The distance of the point (1, 3, –7) from the plane passing th

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 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

111 Views

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.

156 Views

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°

118 Views

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
166 Views

Advertisement
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

Advertisement

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


C.

fraction numerator 10 over denominator square root of 83 end fraction

Normal vector

open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 1 cell negative 2 end cell 3 row 2 cell negative 1 end cell cell negative 1 end cell end table close vertical bar space equals space 5 straight i with hat on top space plus space 7 straight j with hat on top space plus 3 straight k with hat on top
So space plane space is space
5 left parenthesis straight x minus 1 right parenthesis space plus space 7 left parenthesis straight y plus 1 right parenthesis space plus space 3 left parenthesis straight z plus 1 right parenthesis space equals space 0 space
rightwards double arrow space 5 space straight x space plus 7 straight y space plus space 3 straight z space plus space 5 space equals space 0
Distance space fraction numerator 5 plus 21 minus 21 plus 5 over denominator square root of 25 plus 49 plus 9 end root end fraction space equals space fraction numerator 10 over denominator square root of 83 end fraction

222 Views

Advertisement
Advertisement
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)

103 Views

Advertisement