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

12th Standard

Reg.No. :
•
•
•
•
•
•

Maths

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

10 x 1 = 10
1. 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%

2. 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

3. 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)

0.03 xm3

(c)

0.03.x2 m3

(d)

0.03x3m3

4. If w (x, y, z) = x2 (v - 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

5. 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

6. If f(x, y, z) = sin (xy) + sin (yz) + sin (zx) then fxx is

(a)

-y sin (xy) + z2 cos (xz)

(b)

y sin (xy) - z2 cos (xz)

(c)

y sin (xy) + z2 cos (xz)

(d)

-y sin (xy) - z2 cos (xz)

7. If f (x, y) = x3 + y3 - 3xythen $\frac { { \partial }f }{ \partial { x } }$ at x = 2,

(a)

-15

(b)

15

(c)

-9

(d)

16

8. The approximate value of (627)$\frac14$ is ................

(a)

5.002

(b)

5.003

(c)

5.005

(d)

5.004

9. 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)

$\frac{22}{14}$

10. 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