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Determine the values of a,b and h for wh...

Determine the values of a,b and h for which the equation `ax^2+2hxy+by^2+3z^2-4x-6y-4=0`represents a sphere.

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SHARAM PUBLICATION-QUESTION PAPER 2011-EXERCISE
  1. Write the values of m and n for which the vectors (m-1)hat(i) + (n+2)h...

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  2. How many independent constants are there in the general equation of a ...

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  3. Determine the values of a,b and h for which the equation ax^2+2hxy+by^...

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  4. Write the maximum value of x+y subject to 2x+4yle6,xge0,yge0.

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  5. Write the value of k, if |{:(aa1,aa2,aa3),(ab1,ab2,ab3),(ac1,ac2,ac3...

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  6. if A is a 3xx3 matrix and |A| = 3, then write the matric represented b...

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  7. Find r if: 16P(15,r)= 13P(16,r)

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  8. Determine the middle term in the expansion of (1/3a+1/3b)^8.

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  9. A bag contains 7 white and 9 black balls. If a ball is drawn at random...

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  10. Find (dy)/(dx) if y = logtan^(-1)x+e^(2x).

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  11. Find (dy)/(dx) if y = 10^(ln sinx)

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  12. Evaluate overset(lim)(xrarrpi/2)(secx-tanx)

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  13. Find the intervals in which the function y=(lnx)/(x) is increasing and...

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  14. State Cauchy's mean value theorem.

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  15. Integrate: int(e^(2x)-4x^(3))dx

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  16. Find by integration the area bounded by the straight lines y=0,y=x and...

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  17. Evaluate: overset(4)underset(0)int sqrtx dx

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  18. Reduce the following to a linear differential equation x(dy)/(dx)+y=...

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  19. Write the integrating factor of the differential equation (x - lny)(dy...

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  20. Solve (dy)/(dx)=(y^2)/(xy-x^2).

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