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Let In=int0^1x^ntan^(-1)xdx." Then prove...

Let `I_n=int_0^1x^ntan^(-1)xdx." Then prove that "(n+1)I_(n)+(n-1)I_(n-2)=pi/2-1/n" `

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CHHAYA PUBLICATION-QUESTIONS PAPER -2019-WBJEE 2019
  1. lim(xto0+)(e^x+x)^((1)/(x))

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  2. Let f(x) be a derivable function f'(x)gtf(x)" and " f(0)=0. Then

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  3. Let f:[1,3] toR be a continuous function that is differentiable in (1,...

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  4. Let a=min(x^2+2x+3:x inR) and b=lim(thetato0)(1-cos theta)/(theta^2). ...

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  5. Let agtbgt0 and I(n)=a^((1)/n)-b^((1)/(n)),J(n)=(a-b)^((1/(n)) for all...

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  6. If A and B are independent events , then P(B/A)=

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  7. The position vectors of the points A,B,C and D are 3hat(i)-2hat(j)-hat...

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  8. Find value of sin^-1(cos((33pi)/5))

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  9. The system of equations lambdax+y+3z=0,2x+muy-z=0,5x+7y+z=0 has infini...

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  10. Let f:XtoY and A,B are non-void subsets of Y, then

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  11. Let S,T,U be three non-void sets and f:StoT,g:TtoU be so that g@f:StoU...

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  12. Let f(x)=x^4-4x^3+4x^2+c, cinR, Then

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  13. The graphs of the polynomial x^2-1 and cosx intersect

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  14. A point is in motion along a hyperbola y=(10)/(x) so that its abscissa...

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  15. Let In=int0^1x^ntan^(-1)xdx." Then prove that "(n+1)I(n)+(n-1)I(n-2)=p...

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  16. Two particles A and B move from rest along a straight line with consta...

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  17. The area bounded by y=x+1" and "y=cosx and the x-axis, is

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  18. Let A=({:(3,0,3),(0,3,0),(3,0,3):}). Then the roots of the equation de...

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  19. f and g be differentiable on the interval I and let a,b inI, altb. The...

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  20. Find the period of the function f(x) = sin((pi x)/3) + cos ((pi x)/2...

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