The projections of a vector on the three coordinate axis are 6,

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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

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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

127 Views

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


C.

6/7, -3/7, 2/7

Projection of a vector on coordinate axis are
x2-x1, y2-y1, z2-z1
x2-x1 = 6, y2-y1 = -3, z2-z1 = 2

square root of left parenthesis straight x subscript 2 minus straight x subscript 1 right parenthesis squared space plus left parenthesis straight y subscript 2 minus straight y subscript 1 right parenthesis squared space plus space left parenthesis straight z subscript 2 minus straight z subscript 1 right parenthesis squared end root space equals space square root of 36 plus 9 plus 4 end root space equals space 7
The space Direction space cosines space of space the space vector space are space 6 over 7 comma 3 over 7 comma 2 over 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

147 Views

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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