If the mean deviation of the numbers 1, 1 + d, 1+ 2d, ... , 1 +

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

If the mean deviation of the numbers 1, 1 + d, 1+ 2d, ... , 1 + 100d from their mean is 255, then the d is equal to 

  • 10.0

  • 20.0

  • 10.1

  • 10.1


C.

10.1

Mean space left parenthesis straight x with minus on top right parenthesis space equals space fraction numerator sum space of space quantities over denominator straight n end fraction
space equals space fraction numerator begin display style straight n over 2 end style space left parenthesis straight a plus 1 right parenthesis over denominator straight n end fraction space equals space 1 half left square bracket space 1 plus space 1 plus 100 straight d right square bracket space equals space 1 plus 50 space straight d
straight M. straight D. space equals space 1 over straight n space begin inline style stack sum space with space below and space on top end style vertical line straight x subscript straight i space minus straight x with minus on top vertical line
rightwards double arrow space 255 space equals space 1 over 101 left square bracket 50 straight d space plus 49 straight d space plus 48 straight d space plus..... space straight d plus space 0 space plus straight d plus space.... plus 50 straight d right square bracket
space equals space fraction numerator 2 straight d over denominator 101 end fraction open square brackets fraction numerator 50 space straight x 51 over denominator 2 end fraction close square brackets
rightwards double arrow space straight d space equals space fraction numerator 255 space straight x space 101 over denominator 50 space straight x space 51 end fraction space equals space 10.1
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2.

If the roots of the equation bx2+ cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is

  • greater than 4ab

  • less than 4ab

  • greater than -4ab

  • greater than -4ab

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3.

Let A and B denote the statements
A: cos α + cosβ + cosγ = 0
B : sinα + sinβ + sinγ = 0
If cos(β – γ) + cos(γ – α) + cos(α – β) = – 3/2, then

  •  A is true and B is false

  • A is false and B is true

  • both A and B are true

  • both A and B are true

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4.

If A, B and C are three sets such that A ∩ B = A∩ C and A ∪ B = A ∪ C, then

  • A = B

  • A = C

  • B = C

  • B = C

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5.

The projections of a vector on the three coordinate axis are 6, - 3, 2 respectively. The direction cosines of the vector are

  •  6, –3, 2 

  • 6/5, -3/5, 2/5

  • 6/7, -3/7, 2/7

  • 6/7, -3/7, 2/7

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6.

Three distinct points A, B and C are given in the 2 – dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1, 0) to the distance from the point ( - 1, 0) is equal to 1/3 . Then the circumcentre of the triangle ABC is at the point

  • (0,0)

  • (5/4, 0)

  • (5/2, 0)

  • (5/2, 0)

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7.

The remainder left out when 82n –(62)2n+1 is divided by 9 is 

  • 0

  • 2

  • 7

  • 7

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8.

The ellipse x2+ 4y2= 4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is

  • x2+ 16y2= 16 

  • x2+ 12y2= 16 

  • 4x2+ 48y2= 48 

  • 4x2+ 48y2= 48 

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9.

The sum to infinity of the series 1 space plus space 2 over 3 space plus space 6 over 3 squared space plus space 10 over 3 cubed space plus space 14 over 3 to the power of 4 space plus.... space is

  • 2

  • 3

  • 4

  • 4

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10.

The differential equation which represents the family of curves y=c1ec2xe, where c1 and c2 are arbitrary constants, is

  • y' =y2

  •  y″ = y′ y

  • yy″ = y′

  • yy″ = y′

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