33. MATHs Mock Test 33 for NDA

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  Explanation

  Question No.    321
  Topic    Statistics

  Most consistent sales means

  Lowest Coefficient of Variation

  Formula

  CV = (Standard Deviation / Mean) × 100

  Month 1

  CV = (2/30)×100
  = 6.67%

  Month 2

  CV = (3/57)×100
  = 5.26%

  Month 3

  CV = (4/82)×100
  = 4.87%

  Month 4

  CV = (2/28)×100
  = 7.14%

  Lowest CV = Month 3

  Answer    (c) Month 3

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  Explanation

  Question No.    322
  Topic    Probability

  Given

  P(A)=1/3
  P(B)=1/4
  P(A/B)=1/6

  Formula

  P(A/B)=P(A∩B)/P(B)

  1/6 = P(A∩B)/(1/4)

  P(A∩B)=1/24

  Now

  P(B/A)=P(A∩B)/P(A)

  =(1/24)/(1/3)

  =3/24

  =1/8

  Answer    (b) 1/8

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  Explanation

  Question No.    323
  Topic    Probability

  Given

  A and B are mutually exclusive 
  and exhaustive

  Therefore

  P(A)+P(B)=1

  Also

  P(B)=3P(A)

  Let P(A)=x

  Then

  x+3x=1

  4x=1

  x=1/4

  Hence

  P(B)=3/4

  Answer    (a) 3/4

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  Explanation

  Question No.    324
  Topic    Probability

  Two dice thrown

  Total outcomes

  =36

  Required

  Sum ≥ 10

  Possible sums

  10 → (4,6),(5,5),(6,4)
  =3 ways

  11 → (5,6),(6,5)
  =2 ways

  12 → (6,6)
  =1 way

  Total favourable outcomes

  =3+2+1

  =6

  Probability

  =6/36

  =1/6

  Answer    (d) 1/6

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  Explanation

  Question No.    325
  Topic    Average

  Men = 30
  Women = 20

  Average salary of men = 4050

  Average salary of all employees = 3550

  Total salary

  =50×3550

  =177500

  Salary of men

  =30×4050

  =121500

  Salary of women

  =177500-121500

  =56000

  Average salary of women

  =56000/20

  =2800

  Answer    (d) Rs 2800

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  Explanation

  Question No.    326
  Topic    Statistics

  Total Salary

  = Rs 15000

  Full circle angle

  =360°

  Transport angle

  =15°

  Transport expenditure

  =(15/360)×15000

  =625

  Answer    (b) Rs 625

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  Explanation

  Question No.    327
  Topic    Statistics

  Given

  Σ(xᵢ-2)=110

  Σxᵢ - 2n =110 ...(1)

  Also

  Σ(xᵢ-5)=20

  Σxᵢ -5n =20 ...(2)

  Subtract (1)-(2)

  3n=90

  n=30

  Put in (1)

  Σxᵢ -60=110

  Σxᵢ=170

  Mean

  =Σxᵢ/n

  =170/30

  =17/3

  Answer    (c) 17/3

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  Explanation

  Question No.    328
  Topic    Continuity & Differentiability

  Given

  f(x)= x/(1+|x|)

  For x>0

  f(x)=x/(1+x)

  Differentiable

  For x<0

  f(x)=x/(1-x)

  Differentiable

  At x=0

  LHD = RHD = 1

  Hence differentiable everywhere

  Set of points

  =(-∞,∞)

  Answer    (a) (-∞,∞)

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  Explanation

  Question No.    329
  Topic    Functions

  Given

  f:R→R

  f(x)=x|x|

  For x≥0

  f(x)=x²

  For x<0

  f(x)=-x²

  Checking One-One

  Every value has unique pre-image

  Hence One-One

  Range

  (-∞,∞)

  Hence Onto

  Therefore

  Function is both one-one and onto

  Answer    (c) Both one-one and onto

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  Explanation

  Question No.    330
  Topic    Differentiation

  Given

  y = axⁿ

  Limit

  lim δy/δx as δx→0

  represents derivative

  dy/dx

  Differentiate

  y=axⁿ

  dy/dx

  = a.n.xⁿ⁻¹

  Answer    (c) anxⁿ⁻¹