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If 2s=a+b+c show that [[a^2,(s-a)^2,(s...

If 2s=a+b+c show that
`[[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^2,(s-c)^2,c^2]]`=`2s^3(s-a)(s-b)(s-c)`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. A variable plane meets the coordinate axes at A, B, C and is at a cons...

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  2. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  3. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  4. If A=[{:(3,-4),(1,-1):}] then show that A^(k)=[{:(1+2k,-4k),(k,1-2k):}...

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  5. Solve the following system of equations by matrix method x+2y+3z=8, 2x...

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  6. What is the number of solution of the following system: 2x+3y=6, x+y...

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  7. What is int(2x^2+3)/((x^2-1)(x^2+4))dx?

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  8. Write the equation of the plane passing through the point(1,0,0),(0,2,...

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  9. Given an example of a function which is both odd and even function.

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  10. If abs(veca+vecb)=abs(veca-vecb)then what is the angle between vecaand...

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  11. Find the principal value of sin^1(sin"(2pi)/3)

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  12. Find d/dx[e^(x)+sinx/1+logx]

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  13. What is the interval in which y=sinx,x"in[0,2pi]is increasing?

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  14. What is the value of int-1^1xabsxdx

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  15. If cos^-1x+cos^-1y+cos^-1z=pi, prove that x^2+y^2+z^2+2xyz=1.

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  16. Find the domain of the functionf(x)=sqrt(log(12/(x^2-x))).

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  17. Solve the pair of these equationsx+y=10,3x+y=12,

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  18. Show that sin^(-1)(1/sqrt(10))+cos^(-1)(2/sqrt5)=pi/4.

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  19. If a relation R:AtoAis an equivalence relation then prove that R^-1:A ...

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

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