Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

61.

The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is

  • 0o

  • 90o

  • 45o

  • 45o

237 Views

62.

If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres

x2 + y2 + z2 + 6x − 8y − 2z = 13 and x2 + y2 + z2 − 10x + 4y − 2z = 8, then a equals

  • -1

  • 1

  • -2

  • -2

178 Views

63.

The distance between the line straight r with rightwards arrow on top space equals space 2 straight i with hat on top space minus 2 straight j with hat on top space plus 3 straight k with hat on top space plus space straight lambda space left parenthesis straight i with hat on top minus straight j with hat on top space plus 4 straight k with hat on top right parenthesis and the plane straight r with rightwards arrow on top. left parenthesis straight i with hat on top space plus 5 straight j with hat on top space plus straight k with hat on top right parenthesis space equals space 5 space is

  • 10/9

  • fraction numerator 10 over denominator 3 square root of 3 end fraction
  • 3/10

  • 3/10

104 Views

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64.

For any vector straight a with rightwards arrow on top  the value of left parenthesis straight a with rightwards arrow on top space straight x straight i with hat on top right parenthesis squared space plus left parenthesis straight a with rightwards arrow on top space straight x straight j with hat on top right parenthesis squared space plus left parenthesis straight a with rightwards arrow on top space straight x straight k with hat on top right parenthesis squared is equal to

  • 3 straight a with rightwards arrow on top squared
  • straight a with rightwards arrow on top squared
  • 2 straight a with rightwards arrow on top squared
  • 2 straight a with rightwards arrow on top squared


C.

2 straight a with rightwards arrow on top squared
Let space straight a with rightwards arrow on top space equals space straight x straight i with hat on top plus straight y straight j with hat on top plus straight z straight k with hat on top
straight a with rightwards arrow on top space straight x space straight i with hat on top space equals space straight z straight j with hat on top space minus space straight y straight k with hat on top
rightwards double arrow left parenthesis straight a with rightwards arrow on top space straight x space straight i with hat on top right parenthesis squared space equals space straight y squared plus straight z squared
rightwards double arrow left parenthesis straight a with rightwards arrow on top space straight x space straight j with hat on top right parenthesis space equals space straight x squared plus straight z squared
rightwards double arrow left parenthesis straight a with rightwards arrow on top space straight x space straight k with hat on top right parenthesis space equals space straight x squared plus straight y squared
similarly space left parenthesis straight a with rightwards arrow on top space straight x space straight j with hat on top right parenthesis squared space equals space straight x squared plus straight z squared
and space open parentheses straight a with rightwards arrow on top space straight x stack space straight k with hat on top close parentheses squared space equals space straight x squared plus straight y squared
rightwards double arrow space left parenthesis straight a with rightwards arrow on top space straight x space straight i with hat on top right parenthesis squared space plus space left parenthesis straight a with rightwards arrow on top space straight x straight j with hat on top right parenthesis squared space plus space left parenthesis straight a with hat on top space straight x straight k with hat on top right parenthesis squared space equals space 2 space left parenthesis straight x squared space plus straight y squared plus space straight z squared right parenthesis space equals space 2 straight a with rightwards arrow on top squared
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65.

If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

  • (-1, 7/3)

  • (-1/3, 7/3)

  • (1, 7/3)

  • (1, 7/3)

112 Views

66.

Let a, b and c be distinct non-negative numbers. If the vectors straight a straight i with hat on top space plus straight a space straight j with hat on top space plus space straight c straight k with hat on top comma space space straight i with hat on top space plus straight k with hat on top space and space straight c straight i with hat on top space plus straight c straight j with hat on top space plus straight b straight k with hat on top space 

  • the Geometric Mean of a and b

  • the Arithmetic Mean of a and b

  • equal to zero

  • equal to zero

117 Views

67.

If straight a with rightwards arrow on top comma straight b with rightwards arrow on top comma space straight c with rightwards arrow on top are non -coplanar vector λ is a real number then

open square brackets straight lambda left parenthesis straight a with rightwards arrow on top space plus straight b with rightwards arrow on top right parenthesis space straight lambda squared space straight b with rightwards arrow on top straight lambda space straight c with rightwards arrow on top close square brackets space equals space open square brackets straight a with rightwards arrow on top space straight b with rightwards arrow on top space plus straight c with rightwards arrow on top straight b with rightwards arrow on top close square brackets space for

  • exactly one value of λ

  • no value of λ

  • exactly three values of λ

  • exactly three values of λ

261 Views

68.

The value of integral subscript negative straight pi end subscript superscript straight pi space fraction numerator cos squared space straight x over denominator 1 plus space straight a to the power of straight x end fraction space dx comma space straight a greater than 0 space is

  • a π

  • π/2

  • π/a

  • π/a

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69. Let space straight a with rightwards arrow on top space equals space straight i with hat on top space minus straight k with hat on top comma space straight b with rightwards arrow on top space equals space straight x straight i with hat on top space plus straight j with hat on top space plus left parenthesis 1 minus straight x right parenthesis space straight k with hat on top space and space
straight c with rightwards arrow on top space equals space straight y straight i with hat on top space plus straight x space straight j with hat on top space plus left parenthesis 1 plus straight x minus straight y right parenthesis straight k with hat on top space. Then space left square bracket straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top right square bracket depends on
  • only y

  • only x

  • both x and y

  • both x and y

99 Views

70.

Three houses are available in a locality. Three persons apply for the houses. Each applies to one house without consulting others. The probability that all the three apply for the same house is 

  • 2/9

  • 1/9

  • 8/9

  • 8/9

152 Views

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