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If y=e^(tan^-1x), prove that (1+x^2)y2+(...

If `y=e^(tan^-1x),` prove that `(1+x^2)y_2+(2x-1)y_1=0`

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If logy=tan^(-1)x , show that (1+x^2)y_2+(2x-1)y_1=0 .

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If y=(sin^(-1)x)^2 ,prove that (1-x^2)y_2-x y_1-2=0.

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. Show that the function f given by f(x)=tan^(-1)(sinx+cosx), x" ">" "0 ...

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  2. Find the matrix X so that X[[1, 2, 3],[ 4 ,5, 6]]= [[-7,-8,-9],[2,4,6]...

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  3. If y=e^(tan^-1x), prove that (1+x^2)y2+(2x-1)y1=0

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  4. Find int e^(2x) sin (3x + 1) dx

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  5. Given =[(2,-3),(-4, 7)] , compute A^(-1) and show that 2A^(-1)=9I-A .

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  6. Differentiate tan^(-1)((1+cosx)/sinx) with respect to x

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  7. Find the value of tan^(-1) sqrt3 - cot^(-1) (-sqrt3)

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  8. The total cost C(x) in Rupees, associated with the production of x ...

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  9. Integrate the functions (cos2x+2sin^2x)/(cos^2x)

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  10. Find the differential equation representing the family of curves y=ae^...

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  11. If the matrix A = [[0,a,-3],[2,0,-1],[b,1,0]] is skew symmetric, find ...

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  12. If theta is the angle between two vectors hati-2hatj+3hatk and 3hati-2...

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  13. Find the magnitude of each of the two vectors veca and vec b having th...

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  14. A black and a red dice are rolled. (a)   Find the conditional proba...

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  15. Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1...

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  16. Find (dy)/dx, if (x^2+y^2)^2=xy

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  17. If a * b, denoted the larger of 'a' and 'b' and if a o b = a*b + 3 , ...

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  18. If x=a(2theta-sin2theta) and y=a(1-cos2theta) find (dy)/(dx) when thet...

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  19. If y="sin"(sinx),"p r o v et h a t" (d^2y)/(dx^2)+tanx(dy)/(dx)+yco...

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  20. Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]

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