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Chapter 8: Differentials and Partial Derivatives
- Online Test
Chapter 8: Differentials and Partial Derivatives
TEST : 1
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q1.
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%
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Answer :
Option B
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q2.
The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?
A.
1/31
B.
1/5
C.
5
D.
31
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Answer :
Option B
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q3.
If
u
(
x, y
) = e
^{x2+y2}
, then ∂u/∂x is equal to
A.
e
^{x2+y2}
B.
2
xu
C.
x
^{2}
u
D.
y
^{2}
u
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Answer :
Option B
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q4.
If
v
( x,
y
) = log(e
^{x}
+ e
^{y}
) , then ∂
v
/∂
x
+ ∂
y/∂v
is equal to
A.
e
^{x}
+ e
^{y}
B.
1 / e
^{x}
+ e
^{y}
C.
2
D.
1
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Answer :
Option D
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q5.
If w(
x, y
) =
x
^{y}
,
x
> 0 , then ∂w/∂
x
is equal to
A.
x
^{y}
log
x
B.
y
log
x
C.
yx
^{y}
^{−1}
D.
x
log
y
View Solution
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Answer :
Option C
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q6.
If
f
( x,
y
) = e
^{xy}
, then ∂
^{2}
f /
∂x∂y is equal to
A.
xye
^{xy}
B.
(1 + xy)e
^{xy}
C.
(1 +
y
) e
^{xy}
D.
(1 +
x
) e
^{xy}
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q7.
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
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Answer :
Option D
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q8.
The change in the surface area S = 6
x
^{2}
of a cube when the edge length varies from
x
_{0}
to
x
_{0}
+
dx
is
A.
12
x
_{0}
+
dx
B.
12
x
_{0}
dx
C.
6
x
_{0}
dx
D.
6
x
_{0 }
+
dx
View Solution
Add Work Space
Answer :
Option B
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q9.
The approximate change in the volume V of a cube of side
x
metres caused by increasing the side by 1% is
A.
0.3x
dx
m
^{3}
B.
0.03
x
m
^{3}
C.
0.03
x
^{2}
m
^{3}
D.
0.03
x
^{3}
m
^{3}
View Solution
Add Work Space
Answer :
Option C
Explaination / Solution:
# Chapter 8: Differentials and Partial Derivatives
# TN 12th Maths
Prepare / Learn
Q10.
If
g
( x,
y
) = 3x
^{2}
− 5
y
+ 2
y
^{2}
,
x
(t) = e
^{t}
and
y
(t) = cos t , then
dg
/
dt
is equal to
A.
6e
^{2t}
+ 5sin t − 4 cos t sin t
B.
6e
^{2t}
− 5sin t + 4 cos t sin t
C.
3e
^{2t}
+ 5sin t + 4 cos t sin t
D.
3e
^{2t}
− 5sin t + 4 cos t sin t
View Solution
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Answer :
Option A
Explaination / Solution:
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