QUESTION BANK (OBJECTIVE TYPE)
MA1001-CALCULUS AND SOLID GEOMETRY
UNIT-II-FUNCTIONS OF SEVERAL VARIABLES
1. If Z=
+3
then what is
(i) 2y+3x (ii) 3y
2. u=
(iii) 2x+3y
(iv) 2x
is homogeneous function of degree
(i) 2
3.If u=a
?
(ii) 3
+2hxy+b
(iii) 1
then using Euler’s theorem find x
(i) u
(ii) 2u
4. If f(x , y) =
then what is
(i)-e
(ii)
5. if z= log (
(i) 1
+xy+
(iii) 3u
) then what is x
(ii)
+y
9. If f (x , y) =
(iv)
=?
(iii)
(iv)
?
(ii) -1
(iii) 0
8. If f (x , y) = cosxcosy then
(i) 1
(iv)-
=?
(iii) 2
(ii)
(ii) 0
then
(iv) 2
(0, 0)=?
(iii) -1
(1 , 1) is
=?
(iv) n(n-1)
(iii)e
7. If f(x , y) =
(i) 1
+y
(1 , 1) ?
6.If f(x,y) is an implicit function then
(i)
(iv) 4
(iv)
(i)
10. If rt -
(ii) ½
(iii) – ½
(iv) 0
at ( a , b ) then the point is
(i) Maximum point (ii) minimum point (iii) saddle point (iv) none of these
11. The stationary points of
(i) (-3 , 0)
12. If x=
(ii) ( 0 , 3)
(ii) 2(
and y=r
(i)
14. If v=
(i) 1+
(iii) ( 0 , -3)
and y=2uv then J
(i)
13. If x=r
are
is
(iii) 4(
Then what is
(ii) r
+
(iv) ( 3 , 0 )
then
(iv) 4
=?
(iii) 2r
(iv) 0
(iii)
(iv) 1+
is
(ii)
15.u and v are functionally dependent if their jacobian value is
(i)zero
(ii)one
16.if
and
(i)0
=
(iii)non-zero
then
(ii)1
(iv)greater than zero
=?
(iii)-1
(iv)2
17.The stationary points of f(x,y)=
(i)
are
(ii)
18.The point (0,0) for f(x, y)=
is
(i)a maximum point (ii) a minimum point (iii)a saddle point (iv)none of
these
19.If f(x, y)=
(i) r
where x= rcos
(ii)
and y= rsin then
(iii) 1
(iv) 0
is
20.If f(x, y)=
y+siny+
(i)2 -e
then
(1, ) is
(ii)2π
21. u =
(iii)2π+e
is homogeneous function of degree
(ii) 1
22. If u =
(i) -3
(i)2r
25.If u=
(i)2x
(iii) 2
then x
(i) sinu
23. If u =
(iv) 0
+y =?
(ii) cosu
,v=
(iv) 3
(iii) sin2u
(iv) tanu
(ii) 3
(iii) -
(iv)
, y= r
z=z then
then
= ?
(ii)
and v=x+y then
(ii) 2x+2
=?
(iv)r
(iii)
=?
(iii) 2y-2
(iv) 2x - y
ANSWERS
1.(iii) 2x+3y
2. (iii) 1
3. (ii) 2u
4.(iii)e
5. (iii) 2
6.i)
7. (iii) 0
8. (iii) – 1
9. (ii) ½
10. (iii) saddle point
11. (i) (-3 , 0)
12. (iii) 4(
13. (ii) r
14. (iii)
15. (i)zero
16. (ii)1
17. (ii)
18. (iii) a saddle point
19. (iv) 0
20. (iii)2π+e
21.
22. (iii) sin2u
23. (iii) 24. (iv)r
25. (ii) 2x+2