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 Multiple Choice QuestionsMultiple Choice Questions

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351. If space straight a with rightwards arrow on top space equals space fraction numerator 1 over denominator square root of 10 end fraction space left parenthesis 3 straight i with hat on top space plus straight k with hat on top right parenthesis space and space straight b with rightwards arrow on top space equals space 1 over 7 left parenthesis 2 straight i with hat on top space plus space 3 straight j with hat on top space minus 6 straight k with hat on top right parenthesis comma space then space the space value space of space left parenthesis 2 straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis. left square bracket left parenthesis straight a with rightwards arrow on top space straight x space straight b with rightwards arrow on top right parenthesis space straight x left parenthesis straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top right parenthesis right square bracket space is
  • -5

  • -3

  • 5

  • 5


A.

-5

left parenthesis 2 straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis. left square bracket left parenthesis straight a with rightwards arrow on top space straight x straight b with rightwards arrow on top right parenthesis space straight x space left parenthesis straight a with rightwards arrow on top space plus 2 straight b with rightwards arrow on top right parenthesis right square bracket
equals negative space left parenthesis 2 straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis. left square bracket space left parenthesis straight a with rightwards arrow on top space plus 2 straight b with rightwards arrow on top right parenthesis straight x space left parenthesis straight a with rightwards arrow on top space straight x straight b with rightwards arrow on top right parenthesis space right square bracket
equals space minus space left parenthesis 2 straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis. left square bracket left parenthesis straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top right parenthesis. straight b with rightwards arrow on top right parenthesis straight a with rightwards arrow on top minus left parenthesis straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top right parenthesis. straight a with rightwards arrow on top right parenthesis straight b with rightwards arrow on top right square bracket
space equals space minus space left parenthesis 2 straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis. left square bracket left parenthesis straight a with rightwards arrow on top. straight b with rightwards arrow on top right parenthesis plus 2. straight b with rightwards arrow on top. straight b with rightwards arrow on top right parenthesis straight a with rightwards arrow on top minus left parenthesis straight a with rightwards arrow on top. straight a with rightwards arrow on top plus 2 straight b with rightwards arrow on top. straight a with rightwards arrow on top right parenthesis straight b with rightwards arrow on top right parenthesis right square bracket
equals space minus space left parenthesis 2 straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis. left square bracket 0 space plus 2 straight a with rightwards arrow on top minus left parenthesis 0 space plus straight b with rightwards arrow on top right parenthesis right square bracket
equals negative left parenthesis 2 straight a with rightwards arrow on top space minus straight b with rightwards arrow on top right parenthesis. space left parenthesis 2 straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis
equals negative space left parenthesis 2 straight a with rightwards arrow on top minus straight b with rightwards arrow on top right parenthesis squared space equals space minus 4 straight a with rightwards arrow on top squared space plus 4 straight a with rightwards arrow on top. straight b with rightwards arrow on top minus straight b with rightwards arrow on top squared
space equals space minus space 4 plus 0 minus 1 space equals space minus space 5
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352.

The vector straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are not perpendicular  and straight c with rightwards arrow on top space and space straight d with rightwards arrow on top are two vectors satisfying: straight b with rightwards arrow on top space straight x straight c with rightwards arrow on top space equals space straight b with rightwards arrow on top space straight x straight d with rightwards arrow on top space and space straight a with rightwards arrow on top. straight b with rightwards arrow on top space equals space 0. The vector straight d with rightwards arrow on top is equal to

  • straight b with rightwards arrow on top space minus space open parentheses fraction numerator straight b. straight c over denominator straight a with rightwards arrow on top. straight d with rightwards arrow on top end fraction close parentheses straight c with rightwards arrow on top
  • straight c with rightwards arrow on top space plus open parentheses fraction numerator straight a with rightwards arrow on top. straight c with rightwards arrow on top over denominator straight a with rightwards arrow on top. straight b with rightwards arrow on top end fraction close parentheses straight b with rightwards harpoon with barb upwards on top
  • straight b with rightwards arrow on top space plus space open parentheses fraction numerator straight b with rightwards arrow on top. straight c with rightwards arrow on top over denominator straight a with rightwards arrow on top. straight b with rightwards arrow on top end fraction close parentheses straight c with rightwards arrow on top
  • straight b with rightwards arrow on top space plus space open parentheses fraction numerator straight b with rightwards arrow on top. straight c with rightwards arrow on top over denominator straight a with rightwards arrow on top. straight b with rightwards arrow on top end fraction close parentheses straight c with rightwards arrow on top
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353.

