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If x,y,z are positive and are the pth, q...

If x,y,z are positive and are the pth, qth and rth terms of a G.P. then prove that
`|[logx,p,1],[logy,q,1],[logz,r,1]|=0`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Factorize the following. [[a,b,c],[b+c,c+a,a+b],[a^2,b^2,c^2]]

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  2. Find B if B^(2)=[{:(17,8),(8,17):}]

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  3. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

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  4. Find the adjoint matrix of the matrix [[2,5],[1,4]]

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  5. Solve the following : [[x,1,3],[1,x,1],[3,6,3]]=0

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  6. Find the point on the curve y^2 - x^2 + 2x - 1 =0 where the tangent ...

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  7. Find (dy)/(dx), if y=tan^(-1)((cosx)/(1+sinx)).

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  8. Find the equation of the tangent and normal to the curve y(x-2)(x-3)-x...

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  9. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  10. If y=x+frac[1][x+frac[1][x+...infty]] find frac[dy][dx], the rhs bein...

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  11. Solve (x+y+1)frac[dy][dx]=1

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  12. Integrate intfrac[tanx+tanalpha][tanx-tanalpha]dx

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  13. Integrate the following int0^1x^7/sqrt(1-x^2)dx

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  14. Find the area of the circle x^2+y^2=2ax.

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  15. int0^2[x^2]dx

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  18. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

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  19. The plane 4x+7y+4z+81=0 is rotated through a right angle about its lin...

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  20. Find the equation of lines joining the points. (4,-6,1) and (0,3,-1)

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