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Show that: int0^("pi"/2)"\ "sqrt(tan"x")...

Show that: `int_0^("pi"/2)"\ "sqrt(tan"x")` `+"\ "sqrt(cot"x")=sqrt(2)"pi"`

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Discuss the continuity of the following function at x = 0 : "f"("...

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  2. Solve the following differential equation: "x"("dy")/("dx")+"y"="x"lo...

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  3. Show that: int0^("pi"/2)"\ "sqrt(tan"x") +"\ "sqrt(cot"x")=sqrt(2)"pi...

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  4. Prove that the curves "x"="y"^2 and "x y"="k" intersect at right an...

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  5. Using properties of determinants, prove that following |(a+b+2c,a,b),(...

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  6. If |[x+2, 3],[x+5, 4]|=3 , find the value of x

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  7. Let "T" be the set of all triangles in a plane with "R" as relation...

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  8. Show that the points (1,0), (6,0), (0,0) are collinear.

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  9. If "f"("x")=sqrt((sec"x"-1)/(sec+1))" " find "f '"("x")dot Also f...

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  10. If xsqrt(1+y)+ysqrt(1+x)=0, find ("dy")/("dx") . To prove (dy)/(dx)=...

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  11. Find the maximum are of the isosceles triangle inscribed in the ell...

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  12. show that the semi vertical angle of a right circular cone of given ...

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  13. If the equation of a line "A B" is ("x"-3)/1=("y"+2)/(-2)=("z"-5)/4...

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  14. If "f"("x") is an invertible function, find the inverse of "f"("x")...

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  15. If [[(x+3y),y],[7-x,4]]=[(4,-1),(0,1)], find the values of x and y.

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  16. Solve for x: tan^-1((1-x)/(1+x))=1/2 tan^-1 x, x > 0

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  17. Evaluate: int("x"+cos6"x")/(3"x"^2+sin6"x")" dx"

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  18. Form the differential equation representing the parabolas having ve...

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  19. Solve the following differential equation: (3"x y"+"y"^2)"dx"+("x"^...

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  20. If int("e"^("a x")+"b x")"dx"=4"e"^(4"x")+(3"x"^2)/2"\ ","\ " find the...

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