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If the arithmetic mean of the product of...

If the arithmetic mean of the product of all pairs of positive integers whose sum is n is `A_n` then `lim_(n->oo) n^2/(A_n)` equals to

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ARIHANT MATHS-LIMITS-Exercise (Single Integer Answer Type Questions)
  1. If .^(2n+1)P(n-1):^(2n-1)P(n)=7:10, then .^(n)P(3) equals

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  2. Let f(x)=x^4-x^3 then find f '(2)

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  3. If the arithmetic mean of the product of all pairs of positive intege...

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  4. The value of lim(n->oo)sum(k=1)^n(6^k)/((3^k-2^k)(3^(k+1)-2^(k+1)) is ...

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  5. The value of lim(xto (pi)/2) sqrt((tanx-sin{tan^(-1)(tanx)})/(tanx+cos...

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  6. Express in the form of complax number if z= i^5

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  7. If the two AB:(int(0)^(2t)((sinx)/x+1)dx)x+y=3t and AC:2tx+y=0 interse...

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  8. Find dy/dx if e^x=logy-sinx

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  9. If L=lim(xto(pi^(+))/2)(costan^(-1)(tanx))/(x-pi//2) then cos(2piL) is

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  10. Number of solutions of the equation cot( theta ) + cot( theta +(pi)/(...

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  11. If C satisfies the equation lim(xto oo)((x+c)/(x-c))^(x)=4 then |(e^(c...

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  12. If f(x)=lim(t to 0)[(2x)/(pi).tan^(-1)(x/(t^(2)))],then f(1) is …….

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  13. Differentiate x^3 - 5 sinx w.r.t x

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  14. If l=lim(xto1^(+))2^(-2^(1/(1-x))) and m=lim(xto1^(+))(x sin (x-[x]))/...

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  15. The value of lim(xto 0)[(sinx.tanx)/(x^(2))] is …….. (where [.] deno...

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  16. underset(nrarroo)limunderset(r=1)overset(n)Sigma(r)/(1xx3xx5xx7xx9xx.....

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  17. Find dy/dx if y= sin^4x

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  18. If f(x+y+z)=f(x)+f(y)+f(z) with f(1)=1 and f(2)=2 and x,y, z epsilonR ...

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  19. If underset(ntooo)lim(n.3^(n))/(n(x-2)^(n)+n.3^(n+1)-3^(n))=1/3, then ...

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  20. Let p(x) be a polynomial of degree 4 having extremum at x = 1,2 and l...

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