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If 2x= y^(1/5)+y^(-1/5) prove that (x^2-...

If `2x= y^(1/5)+y^(-1/5)` prove that `(x^2-1)y_2+xy_1 = 25y`

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UNITED BOOK HOUSE-SET 2-EXERCISE
  1. The direction agnles of a straight line are 120^@,45^@,30^@. Is the s...

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  2. Find K, for which the two planes x+ky+5z+2=0 and 3x-2y+kz-1=0 are perp...

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  3. Prove that, if P(A//B)=P(A) then P(A^c//B)=P(A^c).

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  4. Find the probability of guessing correctly at least 5 of the eight ans...

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  5. Solve: tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)= tan^(-1)3x.

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  6. If A=[[1,2,5].[-1,3,-4]] and B= [[3,-2,1],[0,-1,4],[5,2,-1]] show that...

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  7. If A= [[3,-1],[1,2]],B=[[3],[1]],C=[[1],[-2]] find the matrix X such t...

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  8. Prove that [[a^2,bc,c^2+ca],[a^2+ab,b^2,ca],[ab,b^2+bc,c^2]]= 4a^2b^2c...

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  9. If x^2+y^2= t-1/t and x^4+y^4 = t^2+1/t^2,show that , x^3y (dy)/(dx) =...

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  10. If 2x= y^(1/5)+y^(-1/5) prove that (x^2-1)y2+xy1 = 25y

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  11. Solve: (2x+4y+3)(dy)/(dx)= 2y+x+1

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  12. Solve: x(1-x^2)dy+(2x^2y-y-5x^3)dx=0.

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  13. If the magnitude of difference of two unit vectors is sqrt3, then show...

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  14. If the vector ahat i+ a hat j+ c hatk, hat i+hatk and chat i+c hat j+b...

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  15. Evaluate : int(-pi/2)^(pi/2)[f(x)+f(-x)][g(x)+g(-x)] dx

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  16. Using the definition of difinite integral as the limit of sum , evalua...

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  17. There are three coins, One is two headed coin, another is a biased coi...

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  18. If X follows a binomial distribution with mean 3 and variance 3/2 find...

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  19. A 5 ft long man walks away from the foot of a 12 1/2 ft high lamp post...

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  20. Mark the area bounded by the curves y^2= 4x and x^2= 4y and find the m...

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