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If xgt0,ygt0 and x+y=1, then find the mi...

If `xgt0,ygt0` and x+y=1, then find the minimum value of x log x + y log y.

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PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. For the function f(x) = 2x^3-8x^2+10x+5, find the interval (s) in wh...

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  2. Investigate the increasing or decreasing behaviour of the following fu...

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  3. If xgt0,ygt0 and x+y=1, then find the minimum value of x log x + y log...

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  4. Evaluate the following integrals : intx.e^xdx

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  5. Evaluate the following integrals : inte^(tan^-1x)/(1+x^2)dx

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  6. Evaluate the following integrals : intsecx(secx+tanx)dx

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  7. Evaluate the following integrals : int3^6abs(x-4)dx

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  8. Solve the following differential equations : xdy+ydx=0,at x=1,y=1

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  9. Solve the following differential equations : dy/dx+sqrt((1-y^2)/(1-x...

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  10. Solve the following differential equations : tan x cdotcos^2ydx+tan ...

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  11. Solve the following differential equations : x(1+y^2)dx+y(1+x^2)dy=0...

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  12. Let{x} and [x] denote the fractional and integral parts of a real numb...

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  13. If y = 2[x]+3 and y = 3[x-2]+5 and find [x+y]

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  14. Solve abs([x]-2x)=4

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  15. Solve (x)^2+(x+1)^2=25 {where (x) denotes the least integer function}

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  16. If 0ltxlt1000 and [x/2]+[x/3]+[x/5]=31/30x, where [x] is the greatest...

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  17. Resolve x^2/((x-1)(x-2)(x-3)) into partial fractions.

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  18. Resolve (x^4-x^2+1)/(x^2(x^2+1)^2 into partial fractions.

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  19. Resolve (2x^2-11x+5)/((x-3)(x^2+2x+5)) into partial fractions.

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  20. If A={a,b,c,d,e}:B={c,d,e,f,g} and S={a,b,c,d,e,f,g,h,i,j}. Then evalu...

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