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If y=A e^(m x)+B e^(n x), show that (d^2...

If `y=A e^(m x)+B e^(n x),` show that `(d^2y)/(dx^2)-((m+n)dy)/(dx)+m n y=0.`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Find the area enclosed by the parabola 4y=3x^2 and the line2y = 3x + ...

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  2. Find the projection of the vector vec a=2 hat i+3 hat j+2 hat k on th...

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  3. If y=A e^(m x)+B e^(n x), show that (d^2y)/(dx^2)-((m+n)dy)/(dx)+m n y...

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  4. Find : int(x+3)/(sqrt(5-4x-2x^2))dx

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  5. Find the shortest distance between the following lines: vec r=2 hat i...

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  6. For what value of lambda the function defined by f(x)={lambda(x^2+2),i...

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  7. If x=a e^t(sint+cost) and y=a e^t(sint-cost), prove that (dy)/(dx)=(x+...

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  8. Evaluate : int0^(pi/4)log(1+tanx)dxdot

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  9. Find : intx/((x-1)^2(x+2))dx

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  10. A point on the hypotenuse of a right triangle is at distances a and b ...

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  11. int[x+2]/[2x^2+6x+5].dx

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  12. Write the sum of the order and degree of the differential equation 1+...

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  13. Two schools A and B decided to award prizes to their students for thre...

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  14. If A=(1 2 3-1)a n dB=(1 3-1 1), write the value of |A B| .

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  15. Write the differential equation obtained by eliminating the arbitrary ...

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  16. If vec a and vec b are unit Vectors, then what is the angle betwe...

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  18. Find a Vector in the direction of vec a= hat i-2 hat j that has magni...

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  19. Let A = R × R and * be the binary operation on A defined by (a, b) ...

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  20. Find the inverse of the matrix A=[1 3 3 1 4 3 1 3 4]

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