Will you please provide me question paper for IIT JAM joint admission mathematics subject in PDF file format ?

Here I am giving you question paper for IIT JAM joint admission mathematics subject in PDF file attached with it so you can get it easily.

Q.18 (a) Show that the point (0,0) is neither a point of local minimum nor a point of local maximum for the functiongiven by 2:f→ 422(,)34fxyxxyy=−+ for ()2,.xy∈ (6)

(b) Find all the critical points of the function given by for2:f→
()33,31240fxyxyxy=+−−+()2,xy∈ . Also, examine whether the function attains a local maximum or a local minimum at each of these critical points. f(9)

Find the area of the portion of the surface 2zxy2 =− in which lies inside the solid cylinder. 3 221xy+≤(

Let be the position vector field in and let be a differentiable function. Show that ˆˆˆrxiyjzk=++ 3 :f→ (){}0for0frrr∇×= ≠
. (6) (b) Let be the region inside the solid cylinder W224xy+≤ between the plane 0z= and the paraboloid Let be the boundary of Using Gauss’s divergence theorem, evaluate 2.zxy=+ 2 S.Wˆ,SFndS⋅∫∫ where ()()()222ˆˆˆ432Fxyixyjxzz=+−+++
k
and is the outward unit normal vector to ˆn.S

IIT JAM Mathematics Question paper

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