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Verify that "y"="Acos x"-"Bsinx" is sol...

Verify that `"y"="Acos x"-"Bsinx"` is solution of the differential equation `(d^2y)/("dx"^2)+"y"=0`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Evaluate int0^2(2x^2+\ x+5)dx as limit of a sum.

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  2. Solve the following differential equation: ("y"^2- "x"^2)"dy"=3"x y ...

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  3. Verify that "y"="Acos x"-"Bsinx" is solution of the differential eq...

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  4. A window is in the form of a rectangle surmounted by a semi-circle. ...

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  5. An open box, with a square base, is to be made out of a given quanti...

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  6. Find the intervals in which the function "f"("x")="x"^"3"- "12"x^2+ ...

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  7. Evaluate: int sqrt(tan theta) d theta

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  8. Using matrices, solve the following system of equations: 3"x"-"y"+"...

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  9. Differentiate sqrt ("tan x")" w.r.t x from first principle.

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  10. Evaluate: \lim{x\rightarrow \infty }sqrt(x^2+x+1)-x

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  11. Prove that int"o"^"a""f"("x")"dx"=""int"o"^"a""f "("a"-"x")"dx"dot

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  12. Evaluate : int("x"^2+1)/(("x"+1)^2)"dx"

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  13. Evaluate: int1/(1+x+x^2+x^3)\ dx

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  14. Find the coordinates of the point where the line ("x"+1"")/2=("y"+2...

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  15. Using properties of determinants, prove the following: \begin{vmatri...

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  16. Solve the following differential equation: "sinx"("dy")/("dx")+y"co...

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  17. Express the matrix [(7,1,5),(-4,0,3),(-2,6,1)]as the sum of a symmetri...

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  18. Two cards are drawn successively with replacement from a well shuff...

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  19. Find the image of the point (1,2, 3) in the plane "x"+2"y"+4"z"=38

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  20. A and B toss coin alternately till one of them gets a head and wins...

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