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12th Standard Maths Differentials and Partial Derivatives English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. If v (x, y) = log (ex + ev), then \(\frac { { \partial }v }{ \partial x } +\frac { \partial v }{ \partial y } \) is equal to

    (a)

    ex + ey

    (b)

    \(\frac{1}{e^x + e^y}\)

    (c)

    2

    (d)

    1

  2. If f (x, y) = exy then \(\frac { { \partial }^{ 2 }f }{ \partial x\partial y } \) is equal to

    (a)

    xyexy

    (b)

    (1 +xy)exy

    (c)

    (1 +y)exy

    (d)

    (1 + x)exy

  3. If u(x, y) = x2+ 3xy + y - 2019, then \(\frac { \partial u }{ \partial x } \)(4, -5) is equal to

    (a)

    -4

    (b)

    -3

    (c)

    -7

    (d)

    13

  4. If the radius of the sphere is measured as 9 em with an error of 0.03 cm, the approximate error in calculating its volume is

    (a)

    9.72 cm3

    (b)

    0.972 cm3

    (c)

    0.972π cm3

    (d)

    9.72π cm3

  5. If u = log \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \), then \(\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +\frac { { \partial }^{ 2 }u }{ { \partial y }^{ 2 } } \) is

    (a)

    \(\sqrt { { x }^{ 2 }+{ y }^{ 2 } } \)

    (b)

    0

    (c)

    u

    (d)

    2u

  6. If u = log (x3 + y3 + z3 - 3xyz) then \(\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z } \) =

    (a)

    \(\frac { 3 }{ x+y+z } \)

    (b)

    x+y+z

    (c)

    \(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

    (d)

    \(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

  7. If u = yx then \(\frac { \partial u }{ \partial y } \) = ............

    (a)

    xyx-1

    (b)

    yxy-1

    (c)

    0

    (d)

    1

  8. If x = r cos θ, y = r sin, then \(\frac { \partial r }{ \partial x } \) = ....................

    (a)

    sec θ

    (b)

    sin θ

    (c)

    cos θ

    (d)

    cosec θ

  9. If u = \((\frac{y}{x})\) then x \(x\frac { \partial u }{ \partial x } +y\frac { \partial u }{ \partial y } \) = .....................

    (a)

    0

    (b)

    1

    (c)

    2u

    (d)

    u

  10. If is a homogeneous function of x and y of degree n, then \(x\frac { { \partial }^{ 2 }u }{ \partial { x }^{ 2 } } +y\frac { { \partial }^{ 2 }u }{ \partial x\partial y } \) = .............. \(\frac { { \partial }u }{ \partial { x } } \)

    (a)

    n

    (b)

    0

    (c)

    1

    (d)

    n - 1

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