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If x=tan(1/alogy)\ , show that (1-x^2)(d...

If `x=tan(1/alogy)\ ,` show that `(1-x^2)(d^2\ y)/(dx^2)+(2x-a)(dy)/(dx)=0`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4...

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  2. Using properties of determinants, solve the following for x: |[x-2, ...

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  3. If x=tan(1/alogy)\ , show that (1-x^2)(d^2\ y)/(dx^2)+(2x-a)(dy)/(dx)=...

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  4. Evaluate: int0^(pi/2)(x+sinx)/(1+cosx)

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  5. Solve the following differential equation: x\ dy-y\ dx=sqrt(x^2+y^2...

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  6. Solve the following differential equation: (y+3x^2)(dx)/(dy)=x

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  7. A speaks truth in 60% and Bin 80% of the cases. In what percentage of ...

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  8. If vec a and vec b are two vectors such that | vec a+ vec b|=| vec a...

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  9. In answering a question on a multiple choice test, a student either...

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  10. An urn contains 4 white and 3 red balls. Let X be the number of red...

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

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

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

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

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

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

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

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

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

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

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