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Evaluate the following: lim(xto1/3)(3x^2...

Evaluate the following: `lim_(xto1/3)(3x^2+5x-2)/(9x^2-1)`

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RESONANCE DPP-JEE MAINS-All Questions
  1. int(dx)/((x^2+4x+5)^2)i se q u a lto 1/2[tan^(-1)(x+1)+("x"+2)/("x"^...

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  2. In a triangle, with usual notations, the length of the bisector of ang...

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  3. Evaluate the following: lim(xto1/3)(3x^2+5x-2)/(9x^2-1)

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  4. If varphi(x)=int(1/x)^(sqrt(x))sin(t^2)dt then varphi^(prime)(1)= ...

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  5. In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdo...

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  6. An ordinary cubical dice having six faces marked with alphabets A, ...

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  7. If f(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4) then f^(prime)(2) has th...

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  8. Three equal circles each of radius r touch one another. The radius of ...

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  9. Let V be the vertex and L be the latusrectum of the parabola x^2=2y+4x...

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  10. If I(m,n)=int0^1 t^m(1+t)^n.dt, then the expression for I(m,n) in term...

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  11. In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...

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  12. ((lim)(xvecoo)int0x(tan^(-1)t)^2dt)/(sqrt(x^2+1))h a st h ev a l u e ...

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  13. The inverse of the matrix A=|(1,1,1),(1,omega,omega^2),(1,omega^2,omeg...

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  14. The number of odd divisor of the number N=2^(10). 3^5 .7^2, are 16 ...

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  15. The equation |x+1|^(log)(("x"+1))(3+2-x^(2))=(x-3)|x| has a. unique s...

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  16. Suppose f: R->R is a differentiable function and f(1)=4. Then value o...

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  17. In a A B C ,A : B : C=3:5: 4. Then a+b+csqrt(2) is equal to 2b b. 2c ...

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  18. For x in R, the expression (x^2+2x+c)/(x^2+4x+3c) can take all real va...

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  19. Prove that: int0^1tan^-1.(1/(1-x+x^2))dx=2int0^1tan^-1xdx

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  20. A seven digit number is choosen. What the probability that even number...

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