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By using properties of determinants, prove the following `|(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x+4)(4-x)^2`

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By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=k^2(3y+k)

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Solve the following differential equation: (dy)/(dx)+y=cosx-sinx

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  2. Find the particular solution, satisfying the given condition, for t...

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  3. By using properties of determinants, prove the following |(x+4,2x,2x),...

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  4. Write the vector equation of the following line: (x-5)/3=(y+4)/7=(6-z...

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  5. Using integration, find the area of the triangle ABC, coordinates o...

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  6. Find the area of circle 4x^2+4y^2=9 which is interior to the parabo...

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  7. If siny=sin(a+y),\ \ prove that (dy)/(dx)=(sin ^2\ (a+y))/(sina)

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  8. If (cos"x")^y=(sin y)^x , find (dy)/(dx)

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  9. Solve the following differential equation: ((x^2-1)dy)/(dx)+2x y=1/(x...

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  10. Solve the following differential equation: sqrt(1+x^2+y^2+x^2\ y^2)\ ...

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  11. If y=logtan(pi/4+x/2),\ show that (dy)/(dx)=secxdot Also find the ...

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  12. If y=cos^(-1)((2^x+1)/(1+4^x), find (dy)/(dx)

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  13. Evaluate : int0^pi(xtan\ x)/(sec\ x+tan\ x)\ dxdot

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  14. From the following matrix equation, find the value of x:[[x+y,4],[-5,...

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  15. Prove the following: tan[pi/4+1/2cos^(-1)(a/b)]+tan[pi/4-1/2cos^(-1)...

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  16. Form the differential equation representing the family of ellipses ...

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  17. Prove the following, using properties of determinants: |[a+b+2c,a,b],[...

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  18. Find the inverse of A=[[3,-1],[-4,1]] using elementary transformations...

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  19. Using properties of determinants, prove the following |(a^2,ab,ac),(ab...

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  20. If y=(t a n^(-1)\ x)^2 , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...

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