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Let lambda=int0^1(dx)/(1+x^3),p=(lim)(n...

Let `lambda=int_0^1(dx)/(1+x^3),p=(lim)_(n->oo)[(prod_(r=1)^n(n^3+r^3))/(n^(3n))]^(-1/n)` then `ln p` is equal to (a)`ln2-1+lambda` (b) `ln2-3+3lambda` (c)`2ln2-lambda` (d) `ln4-3+3lambda`

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RESONANCE DPP-JEE MAINS-All Questions
  1. If int((x-1)dx)/(x^2sqrt(2x^2-2x+1))=(sqrt(f(x)))/(g(x))+C ,t h e n f...

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  2. If vec a , vec ba n d vec c are unit vectors, then | vec a- vec b|^2+...

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  3. Let lambda=int0^1(dx)/(1+x^3),p=(lim)(n->oo)[(prod(r=1)^n(n^3+r^3)...

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  4. For f(x)=sin^2x ,x in (0,pi) point of inflection is: pi/6 (b) (2pi)/4...

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  5. If z1& z1 represent adjacent vertices of a regular polygon on n sides...

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  6. If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a complex number then a. arg(...

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  7. If vec a+2"" vec b+3"" vec c="" vec0 and |"" vec a|=6,|"" vec b|=3a n...

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  8. Function f(x)=sin(lnx)-"cos"(lnx) is (a)M.I. in [e^(2npipi/4),e^(2np...

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  9. tan(sec^(-1) (1/x))=sin(cos^(-1) (1/sqrt(5)))

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  10. If f(x)={(sina x^2)/(x^2); x!=0 3/4+1/(4a); x=0, is continuous everyw...

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  11. The value of sin(pi/3-sin^(-1)(4/5)) is (a) (3sqrt(3)-4)/(10) (b) (3...

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  12. If greatest and least values of f(x)=sin^(-1)(x/(sqrt(x^2+1)))-lnx in...

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  13. "lim"(x->0)(ln(t a n(pi/4+a x)))/(sinb x),b!=0 is equal to (a)a/b (b...

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  14. If An=int0^(pi/2)(sin(2n-1)x)/(sinx)dx ;Bn=int0^(pi/2)((sinn x)/(sinx...

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  15. Which of the following functions is periodic (a) cos^2x+sinx^3+"tan"...

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  16. Solve the following system of inequations: 4(tan^(-1)x)^2-8tan^(-1)x+3...

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  17. The number of values of k for which the system of the equations (k+1)x...

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  18. Projection of line (x+1)/2+(y+1)/(-1)=(z+3)/4 on the plane x+2y+z=6; h...

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  19. ("lim")(x→0^+)("sin"[cosx])/(1-[cosx]) ([.] denotes the greatest integ...

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  20. If [dot] represents the greatest integer function, then int4^(10)([x^2...

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