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Let S be the set of all rational num...

Let `S` be the set of all rational number except 1 and * be defined on `S` by `a*b=a+b-a b ,` for all `a ,bSdot` Prove that (i) * is a binary operation on `( i i ) * is commutative as well as associative.

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Using properties of determinants, prove the following : |[a, a^2,bc]...

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

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

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

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  5. Find the equation of the plane that contains the point (1, – 1, 2) ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If (a+4 3b8-6)=(2a b+2 8a-8b), write the value of a-2bdot

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  20. Show that the vectors vec a , vec b , vec c are coplanar if and on...

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