If the line  and  intersect, then k is equal to from Mathem

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

The area bounded between the parabolas x2=y/4 and x2 = 9y, and the straight line y = 2 is

  • 20 square root of 2
  • fraction numerator 10 space square root of 2 over denominator 3 end fraction
  • fraction numerator 20 space square root of 2 over denominator 3 end fraction
  • fraction numerator 20 space square root of 2 over denominator 3 end fraction
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12.

If the line fraction numerator straight x minus 1 over denominator 2 end fraction space equals space fraction numerator straight y plus 1 over denominator 3 end fraction space equals space fraction numerator straight z minus 1 over denominator 4 end fraction and fraction numerator straight x minus 3 over denominator 1 end fraction space equals fraction numerator straight y minus straight k over denominator 2 end fraction space equals space straight z over 1 intersect, then k is equal to

  • -1

  • 2/9

  • 9/2

  • 9/2


C.

9/2

To find value of 'k' of the given lines L1 and L2 are intersecting each other.
Let straight L subscript 1 space colon space fraction numerator straight x minus 1 over denominator 2 end fraction space equals space fraction numerator straight y plus 1 over denominator 3 end fraction space equals fraction numerator straight z minus 1 over denominator 4 end fraction space equals space straight p
and space straight L subscript 2 colon thin space fraction numerator straight x minus 3 over denominator 1 end fraction space equals space fraction numerator straight y minus straight k over denominator 2 end fraction space equals space fraction numerator straight z minus 0 over denominator 1 end fraction space equals space straight q
⇒ Any point P on line L1 is of type
P(2p+1), 3p-1, 4p+1) and any point Q on line L2 is of type Q (q+3, 2q+k, q).
Since, L1 and L2 are intersecting each other, hence, both points P and Q should coincide at the point of intersection, i.e, corresponding coordinates of P and Q should be same.
2p+1 =q +3,
3p-1 =2q +k
4p+1 = q
solving these we get value of p and q as
p = -3/2 and q = -5
Substituting the values of p and q in the third equation
3p-1 = 2q+k, we get
3 open parentheses fraction numerator negative 3 over denominator 2 end fraction close parentheses minus 1 space equals space 2 space left parenthesis negative 5 right parenthesis space plus straight k
space straight k space equals space 9 over 2

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13.

Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

  • 3/8

  • 1/5

  • 1/4

  • 1/4

206 Views

14.

If z ≠ 1 and fraction numerator straight z squared over denominator straight z minus 1 end fraction is real, then the point represented by the complex number z lies

  • either on the real axis or on a circle passing through the origin

  • on a circle with centre at the origin

  • either on the real axis or on a circle not passing through the origin

  • either on the real axis or on a circle not passing through the origin

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15.

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

  • 10/3

  • 3/5

  • 6/5

  • 6/5

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16.

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty, is

  • 52

  • 35

  • 25

  • 25

248 Views

17.

An ellipse is drawn by taking a diameter of the circle (x–1)2 + y2 = 1 as its semiminor axis and a diameter of the circle x2 + (y – 2)2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

  • 4x2+ y2 = 4

  • x2 +4y2 =8

  • 4x2 +y2 =8

  • 4x2 +y2 =8

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18.

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

  • -1/4

  • -4

  • -2

  • -2

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19.

A spherical balloon is filled with 4500π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is

  • 9/7

  • 7/9

  • 2/9

  • 2/9

1221 Views

20.

Let A = open square brackets table row 1 0 0 row 2 1 0 row 3 2 1 end table close square brackets. If u1 and u2 are column matrices such that Au1 = open square brackets table row 1 row 0 row 0 end table close square brackets and Au2 = open square brackets table row 0 row 1 row 0 end table close square brackets, then u1 +u2 is equal to

  • open square brackets table row cell negative 1 end cell row 1 row 0 end table close square brackets
  • open square brackets table row cell negative 1 end cell row cell space space space 1 end cell row cell negative 1 end cell end table close square brackets
  • open square brackets table row cell negative 1 end cell row cell negative 1 end cell row 0 end table close square brackets
  • open square brackets table row cell negative 1 end cell row cell negative 1 end cell row 0 end table close square brackets
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