If the image of the point P(1, –2, 3) in the plane, 2x + 3y �

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

21.

The area (in sq. units) of the region
{(x, y} : x  ≥ 0, x + y ≤ 3, x2 ≥ 4y and y ≤ 1 +√x}

  • 5/2

  • 59/12

  • 3/2

  • 3/2

559 Views

22.

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends,3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is

  • 484

  • 485

  • 468

  • 468

580 Views

23.

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

24. Let space straight a with rightwards arrow on top space equals space 2 straight i with hat on top space plus straight j with hat on top minus 2 straight k with hat on top space and space straight b with rightwards arrow on top space equals straight i with hat on top space plus straight j with hat on top. space Let space straight c with rightwards arrow on top space be space straight a space vector space such space that space vertical line straight c with rightwards arrow on top minus straight a with rightwards arrow on top vertical line equals 3
vertical line left parenthesis straight a with rightwards arrow on top space straight x straight b with rightwards arrow on top right parenthesis space straight x straight c with rightwards arrow on top vertical line space equals space 3 space and space the space angle space between space straight c with rightwards arrow on top space and space straight a with rightwards arrow on top space straight x space straight b with rightwards arrow on top space be space 30 to the power of straight o. space Then space straight a with rightwards arrow on top. straight c with rightwards arrow on top space is space
equal space to space
  • 1/8

  • 25/8

  • 2

  • 2

211 Views

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25.

The integral  integral subscript straight pi over 4 end subscript superscript fraction numerator 3 straight pi over denominator 4 end fraction end superscript fraction numerator dx over denominator 1 plus space cos space straight x end fractionis equal to

  • -1

  • -2

  • 2

  • 2

194 Views

26.

If left parenthesis 2 space sin space straight x right parenthesis space dy over dx space plus space left parenthesis space straight y space plus 1 right parenthesis space cos space straight x space equals space 0 space and space straight y left parenthesis 0 right parenthesis space equals 1 space then space straight y open parentheses straight pi over 2 close parentheses is equal to

  • 4/3

  • 1/3

  • -2/3

  • -2/3

220 Views

27.

Let In ∫tan x dx,(n> 1) . I4 + I6 = a tan5x + bx5 + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

  • open parentheses negative 1 fifth comma 0 close parentheses
  • open parentheses negative 1 fifth comma 1 close parentheses
  • open parentheses 1 fifth comma 0 close parentheses
  • open parentheses 1 fifth comma 0 close parentheses
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28.

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


C.

2 square root of 42

Line space PQ space semicolon space fraction numerator straight x minus 1 over denominator 1 end fraction space equals fraction numerator straight y plus 2 over denominator 4 end fraction space equals space fraction numerator straight z minus 3 over denominator 5 end fraction
Let space straight F space left parenthesis straight lambda space plus 1 comma space 4 straight lambda minus 2 comma space 5 straight lambda plus 3 right parenthesis
straight F space lies space on space the space plane
2 left parenthesis straight lambda plus 1 right parenthesis space plus space 3 left parenthesis 4 straight lambda minus 2 right parenthesis minus 4 left parenthesis 5 straight lambda plus 3 right parenthesis space plus space 22 space equals space 0
rightwards double arrow space minus 6 straight lambda space plus space 6 space equals space 0
rightwards double arrow space straight lambda space equals 1
straight F space left parenthesis 2 comma 2 comma 8 right parenthesis
PQ space equals space 2 PF space equals space 2 square root of 42
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29.

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
222 Views

30.

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one–by–one, with replacement, then the variance of the number of green balls drawn is

  • 6/25

  • 12/5

  • 6

  • 6

325 Views

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