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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 BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Differentiate " "sqrt("tan x")" w"dot"r"dot"t"dot x from first princi...

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  2. Evaluate: (lim)(xvecoo)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 : int("dx")/("x"^3+"x"^2+"x"+1)

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  6. Evaluate int0^2("x"^2+"\ x"+2) as lim it of sums.

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  7. Find the area of the region bounded by the parabola "x"^2=4"y\ " an...

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

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  9. Using properties of determinants, prove the following |(3a,-a+b,-a+c),...

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  10. Solving the following differentia equation: "s i n x"("dy")/("dx")...

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  11. Express the matrix as A=[(1,3,5),(-6,8,3),(-4,6,5)] the sum of a symme...

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  12. Evaluate : int(2"x"dot"tan"^(-1)x)/(1+"x"^4)" dx"

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

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

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

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  16. If "y"=sqrt("x")+1/"x", Show that 2"x"("dy")/("dx")+"y"=2"\ "sqrt("...

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

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

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

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