For two data sets, each of size 5, the variances are given to be

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Consider the following relations:
R = {(x, y)| x, y are real numbers and x = wy for some rational number w}; S = {(m/p, p/q)| m, n, p and q are integers such that n, q ≠ 0 and qm = pn}. Then

  • R is an equivalence relation but S is not an equivalence relation

  • neither R nor S is an equivalence relation

  • S is an equivalence relation but R is not an equivalence relation

  • S is an equivalence relation but R is not an equivalence relation

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2.

The Number of complex numbers z such that |z– 1| = |z + 1| = |z – i| equals 

  • 0

  • 1

  • 2

  • 2

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3.

If α and β are the roots of the equation x2 – x +1 =0, then α2009 + β2009 =

  • -2

  • -1

  • 1

  • 1

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4.

A person is to count 4500 currency notes. Let a denote the number of notes he counts in the nth minute. If a1 = a2 = ... = a10 = 150 and a10, a11, ...are in an AP with common difference -2, then the time taken by him to count all notes is

  • 24 min

  • 34 min

  • 125 min

  • 125 min

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5.

The equation of the tangent to the curve y = x +4/x2, that is parallel to the x-axis, is

  • y= 0

  • y= 1

  • y= 2 

  • y= 2 

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6.

Let p(x) be a function defined on R such that limit as straight x space rightwards arrow infinity of space fraction numerator straight f left parenthesis 3 straight x right parenthesis over denominator straight f left parenthesis straight x right parenthesis end fraction = 1, p'(x)  p'(1-x),for all x∈[0,1] p(0) = 1 and p(1) = 41. Then integral subscript 0 superscript straight x space straight p space left parenthesis straight x right parenthesis space dx equals

  • √41

  • 21

  • 41

  • 41

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7.

Let S be a non empty subset of R. Consider the
following statement:
P: There is a rational number x∈S such that x > 0.
Which of the following statements is the negation of the statement P?

  • There is a rational number x∈S such that x ≤ 0.

  • There is no rational number x∈ S such that x≤0.

  • Every rational number x∈S satisfies x ≤ 0.

  • Every rational number x∈S satisfies x ≤ 0.

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8.

Let cos (α + β) = 4/5 and let sin (α - β) = 5/13, where 0 ≤α,β ≤ π/4. Then tan 2α is equal to

  • 25/16

  • 56/33

  • 19/12

  • 19/12

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9.

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

  • 5/2

  • 11/2

  • 6

  • 6


B.

11/2

because space straight sigma subscript straight x superscript 2 space equals space 4 space and space straight sigma subscript straight y superscript 2 space equals 5
Also comma space straight x with minus on top space equals space 2 space and space straight y with minus on top space equals space 4 space
Now comma space Σx subscript straight i over 5 space equals space 2
rightwards double arrow space straight capital sigma space straight x subscript straight i space equals 10 space semicolon space space Σy subscript straight i space equals space 20
and space straight sigma subscript straight x superscript 2 space equals space open parentheses 1 half Σx subscript 1 superscript 2 close parentheses minus left parenthesis straight x with minus on top space right parenthesis squared space equals space 1 fifth space left parenthesis straight capital sigma space straight y subscript straight i superscript 2 right parenthesis minus 16
rightwards double arrow space Σy subscript straight i superscript 2 space equals space 105
space straight sigma subscript straight x superscript 2 space space equals space 1 over 10 left parenthesis straight capital sigma space straight x subscript straight i superscript 2 space plus space straight capital sigma space straight y subscript straight i superscript 2 right parenthesis space minus open parentheses fraction numerator begin display style straight x with minus on top end style plus begin display style straight y with minus on top end style over denominator 2 end fraction close parentheses squared
space equals space 1 over 10 left parenthesis 40 plus 105 right parenthesis minus 9 space equals space fraction numerator 145 minus 90 over denominator 10 end fraction space equals space 55 over 10 space equals space 11 over 2
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10.

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

  • there is a regular polygon with r/R = 1/2

  • there is a regular polygon with straight r over straight R space equals space fraction numerator 1 over denominator square root of 2 end fraction

  • there is a regular polygon with r/R = 2/3

  • there is a regular polygon with r/R = 2/3

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