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Using properties of determinants, prove the following: `|[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|=1`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. An urn contains 4 white and 3 red balls. Let X be the number of red ba...

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  2. If y=(sin^(-1)\ x)/(sqrt(1-x^2)) , show that (1-x^2) (d^2\ y)/(dx^2)-...

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  3. Using properties of determinants, prove the following: |[1,1+p,1+p+q],...

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  4. On a multiple choice examination with three possible answers (out o...

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  5. If vec p is a unit vector and ( vec x-\ vec p).( vec x+\ vec p)...

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  6. Let f: NvecN be defined by f(n)={(n+1)/2,\ "if"\ n\ "i s\ o d d"n/2...

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  7. Solve the following differential equation: cos^2x(dy)/(dx)+\ y=tanx

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  8. Solve the following differential equation: x(dy)/(dx)=y-xtan(y/x)

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  9. Find the distance of the point P(6,5,9) from the plane determined b...

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  10. If matrix A=[[1,-1],[-1 ,1]] and A^2=k A , then write the value of k

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  11. Find the points on the line (x+2)/3=(y+1)/2=(z-3)/2\ at a distance ...

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  12. Evaluate: int(x^4\ dx)/((x-1)(x^2+1))

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  13. If y=cos^(-1)((3x+4\ sqrt(1-x^2))/5), find(dy)/(dx)

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  14. Evaluate the following: int1^2(5x^2)/(x^2+4x+3)\ dx

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  15. If y=e^(asin^(-1)x)\ ,\ -1\ lt=x\ lt=1, then show that (1-x^2)\ (d^...

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  16. Find the coordinates of the foot of the perpendicular and the perpen...

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  17. A bag contains 4 balls. Two balls are drawn at random, and are foun...

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  18. One kind of cake requires 300g of flour and 15g of fat, another kin...

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  19. If the length of three sides of a trapezium other than the base is 1...

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  20. Using matrix method, solve the following system of equations: 2/x+...

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