Eamcet - Maths - Partial Differentiation Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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   Time Left : 00 : 30    : 00

If u=(ax+by)2-(x2+y2) and a2+b2=1 then uxx+uyy=

  

  

  

  

If z(x,y) is the implicit function defined by x3+y3+z3=3xyz then xzx+yzy=

  

  

  

  

If u=x2+y2+z2,x=et,y=et sin t,z=et cos t then du/dt=

  

  

  

  

If f(x,y,z)=√(yz)+ √(zx)+ √(xy) then xfx+yfy+zfz=

  

  

  

  

If f=x2yz+y2zx+z2xy then fxyz=

  

  

  

  

If r2=(x-a)2+(y-b)2 then rxx+ryy=

  

  

  

  

If V=πr2h then rVr+2hVh=

  

  

  

  

If u=3(lx+my+nz)2-(x2+y2+z2) and l2+m2+n2=1 then uxx+uyy+uzz=

  

  

  

  

If f(x,y)=x2Tan-1(y/x)-y2 Tan-1(x/y),x≠0,y≠0 then fxy=

  

  

  

  

If V is the volume of a rectangular box with edges x,y,z then Vxyz=

  

  

  

  

If au+b=a2x+y then uxuy=

  

  

  

  

If f(x,y)=xy+(1/x)+(1/y) then fxx?fyy-fxy2 at (1,1) is

  

  

  

  

If u=(y+sin x)3+(y-sin x)2,then uxx=

  

  

  

  

If u3(1+a3)=8(x+ay+b)3 then u3x+u3y=

  

  

  

  

If Z=1n(1+xr+yr) then Zxy=

  

  

  

  

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