Home
Class 12
MATHS
Equation x^2e^x=k has Three real solutio...

Equation `x^2e^x=k` has Three real solution if `k in (0,4e^(-2))` Two real solutions if `k=4e^(-2)` Only one real solution if `k in (4e^(-2),oo)` Only one real solution if `k in (-oo,0)`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

The number of real solutions of the equation e^(x)=x is

Number of real solution of |x+1|=e^(x) is

The equation sin x=x^2+x+1 has (A) one real solution (B) n real solution (C) more thanone real solution (D) two positive solutons

The number of real solution of the equation e^(x)+x=0, is

Prot that the equation k cos x-3s in x=k+1 possess a solution if k in(-oo,4]

number of real solutions of the equation x^(2)+4x+7=0 are

The number of real solutions of the equation e^(|x|)-|x|=0 , is

Find the values of a for which the equation x^(4)+(1-2a)x^(2)+a^(2)-1=0(A) has no real solutions (B) has one real solution (C) has two distinct real solutions (D) has three real solutions(E) has four distinct real solutions

RESONANCE DPP-JEE MAINS-All Questions
  1. The solution set of x in (-pi,pi) for the inequality sin2x+1lt=cosx+2s...

    Text Solution

    |

  2. Equation 12 x^4-56 x^3+89 x^2-56 x+12=0 has four real and distinct roo...

    Text Solution

    |

  3. Equation x^2e^x=k has Three real solution if k in (0,4e^(-2)) Two rea...

    Text Solution

    |

  4. If f is twice differentiable such that f^('')(x)=-f(x) and f^(prime)...

    Text Solution

    |

  5. Equation (x+2)(x+3)(x+8)(x+12)=4x^2 has (A) four real and distinct roo...

    Text Solution

    |

  6. Consider the function f(x)=m x^2+(2m-1)x+(m-2) If f(x)>0AAx in R the...

    Text Solution

    |

  7. The least integral value of ' a ' for which the graphs y=2a x+1 and y=...

    Text Solution

    |

  8. If the ratio of the roots of the equation, x^2+alphax+alpha+2=0 is equ...

    Text Solution

    |

  9. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^3dot(d^2y)...

    Text Solution

    |

  10. Let A=[(1,-1,1),(2,1,-3),(1,1,1)] and B=[(4,2,2),(-5,0,alpha),(1,-2,3)...

    Text Solution

    |

  11. Equation of line B C is 14 x+23 y-40=0 (b) 4x-2y+1=0 4x+2y-1=0 (d) ...

    Text Solution

    |

  12. The equation: (5+2sqrt(6))^x^(2-3)+(5-2sqrt(6))^x^(2-3)=10h a s Four ...

    Text Solution

    |

  13. In a parallelogram as shown in the figure (a != b) : equation of the ...

    Text Solution

    |

  14. The two adjacent one of the diagonals of the parallelogram is along th...

    Text Solution

    |

  15. If (x1, y1)&(x2, y2) are the solutions of the equaltions, (log)(225)(x...

    Text Solution

    |

  16. If g(x) =2f(2x^3-3x^2)+f(6x^2-4x^3-3) AA x in R and f''(x) gt 0 AA x ...

    Text Solution

    |

  17. Sum of roots of equations f(x)=0a n dg(x)=0i s 0 (b) 2(a+d) (c) 1...

    Text Solution

    |

  18. The function f(x)=(4-x^2)/(4x-x^3) discontinuous at only one point di...

    Text Solution

    |

  19. If |O A^(prime)|=|AAprime|=1, then the values of ' m ' for which (g(...

    Text Solution

    |

  20. Comprehension (For Q.No.1 to 3) Let f(x)=x^2+2a x+b ,g(x)=c x^2+2dx+1...

    Text Solution

    |