Mathematics - II (3110015) MCQs

MCQs of Vector Calculus

Showing 1 to 10 out of 79 Questions
1.
If fx,y,z=3x2y+2y-3z, then f=
(a) 6x2y,3x2,3
(b) 6xy,3x2+2,3
(c) 6xy,3x2,-3
(d) 6xy,3x2+2,-3
Answer:

Option (d)

2.
The gradient of a scalar function ϕ(x,y,z) is
(a) 2ϕx2i^+2ϕy2j^+2ϕz2k^
(b) ϕx+ϕy+ϕz
(c) ϕxi^+ϕyj^+ϕzk^
(d) 2ϕx2+2ϕy2+2ϕz2
Answer:

Option (c)

3.
Let r¯=xi^+yj^+zk^ and r=r¯. Then er=
(a) err
(b) err¯
(c) errr¯
(d) e-rr r¯
Answer:

Option (c)

4.
Let r¯=xi^+yj^+zk^ and r=r¯. Then logr=
(a) 1r2r
(b) logrrr
(c) 1rr
(d) r
Answer:

Option (a)

5.
If F=f1x,y,zi^+f2x,y,zj^+f3x,y,zk^ is a vector function, then the divergence of F is
(a) 2f1x2i^+2f2y2j^+2f3z2k^
(b) f1x+f2y+f3z
(c) f1xi^+f2yj^+f3zk^
(d) 2f1x2+2f2y2+2f3z2
Answer:

Option (b)

6.
The divergence of a vector function A=3x2i^+5xy2j^+xyz3k^ is
(a) 6x2+10xy+3xyz
(b) 6x2i^+10xyj^+3xyzk^
(c) 6x+10xy+3xyz2
(d) 6x+5xy+3xyz2
Answer:

Option (c)

7.
The divergence of a vector field F=x2y,y2,z2x at a point -1,2,3 is
(a) -5
(b) 10
(c) 14
(d) -6
Answer:

Option (d)

8.
If F=exyi^-cosyj^+sinz2k^, then ·F=
(a) yexy-siny-sin2z
(b) yexy+cosy+sin2z
(c) 0
(d) yexy+siny+sin2z
Answer:

Option (d)

9.
For the scalar function f, div(grad f) is equal to
(a) fxi^+fyj^+fzk^
(b) 0
(c) 2fx2+2fy2+2fz2
(d) 2fx2i^+2fy2j^+2fz2k^
Answer:

Option (c)

10.
If ϕx,y,z=xyz-2y2z+x2z2, then ·ϕ at the point (2,4,1) is
(a) 6
(b) 16
(c) -6
(d) 0
Answer:

Option (a)

Showing 1 to 10 out of 79 Questions