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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

Prove: |[a+b+2c, a, b], [c, b+c+2a, b], [c ,a ,c+a+2b]|=2(a+b+c)^3

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

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Using properties of determinants, prove that |[a, a+b, a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]|=a^3

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By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

Using properties of determinants, show that |1 a a^2 -b c 1 b b^2 -c a 1 c c^2 -a b|=0

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Prove the following: tan[pi/4+1/2cos^(-1)(a/b)]+tan[pi/4-1/2cos^(-1)...

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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+1,ab,ac),(...

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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 veca,vecb, vecc are three vectors such that |veca |= 5, |vecb| =...

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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*b=L C M\ (a , b) for all ...

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  11. Evaluate: int(2x)/((x^2+1)(x^2+3))\ dx

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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 defined...

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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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