The plane x + 2y – z = 4 cuts the sphere x2 + y2 + z2 – x +

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

71.

A random variable X has Poisson distribution with mean 2. Then P(X > 1.5) equals

  • 2/e2

  • 0

  • 1 minus 3 over straight e squared
  • 1 minus 3 over straight e squared
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72.

A and B are two like parallel forces. A couple of moment H lies in the plane of A and B and is contained with them. The resultant of A and B after combining is displaced through a distance

  • 2H/A-B

  • H/A+B

  • H/2(A+B)

  • H/2(A+B)

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73.

The resultant R of two forces acting on a particle is at right angles to one of them and its magnitude is one-third of the other force. The ratio of larger force to smaller one is 

  • 2 : 1

  • 3 colon square root of 2
  • 3:2

  • 3:2

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74.

The plane x + 2y – z = 4 cuts the sphere x2 + y2 + z2 – x + z – 2 = 0 in a circle of radius

  • 3

  • 1

  • 2

  • 2


B.

1

Perpendicular distance of centre open parentheses 1 half comma 0 comma fraction numerator negative 1 over denominator 2 end fraction close parentheses from x + 2y – 2 = 4

fraction numerator open vertical bar begin display style 1 half plus 1 half minus 4 end style close vertical bar over denominator square root of 6 end fraction space equals space square root of 3 over 2 end root
space radius space equals space square root of 5 over 2 minus 3 over 2 end root space equals space 1

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75.

Let x1, x2, …,xn be n observations such that sum from space to space of straight x subscript straight i superscript 2 space equals space 400 space and space stack sum space with space below and space on top straight x subscript straight i space equals space 80 Then a possible value of n among the following is

  • 15

  • 18

  • 19

  • 19

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