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By using properties of determinants , s...

By using properties of determinants , show that : ` {:[( x,x^(2) , yz) ,( y,y^(2) , zx ) ,( z , z^(2) , xy ) ]:} =( x-y)(y-z) (z-x) (xy+yz+ zx) `

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The correct Answer is:
`|{:(1, x ^(2) , x ^(3)), ( 1, y ^(2) , y ^(3)), ( 1, z ^(2) , z ^(3)):}| = (x-y) (y -z) (z-x) (xy + yz + zx)`
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FULL MARKS-EXAMINATION QUESTION PAPER MARCH 2019-MATHEMATICS
  1. Find the coefficient of x ^(3) in the expansion of (2 -3x)^(7).

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  2. Find the nearest point on the line x - 2y=5 from the origin.

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  3. If veca ,vecb, vec c are three vectors such that veca + 2 vecb + vecc ...

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  4. Examine the continuity of the following : cotx+tanx

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  5. Differentiate the following : y=sin^(-1)((1-x^(2))/(1+x^(2)))

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  6. Find (dy)/(dx) if x =a ( t - sin t), y =a (1- cos t)

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  7. Evaluate: int(x-3)sqrt(x+2)dx.

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  8. Construct a suitable domain X such that f:x to N defined by f (n) = n ...

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  9. For the given bases curve y = sin x, draw y = 1/2 sin 2x

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  10. Solve the equation sqrt(6 - 4x - x^(2)) = x + 4

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  11. State and prove any one of the Napier's formulae.

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  12. Do the limit of the function (sin (x - [x]))/(x - [x]) exist as x to 0...

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  13. Prove that for any natural number n, a ^(n) - b ^(n) is divisible by a...

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  14. Evaluate, int (2x +4)/(x ^(2) +4x +6)

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  15. Prove that root(3)(x^(3)+7)-root(3)(x^(3)+4) is approximately equal to...

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  16. Find the unit vectors perpendicular to each of the vectors veca+vecb" ...

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  17. Find (d^(2)y)/(dx ^(2)) if x ^(2) + y ^(2) =4

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  18. The chances of X, Y and Z becoming managers of a certain company are 4...

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  19. By using properties of determinants , show that : {:[( x,x^(2) , yz)...

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  20. Evaluate: int sqrt (x ^(2) + x+1 ) dx

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