Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

41.

If α, β are the roots of the equation x2 + bx + c = 0 and aα + h, β + h are the roots of the equation x2 + qx + r = 0, then h is equal to

  • b + q

  • b - q

  • 12b + q

  • 12b - q


42.

202 - 3x2 = 4053x2 - 2, then x is equal to

  • ± 32

  • ± 23

  • ± 43

  • ± 54


43.

Each of the roots of the equation x3 - 6x2 + 6x - 5 = 0 are increased by h. So that the new transformed equation does not contain x term, then h is equal to

  • 1

  • 2

  • 12

  • 13


44.

The roots of the equation x3 - 14x2 + 56x - 64 = 9 are in

  • AGP

  • HP

  • AP

  • GP


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45.

If 1 is a multiple root of order 3 for the equation x4 - 2x3 + 2x - 1 = 0, then the other root is

  • 0

  • - 1

  • 1

  • 2


46.

limx0sinxsin-1xx2 is equal to

  • 0

  • 1

  • - 1


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47.

The biquadratic equation, two of whose roots are 1 + i, 1 - 2, is

  • x4 - 4x3 + 5x2 - 2x - 2 = 0

  • x4 + 4x3 - 5x2 + 2x + 2 = 0

  • x4 + 4x3 - 5x2 + 2x - 2 = 0

  • x4 + 4x3 + 5x2 - 2x + 2 = 0


A.

x4 - 4x3 + 5x2 - 2x - 2 = 0

When 1 + i, 1 - i are roots, thenSum of the roots = 1 + i + 1- i = 2and product of the roots = 1 + 1 = 2The equation is x2 - 2x + 2 = 0When 1 - 2, 1 + 2 are the roots, thenSum of the roots = 1 - 2 + 1 + 2 = 2Product of the roots = 1 - 2 = - 1The equation is x2 - 2x - 1 = 0The biquadratic equation isx2 - 2x +2x2 - 2x - 1 = 0x4 - 2 + 2x3 = - 1 + 4 + 2x2                          = 2 - 4x - 2 = 0     x4 - 4x3 + 5x2 - 2x - 2 = 0


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48.

iF a is a complex number and b is a real number, then the equation a + a + b = 0 represents a

  • straight line

  • parabola

  • circle

  • hyperbola


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49.

If θ = π6, then the 10th term of  1 + cosθ + isinθ + cosθ + isinθ2 + cosθ + isinθ3 + ...is equal to

  • i

  • - 1

  • 1

  • - i


50.

sin5θsinθ is equal to 

  • 16cos4θ - 12cos2θ + 1

  • 16cos4θ+ 12cos2θ + 1

  • 16cos4θ - 12cos2θ - 1

  • 16cos4θ + 12cos2θ - 1


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