The locus of the extrimities of the latusrectum of the family of

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


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


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


A.

x2 ± ay = a2

Given equation isb2x2 + y2 = a2b2 x2a2 + y2a2b2 = 1      ...iAbove equation of an ellipse with semi-majoraxis (a) and semi-minor axis(ab)Now, eccentricity,        e = 1 - a2b2a2 b2 = 1 - e2              ...iiLet (x, y) be extrmities of latusrecturn, thenx = ae and y = ya = ± b2From Eq (ii), we get     ± ya = 1 - x2a2 ± ay + x2 = a2Hence, locus of latusrectum is          x2 ± ay = a2


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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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