The circle x2+ y2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points if

  • -85 < m < -35

  • -35 < m < 15

  • 15 < m < 65

  • 15 < m < 65

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354.

Let bold a bold space bold equals bold j with bold hat on top bold minus bold k with bold hat on top bold space and bold c bold space bold equals bold space bold i with bold hat on top bold minus bold j with bold hat on top bold minus bold k with bold hat on top. Then, the vector b satisfying a x b + c = 0  and a.b  = 3

  • negative straight i with hat on top plus straight j with hat on top space minus 2 straight k with hat on top
  • 2 straight i with hat on top minus straight j with hat on top space plus 2 straight k with hat on top
  • negative straight i with hat on top minus straight j with hat on top space minus 2 straight k with hat on top
  • negative straight i with hat on top minus straight j with hat on top space minus 2 straight k with hat on top
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355.

If the vectors bold a bold space bold equals bold space bold i with bold hat on top bold space bold minus bold j with bold hat on top bold space bold plus bold 2 bold k with bold hat on top bold comma bold space bold b bold space bold equals bold 2 bold i with bold hat on top bold space bold plus bold 4 bold j with bold hat on top bold space bold plus bold k with bold hat on top bold space bold and bold space bold c bold space bold equals bold space bold lambda bold i with bold hat on top bold space bold plus bold j with bold hat on top bold space bold plus bold mu bold k with bold hat on top are mutually orthogonal, then (λ,μ) is equal to

  • (-3,2)

  • (2,-3)

  • (-2,3)

  • (-2,3)

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356. 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

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357.

If straight u with rightwards arrow on top comma straight v with rightwards arrow on top comma straight w with rightwards arrow on top are non–coplanar vectors and p, q are real numbers, then the equality open square brackets 3 straight u with rightwards arrow on top comma straight p straight v with rightwards arrow on top comma straight p straight w with rightwards arrow on top close square brackets minus open square brackets straight p straight v with rightwards arrow on top comma straight w with rightwards arrow on top comma space straight q straight u with rightwards arrow on top close square brackets space minus space left square bracket 2 straight w with rightwards arrow on top comma straight q straight v with rightwards arrow on top comma straight q straight u with rightwards arrow on top right square bracket space equals space 0 holds for

  • exactly one value of (p, q)

  • exactly two values of (p, q)

  • more than two but not all values of (p, q)

  • more than two but not all values of (p, q)

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358.

If open vertical bar straight Z space equals space 4 over straight z close vertical bar, then the maximum value of |Z| is equal to

  • square root of 3 space plus 1
  • square root of 5 space plus 1
  • 2

  • 2

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359.

The vector straight a with rightwards arrow on top space equals space straight alpha space straight i with hat on top space plus 2 straight j with hat on top space plus straight beta straight k with hat on top lies in the plane of the vectors straight b with rightwards arrow on top space equals straight i with hat on top space plus straight j with hat on top space and space straight c with rightwards arrow on top space equals space straight j with hat on top space plus straight k with hat on top and bisects the angle between straight b with rightwards arrow on top space and space straight c with rightwards arrow on top.Then which one of the following gives possible values of α and β?

  • α = 2, β = 2

  • α = 1, β = 2

  • α = 2, β = 1

  • α = 2, β = 1

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360.

The non−zero verctors straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space and space straight c with rightwards arrow on topare related by straight a with rightwards arrow on top space equals space 8 straight b with rightwards arrow on top space and space straight c with rightwards arrow on top space equals space minus space 7 straight b with rightwards arrow on top.Then the angle between straight a with rightwards arrow on top space and space straight c with rightwards arrow on top is

  • 0

  • π/4

  • π/2

  • π/2

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