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If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z...

If `[[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0`
then prove that xyz=1 when x,y,z are non zero and unequal.

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SHARAM PUBLICATION-MODEL QUESTION PAPER -15-EXERCISE
  1. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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  2. Find two positive numbers whose product is 256 and whose sum is least.

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  3. Integrate:inta/(b+ce^x)dx

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  4. Integrate:int sec(sqrtx)/(sqrtx)dx

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  5. Prove that int0^(pi/2)(sin^nx)/(sin^nx+cos^nx)dx=pi/4

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  6. Find the area bounded by y=sinx,y=0,x=pi/2

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  7. Solve : (x+y)dy +(x-y)dx = 0.

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  8. If hati +hatj+hatk and 2hati -alphahatj+3hatk are orthogonal to each o...

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  9. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  10. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

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  11. If veca=2vecb and vecc=-3vecb, then what is the angle between veca and...

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  12. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

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  13. Find the value of k for which f(x)={{:((sqrt(1+kx)-sqrt(1-kx))/(x)", ...

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  14. Find the derivative of ((x-1)/(x^2+5))^-4 cos^-1((1-x^2)/(1+x^2))

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  15. Use the function f(x) = x^(1/x),x gt 0 to show that e^pi )grt pi^e.

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  16. Find the area enclosed by y=4x-1 and y^(2)=2x.

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  17. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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  18. Show that the inverse of a bijective function is unique.

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  19. Prove the following "tan"^(-1)(2a-b)/(bsqrt(3))+"tan"^(-1)(2b-a)/(as...

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  20. Solve the following LPP graphically Maximizez=20x+10y Subject to x+2...

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