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If y =x log (x/(a+bx))then prove that x^...

If `y =x log (x/(a+bx))`then prove that `x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2`.

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MODERN PUBLICATION-SAMPLE PAPER 2017-EXERCISE
  1. Prove that the vectors 2hati-hatj+hatk, hati-3hatj-5hatk, 3hati-4hatj-...

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  2. If veca=3hati+hatj+2hatk,vecb=2hatj-3hatj+4hatk then verify that vecax...

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  3. Five boys and four girls randomly stand in a line. Find the probabilit...

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  4. If a random variable X has a binomial distribution B (8,1/2) then find...

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  5. A cricket team consisting of 11 players is to be chosen from 8 batsmen...

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  6. Find the inverse of the following matrix: [[0,0,2],[0,2,0],[2,0,0]]

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  7. If P(n-1,3):P(n+1,3)=5:12, find n.

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  8. Solve by Cramer’s rule 2x-y=2, 3x+y=13

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  9. If the matrix A is such that [[1,-1],[2,3]]A=[[-4,1],[7,7]], find A.

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  10. A cylindrical open water tank with a circular base is to be made out o...

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  11. If y =x log (x/(a+bx))then prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^...

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  12. Solve frac[dx][dy]=frac[3x-7y+7][3y-7x-3]

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  13. Evaluate intfrac[dx][cosx(1+2sinx)]

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  14. Show that the line joining the points (0,2,-4) and (-1,1-2) and the l...

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  15. Prove the following by vector method. An angle inscribed in a semi-cir...

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  16. Show that hatitimes (vecatimeshati)+hatjtimes(vecatimeshatj)+hatktime...

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  17. The probability that a student will pass the final examination in both...

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  18. If P(A) = 0.4, P(B//A) = 0.3 and P(B^(c)/A^(c)) = 0.2. Find P(B).

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  19. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  20. Show that C1^2 + 2C2^2 + 3C3^2 + ... + "^nCn^2 = ((2n-1!))/{(n-1)!}^2

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