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Using properties of determinants, prove the following : `|[a, a^2,bc],[b,b^2,ca],[c,c^2,ab]|=(a-b)(b-c)(c-a)(b c+c a+a b)`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. If x=a(cost+tsint)a n d y=a (sin t - t cos t), then find the value of ...

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  2. If (x-y)dot e^((x/(x-y)) = a , Prove that y(dy)/(dx)+x=2ydot

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  3. Using properties of determinants, prove the following : |[a, a^2,bc]...

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  4. Write the value of the determinant |[p,p+1],[p-1,p]| .

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  5. Let S be the set of all rational number except 1 and * be defined on...

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  6. Find the distance of the point P(–1, –5, –10) from the point of int...

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  7. Find the equation of the plane that contains the point A(1,-1,2) and ...

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  8. A cottage industry manufactures pedestal lamps and wooden shades, e...

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  9. Find the shortest distance between the lines l1 and l2 whose vector ...

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  10. Find a unit vector perpendicular to both of the vectors vec a+ vec b ...

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  11. Find a vector in the direction of vector 2 hat i-3 hat j+6 hat k k whi...

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  12. Write the projection of vector hat i+ hat j+ hat k along the vector ...

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  13. Evaluate : int0^pi(xtanx)/(secx+tanx)dx

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  14. Show that a cylinder of a given volume which is open at the top has...

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  15. Find the area of the smaller region bounded by the ellipse (x^2)/9+(y^...

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  16. Write the value of cos^(-1)(-1/2)+2sin^(-1)(1/2)

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  17. Let R="{("a , a^3")":a is a prime number less than 5} be a relation. F...

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  18. Evaluate : int0^(pi/4)tanxdx

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  19. Evaluate : int(dx)/(sin^2xcos^2x)

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  20. If A is a3x3 matrix, |A| != 0 and |3A|=k|A| , then write the value of ...

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