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Prove the following, using properties of...

Prove the following, using properties of determinants: `|[a+b+2c,a,b],[c,b+c+2a,b],[c,a,c+a+2b]|=2(a+b+c)^3`

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Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

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3. Using properties of determinants, show that :|[b+c,a,b] , [c+a,c,a] , [a+b,b,c]| = (a + b + c) (a-c)^2

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Using properties of determinants, prove that: |[b^2+c^2,a^2,a^2],[b^2,c^2+a^2,b^2],[c^2,c^2,a^2+b^2]|=4a^2b^2c^2

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
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  2. Form the differential equation representing the family of ellipses ...

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

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

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

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  6. 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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  7. If ā,b,c are three vectors such that |veca |= 5, |vecb| = 12 and | ...

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  8. Solve the following differential equation: 2x^2(dy)/(dx)-\ 2x y+y^2=0

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  9. Find the particular solution of the following differential equation...

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  10. Let * be a binary operation of N given by a a*b=L C M\ (a , b) for all...

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  12. Evaluate: int(5x+3)/(sqrt(x^2+4x+10))\ dx

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  13. Find the Vector and Cartesian equations of the line passing through...

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  14. Evaluate : int((x-4)e^x)/((x-2)^3)\ dx

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  15. Show that y=log(1+x)-(2x)/(2+x), x gt 1 is an increasing function of x...

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  16. Find the equation of the normal at the point (a m^2, a m^3) for the ...

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  17. Evaluate : int(e^x)/(sqrt(5-4e^x-\ e^(2x)))\ dx

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  18. Find the relationship between a and b so that the function f define...

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  19. If x^y=e^(x-y), show that (dy)/(dx)=(logx)/({log(x e)}^2)

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  20. Obtain the inverse of the following matrix, using elementary operation...

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