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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. With 4 different elements how many different determinant of order 2 ca...

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  2. What is the value of a so that 6hati+2hatj-3hatk and hati-4hatj+ahatk...

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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. Find the feasible solution region of the following system:-x+yge-1,x+y...

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  5. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

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  6. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

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  7. If A+B+C=pi,then show that Abs((-1,cosC,cosB),(cosC,-1,cosA),(cosB,cos...

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  8. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  9. If A=[(1,2),(2,3),(3,4)]and B=[(2,3,0),(1,2,3)],then verify that (AB)^...

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  10. Find A^-1 if A=[(4,-1),(2,3)]

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  11. Express[(3,-1,0),(2,2,5),(1,3,2)]as sum of a symmetric and a skew symm...

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  12. Find the point on the curve x^2 + y^2 - 4xy + 2 = 0 where the normal...

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  13. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  14. Find the interval where f(x)=sinx,x in[0,2pi] increasing.

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  15. If siny=xcos(a+y),show that dy/dx=cos^2(a+y)/cosaand find the value of...

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  16. Determine the area of the region bounded by y^2=x^3 and the double ord...

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  17. int(xe^x)/(1+x^2)dx

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  18. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

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  19. Find the solution of the following differential equations: xdy/dx+sqrt...

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  20. int(pi//6)^(pi//3)dx/(1+sqrtcotx)

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