If the radius of the sphere is measured as 9 cm 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

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)

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

If f(x, y) = 2x² - 3xy + 5y + 7 then f(0, 0) and f(1, 1) is _____________

(a)

7, 11

(b)

11, 7

(c)

0, 7

(d)

1, 0

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

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