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tan{(1/2)sin^(-1)((2x)/(1+x^(2)))+1/2cos...

`tan{(1/2)sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}`.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Give an example of a relation which is not a function.

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  2. Write the integrating factor of the differential equation dy/dx(x+y+1)...

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  3. tan{(1/2)sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}.

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  4. What is the angle between vecaand vecb if abs(veca+vecb)=abs(veca-vecb...

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  5. If M=[(1,1,1),(1,1,1),(1,1,1)],then what is M^50 ?

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  6. Write the value x for which d/dxsin(sin^-1x)=1

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  7. What is the value of int(-1)^(1)ln(frac[4-x][4+x])dx?

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  8. Prove the following statements "cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=...

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  9. Show that if R is an equivalence relation on X then dom R=rngR =X.

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  10. Solve graphically: Maximize Z=5x+6y subject to 2x+3yle6,x, yge0

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  11. Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]

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  12. Let f = {(1,3), (2,4), (3,7)} and g = {(3,2), (4,3), (7,1)} determine ...

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  13. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  14. If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in G...

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  15. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  16. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

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  17. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  18. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

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  19. Prove that d/dxlntan(pi/4+x/2)=secx.

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  20. Determine the point on the curve y = ln x, at which the tangent will b...

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