Exercise 8.8: Choose the correct answer

EXERCISE 8.8

Choose the correct or the most suitable answer from the given four alternatives :

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

(1) 0.2%

(2) 0.4%

(3) 0.04%

(4) 0.08%

2. The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

(1) 1/31

(2) 1/5

(3) 5

(4) 31

3. If u ( x, y ) = ex2+y2 , then ∂u/∂x is equal to

(1) ex2+y2

(2) 2xu

(3) x2u

(4) y2u

4. If v ( x, y ) = log(ex + ey ) , then ∂v/∂x + ∂y/∂v is equal to

(1) ex + ey

(2) 1 / ex + ey

(3) 2

(4) 1

5. If w( x, y ) = xy , x > 0 , then ∂w/∂x is equal to

(1) xy log x

(2) y log x

(3) yxy−1

(4) x log y

6. If f ( x, y ) = exy, then ∂2f / âˆ‚x∂y is equal to

(1) xyexy

(2) (1 + xy)exy

(3) (1 + y ) exy

(4) (1 + x ) exy

7. 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

(1) 0.4 cu.cm

(2) 0.45 cu.cm

(3) 2 cu.cm

(4) 4.8 cu.cm

8. The change in the surface area S = 6x2 of a cube when the edge length varies from x0 to x0 + dx is

(1) 12x0 + dx

(2) 12 x0 dx

(3) 6 x0 dx

(4) 6 x0 + dx

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

(1) 0.3xdx m3

(2) 0.03x m3

(3) 0.03x2 m3

(4) 0.03x3 m3

10. If g ( x, y ) = 3x2 âˆ’ 5 y + 2 y2 , x (t) = et and y (t) = cos t , then dg/dt is equal to

(1) 6e2t + 5sin t − 4 cos t sin t

(2) 6e 2t âˆ’ 5sin t + 4 cos t sin t

(3) 3e2t + 5sin t + 4 cos t sin t

(4) 3e2t âˆ’ 5sin t + 4 cos t sin t

11. If f (x) = x / x+1 , then its differential is given by

Answers: (2)

12. If u ( x, y ) = x2 + 3xy + y âˆ’ 2019 , then ∂u/∂x|(4,−5) is equal to  

(1) −4

(2) −3

(3) −7

(4) 13

13. Linear approximation for g ( x) = cos x at x = Ï€/2 is

(1) x + π/2

(2) − x + Ï€/2

(3) x â€“ Ï€/2

(4) − x â€“ Ï€/2

14. If w( x, y , z) = x2 ( y − z ) + y2 ( z − x) + z2 ( x − y) , then ∂w/∂x + ∂w/∂y + âˆ‚w/∂z is

(1) xy + yz + zx

(2) x ( y + z)

(3) y ( z + x)

(4) 0

15. If f ( x, y , z) = xy + yz + zx , then fx âˆ’ fz is equal to

(1) z âˆ’ x

(2) y − z

(3) x − z

(4) y − x