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Find the number of real root (s) of the equation `ae ^(x) =1+ x + (x ^(2))/(2),` where a is positive constant.

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VK JAISWAL ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

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  2. Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0)...

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  3. Find sum of all possible values of the real parameter 'b' if the diffe...

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  4. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

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  5. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

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  6. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

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  7. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

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  8. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

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  9. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

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  10. The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is

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  11. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

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  12. The least positive vlaue of the parameter 'a' for which there exist at...

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  13. Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and b...

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  14. A tank contains 100 litres of fresh water. S solution containg 1 gm/li...

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  15. If f (x) is continous and differentiable in [-3,9] and f'(x) in [-2,8]...

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  16. It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...

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  17. The number of normals to the curve 3y ^(3) =4x which passes through th...

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  18. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

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  19. Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in...

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  20. If p (1) and p(2) are the lengths of the perpendiculars from origin on...

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