parenthesis 36 minus 12 space straight x plus straight x squared right parenthesis end fraction dx  is equal to 

  • 2

  • 4

  • 1

  • 1

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6.

The number of points having both coordinates as integers that lie in the interior of the triangle with vertices (0,0), (0,41) and (41,0) is

  • 901

  • 861

  • 820

  • 820


D.

820

Required point (x,y) is such  that it satisfies
 x +y < 41
and x> 0 and y>0
Number of positive integral solutions of the equation x +y+ k = 41 will be number of intergral coordinates in the bounded region.


therefore, the total number of integral coordinates,
 = straight C presuperscript 41 minus 1 end presuperscript subscript 3 minus 1 end subscript space equals space straight C presuperscript 40 subscript 2 space equals space fraction numerator 40 space factorial over denominator 2 space factorial space 38 space factorial end fraction space equals space 780

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7.

The integral integral open parentheses 1 plus straight x space minus 1 over straight x close parentheses straight e to the power of straight x plus 1 over straight x end exponent dx is equal to 

  • left parenthesis straight x minus 1 right parenthesis straight e to the power of straight x plus 1 over straight x space plus straight C end exponent
  • xe to the power of straight x plus 1 over straight x end exponent plus straight C
  • left parenthesis straight x plus 1 right parenthesis straight e to the power of straight x plus 1 over straight x space plus straight C end exponent
  • left parenthesis straight x plus 1 right parenthesis straight e to the power of straight x plus 1 over straight x space plus straight C end exponent
131 Views

8.

The Integral integral subscript 0 superscript straight pi square root of 1 plus 4 space sin squared straight x over 2 minus 4 sin straight x over 2 dx end root is equal to

  • π-4

  • fraction numerator 2 space straight pi over denominator 3 end fraction minus 4 minus 4 square root of 3
  • 4 square root of 3 minus 4
  • 4 square root of 3 minus 4
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9.

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P with respect to the additional number of workers x is given by dP over dx space equals space 100 minus 12 square root of straight x. If the firm employs 25 more workers, then
the new level of production of items is

  • 2500

  • 3000

  • 3500

  • 3500

147 Views

10.

If ∫f x dx =Ψ (x),then ∫x5 f(x3)dx is equal to

  • 1 third space open square brackets straight x cubed straight psi left parenthesis straight x cubed right parenthesis minus integral straight x squared space straight psi left parenthesis straight x cubed right parenthesis dx close square brackets space plus straight C
  • 1 third space straight x cubed straight psi left parenthesis straight x cubed right parenthesis minus 3 integral straight x squared space straight psi left parenthesis straight x cubed right parenthesis dx space plus straight C
  • 1 third straight x cubed straight psi left parenthesis straight x cubed right parenthesis minus integral straight x squared space straight psi left parenthesis straight x cubed right parenthesis dx space plus space straight C
  • 1 third straight x cubed straight psi left parenthesis straight x cubed right parenthesis minus integral straight x squared space straight psi left parenthesis straight x cubed right parenthesis dx space plus space straight C
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