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If u=log((x^2+y^2)/(x+y)), prove that x(...

If `u=log((x^2+y^2)/(x+y))`, prove that `x(delu)/(delx)+y(delu)/(dely)=1`

A

`-1`

B

0

C

1

D

2

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If u=log(x^(2)+y^(2)+z^(2)) prove that (del^(2)u)/(del x^(2))+(del^(2)u)/(del y^(2))+(del^(2)u)/(del z^(2) = 2/(x^(2)+y^(2)+z^(2)

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If y=log(x+(1)/(x)), prove that (dy)/(dx)=(x-1)/(2x(x+1))

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IPUCET PREVIOUS YEAR PAPERS-GGSIPU MATHEMATICS 2005-MCQ
  1. The equation of the plane through the intersection of the planes x+y+...

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  2. If A,B,C,D are (2,3,-1),(3,5,-3),(1,2,3),(3,5,7) respectively, then th...

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  3. If u=log((x^2+y^2)/(x+y)), prove that x(delu)/(delx)+y(delu)/(dely)=1

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  4. A five digit number is formed by the digit 1,2,3,4 and 5 without repet...

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  5. Two persons A and B take turns in throwing a pair of dice. The first ...

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  6. The probability that in a year of 22nd centurychosen at random, there ...

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  7. The standard deviationof a variable x is 10.Then the standard deviatio...

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  8. The octal equivalent of the decimal number 0.3125 is :

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  9. The hexadecimal equivalent of the binary number 111100001010001 is

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  10. A real value of x satisfies the equation (3-4ix)/(3+4ix)=alpha-ibeta(a...

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  11. If P, Q, R, S are represented by the complex number 4 +i,1+6i,-4+3i,-1...

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  12. If n is a positive integer, then (1 + i)^n + (1-1)^n is equal to

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  13. The number of ways in which 9 persons can be divided into three equal ...

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  14. A dictionary is printed consisting of 7 lettered words only that can b...

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  15. If the sum of the coefficient in the expansion of x+y^n is 1024, then...

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  16. The value of the determinant |(10!,11!,12!),(11!,12!,13!),(12!,13!,14!...

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  17. If A and B are two matrices such that AB=B and BA=A, then

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  18. If the points (x1,y1),(x2,y2)and(x3,y3) are collinear, then the rank o...

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  19. Consider the system of equations x+y+z=6 x+2y+3z=10 x+2y+lambda...

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  20. If A = |(sin (theta + alpha),cos (theta + alpha),1),(sin (theta + bet...

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