If Aθ = 1tanθ- tanθ1 a

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The angle between the tangents at those points on the curve x = t2 + 1 and y = t2 - t - 6 where it meets x-axis is :

  • ±tan-1429

  • ±tan-1549

  • ±tan-11049

  • ±tan-1829


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22.

If Aθ = 1tanθ- tanθ1 and AB = I, then sec2θB is equal to :

  • Aθ

  • Aθ2

  • A- θ

  • A- θ2


C.

A- θ

   Aθ = 1tanθ- tanθ1Also, AB = I.       B = A- 1               = 11 + tan2θ1- tanθtanθ1               = 1sec2θ1- tanθtanθ1 sec2θB = 1- tanθtanθ1                    = A- θ


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23.

If x = - 5 is a root of 2x + 14822x2762x = 0, then the other roots are :

  • 3, 3.5

  • 1, 3.5

  • 1, 7

  • 2, 7


24.

The simultaneous equations Kx + 2y - z = 1, (K - I)y - 2z = 2 and (K + 2)z = 3 have only one solution when :

  • K = - 2

  • K = - 1

  • K = 0

  • K = 1


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25.

If the rank of the matrix - 1252- 4a - 41- 2a +1 is 1, then the value of a is :

  • - 1

  • 2

  • - 6

  • 4


26.

If sin-1x + sin-1y = π2, then cos-1x + cos-1y is equal to :

  • π2

  • π4

  • π

  • 3π4


27.

The value of 14x - 3dx is equal to :

  • 1

  • 52

  • 12

  • 32


28.

The area of the region bounded by the straight lines x = 0 and x = 2x and the curves y = 2 and y = 2x - x2 is equal to

  • 2log2 - 43

  • 3log2 - 43

  • 1log2 - 43

  • 4log2 - 32


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29.

The value of 0dxa2 + x2 is equal to

  • π2

  • π2a

  • πa

  • 12a


30.

The value of the integral ex1 - x1 + x22dx is

  • ex1 - x1 + x2 + c

  • ex1 + x1 + x2

  • ex1 + x2 + c

  • ex1 - x + c


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