If the roots of the equation 4x3 - 12x2 + 11x + k = 0 are in arit

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 Multiple Choice QuestionsMultiple Choice Questions

201.

If α, β, γ are the roots of the equation x3 + 4x + 1 = 0, then α + β-1 + β + γ-1 + γ + α-1 is equal to

  • 2

  • 3

  • 4

  • 5


202.

Let a  0 and p(x) be a polynomial of degree greater than 2. If p(x) leaves remainders a and - a when divided respectively by x + a and x - a, then the remainder when p(x) is divided by x2 - a2 is:

  • x

  • - x

  • - 2x

  • 2x


203.

If the amplitude of z - 2 - 3i is π4, then the locus of z = x + iy is :

  • x + y - 1 = 0

  • x - y - 1 = 0

  • x + y + 1 = 0

  • x - y + 1 = 0


204.

If w is a complex cube root of unity, then 225 + (3w + 8 w2)2 + (3w2 + 8w)2 is equal to

  • 72

  • 192

  • 200

  • 248


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205.

If x + 12x - 13x + 1 = A2x - 1 + B3x +1, then 16A + 9B is equal to

  • 4

  • 5

  • 6

  • 8


206.

If (x - 2) is a common factor of the expressions x2 + ax + b and x2 + cx + d, then, b - dc - a is equal to

  • - 2

  • - 1

  • 1

  • 2


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207.

If the roots of the equation 4x3 - 12x2 + 11x + k = 0 are in arithmetic progression, then k is equal to

  • - 3

  • 1

  • 2

  • 3


A.

- 3

Since, the roots of the equation 4x3 - 12x2 + 11x + k = 0 are in AP is  α - a, α, α +a

 Sum of roots, 3α = 124 = 3                        α = 1

Since, α is a root, therefore it satisfies the given equation

 4 - 12 + 11 + k = 0                           k = - 3


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 Multiple Choice QuestionsMatch The Following

208.

α, β, γ are the roots of the equation x3 - 10x2 + 7x + 8=0. Match the following and choose the correct answer.

A. α + β + γ           1 - 437B. α2 + β2 + γ2      2 - 78C. 1α + 1β + 1γ       3 86D. αβγ + βγα + γαβ 4 0                                 10

A. A B C D (i) 5 3 1 2
B. A B C D (ii) 4 3 1 2
C. A B C D (iii) 5 3 2 1
D. A B C D (iv) 5 2 3 1

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 Multiple Choice QuestionsMultiple Choice Questions

209.

If f(x) is apolynomial ofdegreen with rational coefficients and 1 + 2i , 2 - 3 and 5 are three roots of f(x) = 0 , then the least value of n is

  • 5

  • 4

  • 3

  • 6


 Multiple Choice QuestionsMatch The Following

210.

Match the following elements of 1- 100423- 46 with their co-factors and choose the correct answer

     Element         Co-factorA    - 1         1     - 2B        1         2         32C        3         3        4D        6         4        6                      5   - 6

A. A B C D (i) 2 4 1 3
B. A B C D (ii) 2 4 3 1
C. A B C D (iii) 4 2 1 3
D. A B C D (iv) 4 1 2 3

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