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Using properties of definite integrals, prove the following : `int_o^pi(xtanx)/(secx\ cos e c\ x)\ dx=(pi^2)/4`

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

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  2. Using integration, find the area of the region enclosed between the...

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  3. Using properties of definite integrals, prove the following : into...

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  4. Evaluate: intcos4x cos3x\ dx

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

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  6. A card is drawn at random from a well-shuffled pack of 52 cards. Fi...

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  7. Solve the following differential equation : xcosy\ dy=(x e^xlogx+e^x)...

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  8. If A=[(2,-3),(3,4)], show the A^2-6A+17I=0. Hence find A^-1

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  9. Using the properties of determinants, prove that following |(a-b,-c^2,...

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  10. An urn contains 7 red and 4 blue balls. Two balls are drawn at rand...

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  11. Find the equation of the sphere passing through the points (3,0,0), (0...

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  12. Find the equation of the plane which is perpendicular to the plane ...

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  13. A particle starting with initial velocity of 30 m/sec moves with a ...

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  14. Find the value of lambda which makes the vectors vec a ,\ vec b a...

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  15. A ball projected with a velocity of 28 m/sec has a horizontal range...

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  16. Find the resultant of two velocities 4 m/sec and 6 m/sec inclined t...

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  17. Show that a right circular cone of least curved surface and given v...

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  18. Find the point on the curve x^2=8y which is nearest to the point (2...

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  19. Solve the following differential equation : (dy)/(dx)+2y=6e^x

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  20. Form the differential equation of the family of curves y=Acos2x+Bsi...

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