If y = x⁴ - 10 and if x changes from 2 to 1.99, the approximate change in y is ________

(a)

-32

(b)

-0.32

(c)

- 10

(d)

10

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

If u = x^y + y^x then u_x + u_y at x = y = 1 is _____________

(a)

0

(b)

2

(c)

1

(d)

∞

lf u = (x-y)⁴+(y-z)⁴ +(z-x)⁴ then \(\sum { \frac { \partial u }{ \partial x } } \) = _____________

(a)

4

(b)

1

(c)

0

(d)

-4

If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then f_xx is _____________

(a)

-y sin (xy) + z² cos (xz)

(b)

y sin (xy) - z² cos (xz)

(c)

y sin (xy) + z² cos (xz)

(d)

-y² sin (xy) - z² cos (xz)

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) = x³ + y³ - 3xy² then \(\frac { { \partial }f }{ \partial { x } } \) at x = 2,_____________

(a)

-15

(b)

15

(c)

-9

(d)

16

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

The approximate value of (627)^\(\frac14\) is ................

(a)

5.002

(b)

5.003

(c)

5.005

(d)

5.004

The cube root of 127 is ............

(a)

5.026

(b)

5.26

(c)

5.028

(d)

5.075

If y = sin x and x changes from \(\frac{\pi}{2}\) to ㅠ the approximate change in y is ..............

(a)

0

(b)

1

(c)

\(\frac{\pi}{2}\)

(d)

\(\frac{22}{14}\)

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

(a)

xy^x-1

(b)

yx^y-1

(c)

0

(d)

1

If u = sin-1 \(\left( \frac { { x }^{ 4 }+{ y }^{ 4 } }{ { x }^{ 2 }+{ y }^{ 2 } } \right) \) and f = sin u then f is a homogeneous function of degree ..................

(a)

0

(b)

1

(c)

2

(d)

4

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