Mathematics - I (3110014) MCQs

MCQs of Partial Derivatives

Showing 1 to 10 out of 43 Questions
1.

The value of lim(x,y)(-1,2)x3+2x2y-3y2 is _____.

(a)

-17

(b)

-7

(c)

-9

(d)

15

Answer:

Option (c)

2.

The points on the curve y2x=2 which is nearest to the origin are _____. 

(a)

(1,±2)

(b)

-1,±2

(c)

2,±2

(d)

-2,±2

Answer:

Option (a)

3.

The gradient of fx,y,z=x3yz at -1,1,2 is _____.

(a)

6,-2,1

(b)

6,2,1

(c)

6,-2,-1

(d)

6,2,-1

Answer:

Option (c)

4.

A function f(x,y) is said to be continuous at point (a,b) if _____.

(a)

f(a,b) must be well define

(b)

lim(x,y)(a,b)f(x,y) must be exist

(c)

lim(x,y)(a,b)f(x,y)=f(a,b)

(d)

All of above

Answer:

Option (d)

5.

Find fP·a¯a¯ , if fx,y,z=xyz , P=-1,1,3 and    a¯=1,-2,2.

(a)

0

(b)

113

(c)

43

(d)

73

Answer:

Option (d)

6.

Number of third order partial derivatives of function of two independent variables is _____.

(a)

9

(b)

8

(c)

4

(d)

2

Answer:

Option (b)

7.

What is the unit vector in the direction of a¯=1,2,2 ?

(a)

1,2,2

(b)

13,23,23

(c)

19,29,29

(d)

13,23,23

Answer:

Option (b)

8.

If u=fr and r2=x2+y2+z2 , then ry= _____.

(a)

yx2+y2+z2

(b)

2x

(c)

2y

(d)

xzx2+y2+z2

Answer:

Option (a)

9.

If f(x,y,z)=x3y2z-2xz+3xy2 then fy= _____.

(a)

2x3yz+6xy

(b)

3x2y2z+6xy

(c)

3x2y2z+3y2

(d)

2x3yz+3y2

Answer:

Option (a)

10.

If fx,y=c be an implicit function, then dydx= _____.

(a)

pq

(b)

-qp

(c)

-fyfx

(d)

-fxfy

Answer:

Option (d)

Showing 1 to 10 out of 43 Questions