The quadratic equation whose roots are 13 + 2

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The sum of the real solutions of equation 2x2 + 51 = 1 + 20x is

  • 5

  • 24

  • 0

  • None of these


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2.

The quadratic equation whose roots are 13 + 2 and 13 - 2, will be

  • 7x2 - 6x + 1 = 0

  • 6x2 - 7x + 1 = 0

  • x2 - 6x + 7 = 0

  • x2 - 7x + 6 = 0


A.

7x2 - 6x + 1 = 0

Given roots are 13 + 2 and 13 - 2i.e., 13 + 2 × 3 - 23 - 2and 13 - 2 × 3 + 23 + 2 3 - 27 and 3 + 27So, the quadratic equation isx2 - Sum of the rootsx + Product of roots = 0 x2 - 3 - 27 + 3 + 27x   + 3 - 273 + 27 = 0    x2 - 67x + 9 - 249 = 0            x2 - 67x + 749 = 0               7x2 - 6x + 1 = 0


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3.

Who said, "Number of transistors per square inch on integrated circuits double every year, since their invention will continue to do so in the foreseable future"?

  • Alan Turing

  • Jon Von Neumann

  • Herbert Simon

  • Gorden Moore


4.

The point on the straight line y = 2x + 11 which is nearest to the circle 16(x2 + y) + 32x - 8y - 50 = 0, is

  • 92, 2

  • 92, - 2

  • - 92, 2

  • - 92, - 2


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5.

The locus of the extrimities of the latusrectum of the family of ellipses b2x2 + y2 = a2b2 having a given major axis, is

  • x2 ± ay = a2

  • y2 ± bx = a2

  • x2 ± by = a2

  • y2 ± ax = b2


6.

In ABC, if 3a = b + c, then value of cotB2cotC2 will be

  • 1

  • 2

  • 3

  • 2


7.

API stands for

  • Access Programming Interface

  • Android Programming Interface

  • Application Programming Interface

  • None of the above


8.

Let A and B be two events of an experiment PA = 14, PA  B = 12, then the value of PBAC is

  • 23

  • 13

  • 56

  • 12


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9.

If z = ilog2 - 3, then the value of cos(Z) will be

  • i

  • 2i

  • 1

  • 2


10.

Two lines of regressions are given by x + 2y - 5 = 0 and 2x + ky - 8 = 0. If σx2 = 12 and σy2 = 4, then the value of k is

  • 1

  • 2

  • 3

  • 4


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