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Prove that int"o"^"a""f"("x")"dx"=""in...

Prove that `int_"o"^"a""f"("x")"dx"=""int_"o"^"a""f "("a"-"x")"dx"dot`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Differentiate sqrt ("tan x")" w.r.t x from first principle.

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

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

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

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

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

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

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

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

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

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

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

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  13. If y=tan^(-1)((sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))) fin...

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  14. Differentiate (x^2+\ 1) with respect to x from first principle.

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  15. Evaluate : int(sinx)/((1-cosx)\ (2-cosx)\ dx

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  16. Using matrices, solve the following system of equations : x+2y-3z=6...

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  17. If y=sin(logx), prove that x^2(d^2y)/(dx^2)+\ x(dy)/(dx)+\ y=0

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  18. Verify Rolle's theorem for the function f(x)=\ x^2-5x+4\ on [1, 4].

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  19. Find the projection of vec b+ vec c on vec a where vec a=2 hat i-\...

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  20. Evaluate int0^2(x^2+\ 2x+1)dx as limit of a sum.

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