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If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=p...

If `"sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi`, show that `xsqrt(1-x^(2))+ysqrt(1-y^(2))+zsqrt(1-z^(2))=2xyz`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

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  2. Let f be defined by f(x)=4x + 3 for all x""inR. Show that it is biject...

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  3. If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi, show that xsqrt(1-x^(2))+ys...

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  4. Prove that int0^(pi/2)lnSinxdx=-pi/2ln2

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  5. Evaluate intfrac[dx][cosx(1+2sinx)]

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  6. Solve the following differential equations (x+tany)dy= sin 2y ""dx

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  7. Express abs((a^2,2ab,b^2),(b^2,a^2,2ab),(2ab,b^2,a^2)) in the form of ...

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  8. If A=[{:(2,1),(-1,3):}],B=[{:(2,3),(1,1):}]andC=[{:(1,0,2),(-2,3,0):}]...

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  9. If f(x)=int0^x e^(2t).sin3tdtthen what is f^1(x)?

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  10. What does the solution set of the inequation 2x+ygt5 represents?

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  11. What is the value of tan(tan^-1""1/2+tan^-1""1/3).

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  12. What is the general solution of tan^-1sqrt(dy/dx)=x?

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  13. Give an example of symmetric matrix.

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  14. If veca and vecb are non-collinear and vecp=xveca+(y+1)vecb,vecq=yveca...

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  15. If y=cos^(-1)((x-1/x)/(x+1/x)),then what is dy/dx?

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  16. What is the restriction on the formula inta^xdx=a^x/(Ina)?

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  17. Write down the symmetric from of the equation of y-axis.

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  18. Solve:"sin"^(-1)2x+"sin"^(-1)x = pi/3.

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  19. Find all possible equivalence relations on X={1,2,3}

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  20. Find the fesible region of the following system:3x-yge0,xge0,yge0

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