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If int(2e^(x) +3e^(-x))/(4e^(x)+7e^(-x))...

If `int(2e^(x) +3e^(-x))/(4e^(x)+7e^(-x))dx=(1)/(14)(ux+v log_(e ) (4e^(x)+7e^(-x)))+C`, where C is a constant of integration, then ` u+v ` is equal to ________.

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JEE MAINS PREVIOUS YEAR-APPLICATION OF DERIVATIVES-All Questions
  1. If int(2e^(x) +3e^(-x))/(4e^(x)+7e^(-x))dx=(1)/(14)(ux+v log(e ) (4e^(...

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  2. If p and q are positive real numbers such that p^2+""q^2=""1 , t...

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  3. A value of C for which the conclusion of Mean Value Theorem holds f...

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  4. The function f(x)""=""t a n^(-1)(sinx""+""cosx) is an increasing fu...

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  5. How many real solutions does the equation x^7+""14 x^5+""16 x^3+""3...

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  6. Suppose the cube x^3""p x""+""q has three distinct real roots wh...

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  7. Given P(x)""=""x^4+""a x^3+""c x""+""d such that x""=""0 is the only ...

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  8. The shortest distance between the line yx=1 and the curve x=y^2 is ...

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  9. Let f: R R be a continuous function defined by f(x)""=1/(e^x+2e^(-...

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  10. Let f:""RrarrR be defined by f(x)={(k-2x , if xle-1),( 2x+3, if x gt...

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  11. The equation of the tangent to the curve y""=""x""+4/(x^2) , that is p...

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  12. The shortest distance between line y"-"x""=""1 and curve x""=""y^2 is ...

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  13. A spherical balloon is filled with 4500p cubic meters of helium gas...

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  14. The intercepts on x-axis made by tangents to the curve, y=int0^x|t|...

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  15. If f and g are differentiable functions in [0, 1] satisfying f(0)""=""...

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  16. A bird is sitting on the top of a vertical pole 20 m high and its e...

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  17. The normal to the curve, x^2+""2x y-3y^2=""0,""a t""(1,""1) : (1) ...

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  18. Consider f(x)=tan^(-1)(sqrt((1+sinx)/(1-sinx))), x in (0,pi/2)dot A n...

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  19. A wire of length 2 units is cut into two parts which are bent respe...

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  20. The radius of a circle, having minimum area, which touches the curve y...

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  21. Twenty metres of wire is available for fencing off a flower-bed in ...

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