Suppose a population A has 100 observations 101, 102, … , 200,

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

Suppose a population A has 100 observations 101, 102, … , 200, and another population B has 100 observations 151, 152, … , 250. If VA and VB represent the variances of the two populations, respectively, then VA/VB is 

  • 1

  • 9/4

  • 4/9

  • 4/9


A.

1

straight sigma subscript straight x superscript 2 space equals space fraction numerator sum from space to space of straight d subscript straight i superscript 2 over denominator straight n end fraction(Here deviations are taken from the mean) Since A and B both have 100 consecutive integers, therefore both have same standard deviation and hence the variance. 
therefore straight V subscript straight A over straight V subscript straight B space equals space 1 space left parenthesis As space begin inline style sum from space to space of end style space straight d subscript straight i superscript 2 space is space same space in space both space the space cases right parenthesis
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2.

If the roots of the quadratic equation x2 + px + q = 0 are tan30° and tan15°, respectively then the value of 2 + q − p is

  • 2

  • 3

  • 0

  • 0

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3.

Let W denote the words in the English dictionary. Define the relation R by :
R = {(x, y) ∈ W × W | the words x and y have at least one letter in common}. Then R is

  • not reflexive, symmetric and transitive

  • reflexive, symmetric and not transitive

  • reflexive, symmetric and transitive

  • reflexive, symmetric and transitive

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4.

The value of sum from straight k equals 1 to 10 of space open parentheses sin space fraction numerator 2 kπ over denominator 11 end fraction plus space straight i space cos space fraction numerator 2 kπ over denominator 11 end fraction close parentheses space is

  • i

  • 1

  • -i

  • -i

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5.

All the values of m for which both roots of the equations x2 − 2mx + m2 − 1 = 0 are greater than −2 but less than 4, lie in the interval

  • −2 < m < 0

  • m > 3

  • −1 < m < 3 

  • −1 < m < 3 

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6.

A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4s prior to passing through P. If g = 10 m/s2 , then the height above the point P from where the body began to fall is

  • 720 m

  • 900 m

  • 320 m

  • 320 m

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7.

A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is

  • x + y = 7

  • 3x − 4y + 7 = 0

  • 4x + 3y = 24

  • 4x + 3y = 24

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8.

The two lines x = ay + b, z = cy + d; and x = a′y + b′, z = c′y + d′ are perpendicular to each other if

  • aa′ + cc′ = −1

  • aa′ + cc′ = 1

  • fraction numerator straight a over denominator straight a apostrophe end fraction space plus fraction numerator straight c over denominator straight c apostrophe end fraction space equals 1
  • fraction numerator straight a over denominator straight a apostrophe end fraction space plus fraction numerator straight c over denominator straight c apostrophe end fraction space equals 1
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9.

The locus of the vertices of the family of parabolas straight y space equals fraction numerator straight a cubed straight x squared over denominator 3 end fraction space plus fraction numerator straight a squared straight x over denominator 2 end fraction minus 2 straight a space is

  • xy space equals space 105 over 64
  • xy space equals space 5 over 4
  • xy space equals space 35 over 16
  • xy space equals space 35 over 16
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10.

In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is

  • 3/5

  • 1/5

  • 2/5

  • 2/5

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