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

12th Standard

Reg.No. :
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Maths

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

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