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

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  2. Using vector method prove that cosA=(b^2+c^2-a^2)/(2bc)

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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. Solve the following by matrix method x-y+z=4, 2x+y-3z=0, x+y+z=2

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  5. In any triangle ABC, prove by vector method that frac[a][sinA]=frac[b]...

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  6. Find the distance of the point (3,-4,5)from the plane 2x+5y-6z-19=0 me...

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  7. Prove that the two lines whose direction cosines are connected by the ...

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  8. Integrate the following inte^(cos^2x)sin2x dx

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  9. Solve the differential equation (dy)/(dx)= (y-x+1)/(y+x+5).

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  10. Prove that int0^(pi/2)lnsinxdx=pi/2ln( 1 /2)

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  11. If x=(sin^(3)t)/(sqrt(cos2t)) and y=(cos^(3)t)/(sqrt(cos2t)), then fin...

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  12. Let f:XrightarrowY and g:YrightarrowZ. Prove that gof is bijective if ...

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  13. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  14. Minimize:Z=20x1+10x2 "Subject to": x1+2x2 le 40 3x1 -x2 ge 30 4x1+3x2 ...

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  15. If y=x sin^-1x+xcos^-1x, then what is dy/dx?

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  16. Give an example of a relation which is symmetric and anti-symmetric.

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  17. What is the value of int0^1sin^2tdt+int0^1cos^2tdt-int0^1dr?

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  18. What is the principal value of sin^(-1)(sin((2pi)/3))?

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  19. What is the value of |[i^(103), 3 ,i^(101)],[i^(56), 5, i^(54)],[i^(23...

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  20. What is the value of hata*hatb+hatb*hatc+hatc*hata if hata+hatb+hatc=v...

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