If the harmonic mean of the roots of 2x2 - bx 

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMatch The Following

1.

Match the following columns.
       
A The centroid of the triangle formed by (2, 3, - 1), (5, 6, 3), (2, -3 ,1) is p (2, 2, 2)
B The circumcentre of the triangle formed by (1,2, 3) (2, 3, 1), (3, 1, 2) is q (3, 1, 4)
C The orthocentre of the triangle formed by (2, 1, 5), (3, 2, 3), (4, 0, 4) is r (1, 1, 0)
D The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is  s (3, 2, 1)
E The incentre of the triangle formed by (0, 0, 0), (3, 0, 0), (4, 0, 4) is t (0, 0, 0)

 

A. A B C D (i) s p q r
B. A B C D (ii) p q r s
C. A B C D (iii) s r q r
D. A B C D (iv) s p t r

 Multiple Choice QuestionsMultiple Choice Questions

2.

If f : R  R, g : R  R are defined by fx = 5x - 3, gx = x2 + 3, then gof - 13 = ?

  • 253

  • 11125

  • 925

  • 25111


3.

If A = x  Rlπ4  x π3 and fx = sinx - x, then fA =?

  • 32 - π3, 12 - π4

  • - 12 - π4, 32 - π3

  • - π3, - π4

  • π4, π3


4.

The value of the sum 1 · 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 +  ... upto n terms is equal to

  • 16n22n2 + 1

  • 16n2 - 12n - 12n + 3

  • 18n2 + 1n2 +5

  • 14nn +1n + 2n + 3


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5.

k = 16 sin27 - icos27 = ?

  •  - 1

  • 0

  •  - i

  • i


6.

If ω is a complex cube root of unity, thenω13 + 29 + 427 +     + ω12 + 38 + 932 +    = ?

  • 1

  • - 1

  • ω

  • i


7.

The common roots of the equations z3 +2z2 + 2z + 1 = 0,  z2014 + z2015 + 1 = 0 are

  • ω, ω2

  • 1, ω, ω2

  • - 1, ω, ω2

  • - ω, - ω2


8.

If a, b, c are distinct and the roots of (b - c)x2 + (c - a)x + (a - b) = 0 are equal, then a, b and c are in

  • anthmet1c progression

  • geometnc progression

  • harmonic progression

  • arithmetico-geometnc progression


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9.

If the roots of x3 - kx2 + 14x - 8 = 0 are in geometric progression, then k is equal to

  • - 3

  • 7

  • 4

  • 0


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10.

If the harmonic mean of the roots of 2x2 - bx + 8 - 2d = 0 is 4, then the value of b is

  • 2

  • 3

  • 4 - 5

  • 4 + 5


C.

4 - 5

Given equation is2x2 - bx + 8 - 25 = 0Let α and β be the roots of the given equationThen α + β =  - ba = - - b2 = b2and αβ = ca = 8 - 252Now, according to the question2αβα + β  = 4  28  - 252b2 = 4 28 - 25b = 4 28  - 254 = b b = 8 - 254 b = 4 - 5


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