The line L given by  passes through the point (13, 32). The lin

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 Multiple Choice QuestionsMultiple Choice Questions

11.

If the angle between the line x =fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 3 over denominator straight lambda end fraction and the plane x + 2y + 3z = 4 is cos-1 square root of 5 over 14 end root then λ equal

  • 2/3

  • 3/2

  • 2/5

  • 2/5

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12.

Statement-1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line: straight x over 1 space equals space fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 2 over denominator 3 end fraction
Statement-2: The line:straight x over 1 space equals space fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 2 over denominator 3 end fraction  bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).

  • Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. 

  • Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. 

  • Statement-1 is true, Statement-2 is false.

  • Statement-1 is true, Statement-2 is false.

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13.

A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ

  • 30°

  • 45°

  • 60°

  • 60°

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14.

The line L given by straight x over 5 space plus straight y over straight b space equals space 1 passes through the point (13, 32). The line K is parallel to L and has the equation straight x over straight c space plus straight y over 3 space equals space 1 . Then the distance
between L and K is

  • fraction numerator 23 over denominator square root of 15 end fraction
  • square root of 17
  • fraction numerator 17 over denominator square root of 15 end fraction
  • fraction numerator 17 over denominator square root of 15 end fraction


D.

fraction numerator 17 over denominator square root of 15 end fraction

Since, the line L is passing through the point (13,32)
Therefore,

13 over 5 space plus 32 over straight b space equals space 1
rightwards double arrow space 32 over straight b space equals space minus 8 over 5
rightwards double arrow space straight b space equals space minus 20
The line K is parallel to the line L then its equation must be

straight x over 5 minus straight y over 20 space equals straight a space
Or
fraction numerator straight x over denominator 5 straight a end fraction minus fraction numerator straight y over denominator 20 straight a end fraction space equals space 1
On space comparing space with space straight x over straight c space plus straight y over 3 space equals space 1 comma space we space straight g space et
20 straight a space equals space minus space 3 comma space straight c space equals 5 straight a space equals space minus 3 over 4
Hence comma space the space distance space between space lines
fraction numerator vertical line straight a minus 1 vertical line over denominator square root of begin display style 1 over 25 plus 1 over 400 end style end root end fraction space equals space fraction numerator open vertical bar begin display style fraction numerator negative 3 over denominator 20 end fraction minus 1 end style close vertical bar over denominator square root of begin display style 17 over 400 end style end root end fraction space equals space fraction numerator 23 over denominator square root of 17 end fraction

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15.

Let k be an integer such that triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point 

  • open parentheses 2 comma 1 half close parentheses
  • open parentheses 2 comma negative 1 half close parentheses
  • open parentheses 1 comma negative 3 over 2 close parentheses
  • open parentheses 1 comma negative 3 over 2 close parentheses
857 Views

16.

The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point

  • open parentheses fraction numerator 1 over denominator 2 comma end fraction 1 third close parentheses
  • open parentheses fraction numerator 1 over denominator 2 comma end fraction 1 half close parentheses
  • open parentheses fraction numerator 1 over denominator 2 comma end fraction 1 half close parentheses
205 Views

17.

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to line, x/1 = y/4= z/5 is Q, then PQ is equal to

  • 6 square root of 7
  • 3 square root of 5
  • 2 square root of 42
  • 2 square root of 42
245 Views

18.

The distance of the point (1, 3, –7) from the plane passing through the point (1, –1, –1), having normal perpendicular to both the linesfraction numerator straight x minus 1 over denominator 1 end fraction space equals space fraction numerator straight y plus 2 over denominator negative 2 end fraction space equals space fraction numerator straight z minus 4 over denominator 3 end fraction space and space fraction numerator straight x minus 2 over denominator 2 end fraction space equals space fraction numerator straight y plus 1 over denominator negative 1 end fraction space equals space fraction numerator straight z plus 7 over denominator negative 1 end fraction is

  • fraction numerator 10 over denominator square root of 74 end fraction
  • fraction numerator 20 over denominator square root of 74 end fraction
  • fraction numerator 10 over denominator square root of 83 end fraction
  • fraction numerator 10 over denominator square root of 83 end fraction
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19.

The lines p(p2+ 1) x – y + q = 0 and (p2+ 1)2x + (p2+ 1) y + 2q = 0 are
perpendicular to a common line for

  • no value of p

  • exactly one value of p

  • exactly two values of p

  • exactly two values of p

115 Views

20.

Let the line fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y minus 1 over denominator negative 5 end fraction space equals space fraction numerator straight z plus 2 over denominator 2 end fraction lie in the plane x + 3y – αz + β = 0. Then (α, β) equals

  • (6, – 17)

  • (–6, 7)

  • (5, –15)

  • (5, –15)

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