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Prove that: |[1, 1, 1],[a, b, c],[a^2, b...

Prove that: `|[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. [{:(1,-2),(3,2):}][{:(x,2),(1,y):}]=[{:(-3,4),(-1,4):}], find x and y...

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  2. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

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  3. Prove that: |[1, 1, 1],[a, b, c],[a^2, b^2, c^2]|=(a-b)(b-c)(c-a)

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  4. If A is square matrix,then prove that A.(adj*A)=absAI.

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  5. If y=sqrt(x+1)Find deltay and dy when X=8 and dx=0.02.

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  6. Shows that the following functions do not possess maximum or minimum. ...

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  7. Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.

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  8. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  9. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  10. Solve xsin""y/xdy=(ysin""y/x-x)dx

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  11. Evaluate int0^(pi/2)sinx/(sinx+cosx)dx.

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  12. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

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  13. Integrate the following int[(2x+1)/sqrt(x^2+10x+29)]dx

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  14. If veca=hati+2hatj-3hatkand vecb=3hati-hatj+2hatk,then find the angle ...

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  15. Find the equation of plane passing through the intersection of the pla...

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  16. Find the co-ordinates of the foot of the perpendicular from the point ...

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  17. Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2

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  18. Prove that the line (x+5)/3=(y+4)/1=(z-7)/-2 and x/1=(y+7)/5=(z-16)/-1...

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  19. Evaluate the following integrals int(3)/(x^3-1)dx

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  20. Show that int0^pixInsinx=pi^2/2In1/2

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