A circular template has a radius of 10 cm. The measurement of radius has an approximate error of 0.02 cm. Then the percentage error in calculating area of this template is

(a)

0.2%

(b)

0.4%

(c)

0.04%

(d)

0.08%

If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is

(a)

0.4 cu.cm

(b)

0.45 cu.cm

(c)

2 cu.cm

(d)

4.8 cu.cm

The approximate change in the volume V of a cube of side x metres caused by increasing the side by 1% is

(a)

0.3xdx m³

(b)

0.03x m³

(c)

0.03x² m³

(d)

0.03x³ m³

If w (x, y, z) = x² (y - z) + y² (z - x) + z²(x - y), then \(\frac { { \partial }w }{ \partial x } +\frac { \partial w }{ \partial y } +\frac { \partial w }{ \partial z } \) is

(a)

xy + yz + zx

(b)

x(y + z)

(c)

y(z + x)

(d)

0

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

(a)

-15

(b)

15

(c)

-9

(d)

16

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

(a)

5.002

(b)

5.003

(c)

5.005

(d)

5.004

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 sin x then \(\frac { { \partial }^{ 2 }u }{ \partial x\partial y } \) = ..........

(a)

cos x

(b)

cos y

(c)

sin x

(d)

0