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Find the coefficient of x ^(3) in the ex...

Find the coefficient of `x ^(3)` in the expansion of `(2 -3x)^(7).`

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The correct Answer is:
`7xx5 xx (16) (-27) =-15120`
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FULL MARKS-EXAMINATION QUESTION PAPER MARCH 2019-MATHEMATICS
  1. It is correct to say A xxA = {(a,a) :a in A} ? Justify your answer.

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  2. A football player can kick a fotball from ground level with an initial...

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  3. Find the coefficient of x ^(3) in the expansion of (2 -3x)^(7).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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