The value of  - 1 + i31 -

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

If α and β are the roots of the equation, 7x2  3x  2 = 0, then the value of α1 - α2 + β1 - β2 is equal to 

  • 124

  • 2736

  • 2716

  • 38


2.

The statement

p  q  p   p p  q is

  • equivalent to p  q  ~ p

  • a contradiction

  • a tautology

  • equivalent to p  q  ~ q


3.

If the line y = mx + c is a common tangent to the hyperbola x2100 - y264 = 1 and the circle x2 + y2 = 36, then which one of the following is true 

  • 4c2 = 369

  • 5m = 4

  • c2 = 369

  • 8m + 5 = 0


4.

If the length of the chord of the circle, x2 + y2 = r2(r > 0) along the line, y – 2x = 3 is r, then r2 is equal to :

  • 95

  • 12

  • 125

  • 245


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5.

If the sum of the second,third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is :

  • 213350 - 1

  • 126349 - 1

  • 113350 - 1

  • 126350 - 1


6.

If the mean and the standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation : 

  • x2 - 20x + 18 = 0

  • 2x2 - 20x + 19 = 0

  • x2 - 10x + 19 = 0

  • x2 - 10x + 18 = 0


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7.

The value of  - 1 + i31 - i30 is : 

  • 65

  • 215i

  • - 215

  •  - 215i


D.

 - 215i

 - 1 + 3i1 - i30 = 2cos2π3sin2π32cosπ4 - isinπ430= 230cos20π + isin20π215cos15π2 - isin15π2= 2151 + 0i0 + i = - 215i


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8.

limx0xe1 + x2 + x4 - 1/x - 11 + x2 + x4 - 1

  • does not exist

  • is equal to 1

  • is equal to e

  • is equal to 0


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9.

Solve L = sin2π16 -  sin2π8 andM = cos2π16 -  cos2π8

  • M = 142 + 14cosπ8

  • M = 122 + 12cosπ8

  • L =  - L = - 122 + 12cosπ8

  • L = 142 - 14cosπ8


10.

If for some α  R, the linesL1 : x + 12 = y - 2 - 1 = z - 11 andL2 :x + 2α = y + 15 - α = z + 11 are coplanar, then the line L2 passes through point :

  • (2, - 10, - 2)

  • (10, 2, 2)

  • ( - 2, 10, 2)

  • (10, - 2, - 2)


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