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If e^y(x+1)=1 , show that (d^2y)/(dx^2)=...

If `e^y(x+1)=1` , show that `(d^2y)/(dx^2)=((dy)/(dx))^2` .

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To solve the problem, we start with the given equation: \[ e^{y(x+1)} = 1 \] ### Step 1: Simplify the equation Since \( e^y \) is equal to 1 when \( y = 0 \), we can rewrite the equation as: \[ e^y = \frac{1}{x + 1} \] ...
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XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. Using the method of integration, find the area of the triangle ABC, c...

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  2. Find the equation of the plane through the line of intersection of t...

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  3. If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .

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  4. Let A=[[2,-1],[3,4]],B=[[5,4],[7,4]],C=[[2,5],[3,8]]. Find a matrix D ...

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  5. If x^my^n = (x + y)^(m+n), prove that (d^2y)/(dx^2)=0.

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  6. Find the area enclosed between the parabola 4y=3x^2 and the straight l...

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  7. A variable plane which remains at a constant distance 3p from the orig...

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  8. Evaluate : int0^(3/2)|xsin pi x| dx

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  9. Determine the value of k for which the following function is continuou...

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  10. Find the distance between the planes 2x – y + 2z = 5 and 5x – 2.5y + ...

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  11. Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1,...

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  12. Find the area bounded by the circle x^2 + y^2 = 16 and the line sqrt3y...

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  13. Using properties of determinants, prove that |(a^2+2a, 2a+1,1), (2a+1,...

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  14. Find the area bounded by the circle x^2 + y^2 = 16 and the line sqrt3y...

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  15. Find the vector equation of line passing through the point (1,2,-4)...

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  16. If |A| = 3 and A^-1 = [(3 -1), (-5/3 2/3)] then write the adj A.

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  17. For what value of k is the function f(x) = { k|x|/x, x<0; 3, x>=0 con...

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  18. Show that the function f given by f(x)=tan^(-1)(sinx+cosx), x" ">" "0 ...

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

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

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