Chapter 8: Differentials and Partial Derivatives - Online Test
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
Answer : Option B
Explaination / Solution:
Q2. The percentage error of fifth root of 31 is
approximately how many times the percentage error in 31?
Answer : Option B
Explaination / Solution:
Q3. If u (
x, y ) = ex2+y2 , then ∂u/∂x
is equal to
Answer : Option B
Explaination / Solution:
Q4. If v (
x, y ) = log(ex + ey
) , then ∂v/∂x + ∂y/∂v is equal to
Answer : Option D
Explaination / Solution:
Q5. If w( x, y
) = xy , x > 0 , then ∂w/∂x is equal to
Answer : Option C
Explaination / Solution:
Q6. If f (
x, y ) = exy, then ∂2f / ∂x∂y is equal to
Answer : Option B
Explaination / Solution:
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
Answer : Option D
Explaination / Solution:
Q8. The change in the surface area S = 6x2 of a cube when the edge
length varies from x0 to x0 + dx is
Answer : Option B
Explaination / Solution:
Q9. The approximate change in the volume V of a cube
of side x metres caused by increasing
the side by 1% is
Answer : Option C
Explaination / Solution:
Q10. If g (
x, y ) = 3x2 − 5 y + 2 y2 , x (t) = et
and y (t) = cos t , then dg/dt
is equal to
Answer : Option A
Explaination / Solution:
