If α and β are the roots of the equatio

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

If the harmonic mean between the roots of (5 + 2) x2 - bx + (8 + 25) = 0 is 4, then the value of b is

  • 2

  • 3

  • 4 - 5

  • 4 + 5


12.

The set of solutions satisfying both x2 + 5x + 6  0 and x2 + 3x - 4 < 0 is

  • (- 4, 1)

  • - 4, - 3  (- 2, 1)

  • - 4, - 3  - 2, 1

  • - 4, - 3   - 2, 1


13.

If the roots of x3 - 42x2 + 336x - 512 = 0, are in increasing geometric progression, then its common ratio is

  • 2 : 1

  • 3 : 1

  • 4 : 1 

  • 6 : 1


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14.

If α and β are the roots of the equation x2 - 2x + 4 = 0, then α9 + β9 is equal to

  • - 28

  • 29

  • - 210

  • 210


C.

- 210

Given quadratic equation isx2 - 2x + 4 = 0whose roots are α and β α + β = 2 and αβ = 4  ...iNow, α9 + β9 = α33 + β33 = α3 + β3α6 + β6 - α3β3= α + βα2 - αβ + β2α23 + β23 - α3β3=  α + β α + β2 - 3αβ α2 + β2α4 + β4 - α2β2 -  α3β3=  α + β α + β2 - 3αβα + β2 - 2αβα2 + β22 - 3α2β2 - α3β3= 24 - 124 - 84 - 82 - 48 - 64    from eq i= 2 - 8 - 4 - 32 - 64= 2 - 8128 - 64= 2 - 864 = - 210


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15.

If a complex number z satisfied z2 - 1 = z2 + 1, then z lies on

  • the real axis

  • the imaginary axis

  • y = x

  • a circle


16.

The period of f(x) = cosx3 + sinx2 is

  • 2π

  • 4π

  • 8π

  • 12π


17.

If sinθ + cosθ = p and sin3θ + cos3θ = q, then p(p2 - 3) is equal to

  • q

  • 2q

  • - q

  • - 2q


18.

If tanπcosθ = cotπsinθ, then a value of cosθ - π4 among the following is

  • 122

  • 12

  • 12

  • 14


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19.

The  set  of solutions  of the  system  of equationsx + y = 2π3and cosx + cosy = 32,where x, y are real, is

  • x, ycosx - y2 = 12

  • x, ysinx - y2 = 12

  • x, ycosx - y = 12

  • Empty set


20.

The origin is translated to (1, 2). The point(7, 5) in the old system undergoes the following transformations successively.

I. Moves to the new point under the given translation of origin.

II. Translated through 2 units along the negative direction of the new X-axis.

III. Rotated through an angle - about the 4 origin of new system in the clockwise direction. The final position of the point (7, 5) is

  • 92, - 12

  • 72, 12

  • 72, - 12

  • 52, - 12


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