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Evaluate: underset(x rarr 0)lim(loge(1+a...

Evaluate: `underset(x rarr 0)lim(log_e(1+alphax)/(e^(2x)-1))`

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UNITED BOOK HOUSE-QUESTION PAPER 2016-EXERCISE
  1. Evaluate: int{1/(logex)-1/(logex)^2}dx

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  2. Find the differential equation of all circles which touch the x-axis a...

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  3. Evaluate: underset(x rarr 0)lim(loge(1+alphax)/(e^(2x)-1))

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  4. IF the projection of veca= lambda hati+hat j+4 hat k on vec b= 2hati+6...

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  5. Find the angle between the planes x-y+2z=9 and 2x+y+z=7.

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  6. If P(A//B)= 0.75, P(B//A) = 0.6 and P(A)=0.4 find the value of P(barA/...

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  7. If the number of heads obtained is denoted by X when two unbiased coin...

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  8. A relation R is defined on the set of all natural numbers IN by: (x,y)...

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  9. If sin^(-1)x+sin^(-1)y+sin^(-1)z = pi then prove that xsqrt(1-x^2)+...

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  10. Express the matric A= [[-3,4,1],[2,3,0],[1,4,5]] as the sum of a symme...

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  11. If p,q,r are not in geometric progression and |[1,q/p,alpha+q/p],[1,r/...

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  12. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

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  13. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

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  14. pv^a=c (a and c are constants) then show that v^2(d^2p)/(dv^2)=a(a+1)...

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  15. Evaluate: inte^x(x-3)/(x-1)^3 dx

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  16. Evaluate: int sqrt(1+cosecx dx)

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  17. Solve: (1+3e^(y//x))dy+3e^(y//x)(1-y/x)dx=0

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  18. If the area of a circle increases uniformly, then show that the rate o...

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  19. The vectors veca,vecb,vecc are such that veca+vecb+vecc=vec0, If |vec...

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  20. If vec alpha = lambda hat i+hatj+3 hatk,vec beta= -hati+2hatj+hatk,vec...

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