Partial Differentiation MCQ

Test your knowledge with important Partial Differentiation MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Partial Differentiation MCQs at Bissoy

• The happiness(H) of a person depends upon the money he earned(m) and the time spend by him with his family(h) and is given by equation H=f(m,h)=400mh2 whereas the money earned by him is also depends upon the time spend by him with his family and is given by m(h)=√(1-h2). Find the time spend by him with his family so that the happiness of a person is maximum.
  ক

  √(1⁄3)

  খ

  √(2⁄3)

  গ

  √(4⁄3)

  ঘ

  0
• If u = xx + yy + zz , find du⁄dx + du⁄dy + du⁄dz at x = y = z = 1.
  ক

  1

  খ

  0

  গ

  2u

  ঘ

  u
• Necessary condition of euler’s theorem is _________
  ক

  z should be homogeneous and of order n

  খ

  z should not be homogeneous but of order n

  গ

  z should be implicit

  ঘ

  z should be the function of x and y only
• If z = xn f(y⁄x) then?
  ক

  y ∂z⁄∂x + x ∂z⁄∂y = nz

  খ

  1/y ∂z⁄∂x + 1/x ∂z⁄∂y = nz

  গ

  x ∂z⁄∂x + y ∂z⁄∂y = nz

  ঘ

  1/x ∂z⁄∂x + 1/y ∂z⁄∂y = nz
• In euler theorem x ∂z⁄∂x + y ∂z⁄∂y = nz, here ‘n’ indicates?
  ক

  order of z

  খ

  degree of z

  গ

  neither order nor degree

  ঘ

  constant of z
• Differentiation of function f(x,y,z) = Sin(x)Sin(y)Sin(z)-Cos(x) Cos(y) Cos(z) w.r.t ‘y’ is?
  ক

  f’(x,y,z) = Cos(x)Cos(y)Sin(z) + Sin(x)Sin(y)Cos(z)

  খ

  f’(x,y,z) = Sin(x)Cos(y)Sin(z) + Cos(x)Sin(y)Cos(z)

  গ

  f’(x,y,z) = Cos(x)Cos(y)Cos(z) + Sin(x)Sin(y)Sin(z)

  ঘ

  f’(x,y,z) = Sin(x)Sin(y)Sin(z) + Cos(x)Cos(y)Cos(z)
• f(x, y) = sin(xy + x3y) / x + x3 Find fxy at (0,1).
  ক

  2

  খ

  5

  গ

  1

  ঘ

  undefined
• f(x, y) = sin(y + yx2) / 1 + x2 Value of fxy at (0,1) is
  ক

  0

  খ

  1

  গ

  67

  ঘ

  90
• The gradient of a function is parallel to the velocity vector of the level curve.
  ক

  True

  খ

  False
• The existence of first order partial derivatives implies continuity.
  ক

  True

  খ

  False
• f(x, y) = sin(xy) + x2 ln(y) Find fyx at (0, π⁄2)
  ক

  33

  খ

  0

  গ

  3

  ঘ

  1
• f(x, y) = x2 + xyz + z Find fx at (1,1,1)
  ক

  0

  খ

  1

  গ

  3

  ঘ

  -1
• Which of the following relations hold true?
  ক

  i × i = j × j = k × k = 1

  খ

  i × j = k, j × i = -k

  গ

  i × i = j × j = k × k = -1

  ঘ

  k × i = -j, i × k = j
• Find the range in which the function f(x) = 8 + 40x3 – 5x4 – 4x5 is increasing.
  ক

  2<z<0, 0<z<3

  খ

  1<z<0, 0<z<2

  গ

  3<z<0, 0<z<2

  ঘ

  3<z<0, 0<z<4
• The total derivative is the same as the derivative of the function.
  ক

  True

  খ

  False
• The symbol used for partial derivatives, ∂, was first used in mathematics by Marquis de Condorcet.
  ক

  True

  খ

  False
• The determinant of the matrix whose eigen values are 6, 4, 3 is given by ___________
  ক

  3

  খ

  24

  গ

  72

  ঘ

  13