If cosα and cosβ (0 < 

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 Multiple Choice QuestionsMultiple Choice Questions

11.

The equation 1 - x + x2 = 5 has :

  • a rational root and an irrational root

  • two rational roots

  • two irrational roots

  • no real roots


12.

What is i1000 + i1001 + i1002 + i1003 equal to where i =  - 1 ?

  • 0

  • i

  •  - i

  • 1


13.

The modulus-amplitude form of 3 +i, where i =  - 1 is :

  • 2cosπ3 + isinπ3

  • 2cosπ6 + isinπ6

  • 4cosπ3 + isinπ3

  • 4cosπ6 + isinπ6


14.

Let [x] denote the greatest integer function. What is the number of solutions of the equation x2 - 4x + [x] = 0 in the interval [0, 2] ?

  • Zero (No solution)

  • One

  • Two

  • Three


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15.

If α and β(  0) are the roots of the quadratic equation x2 + αx - B = 0, then  the quadratic expression -x2 + αx + β  where x  R has

  • Least value - 14

  • Least value - 94

  • Greatest value 14

  • Greatest value  94


16.

What is the value of  - 1 + i323n +  - 1 - i323n

where i =  - 1 ?

  • 3

  • 2

  • 1

  • 0


17.

Suppose f(x) is such a quadratic expression that it is positive for all real x.

If g(x) = f(x) + f'(x) + f "(x), then for any real x

  • gx < 0

  • gx > 0

  • g(x) = 0

  • gx  0


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18.

If cosα and cosβ (0 < α < β < π) are the roots of the quadratic equation 4x2 - 3 = 0, then what is the value of secα x secβ ?

  • - 43

  • 34

  • 34

  • - 34


A.

- 43

Product of roots cosαcosβ = - 341cosαcosβ  = - 43  secαsecβ  = - 43


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19.

The ratio of roots of the equations ax2 + bx + c = 0 and px2 + qx + r = 0 are equal. If D1 and D2 are respective discriminants, then what is D1D2 equal to ?

  • a2p2

  • b2q2

  • c2r2

  • None of the above


20.

The value of  i2n + i2n + 1 + i2n + 2 + i2n + 3, where i =   - 1 is

  • 0

  • 1

  • i

  • - i


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