Home
Class 12
MATHS
The number of solutions to |e^(|x|)-3|=K...

The number of solutions to `|e^(|x|)-3|=K` is

A

Two if `K=0`

B

Three if `Kgt2`

C

Three if `K=2`

D

Four if `K=1`

Text Solution

Verified by Experts

The correct Answer is:
C, D
The graph of `y=|e^(|x|)-3|` is below
To check options find number of intersection of the live `y=k` with the curve in diagram.
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise MATHEMATICS|263 Videos

Similar Questions

Explore conceptually related problems

Find the number of solutions of |x|*3^(|x|) = 1 .

The number of solutions of 3^(|x|)=|2-|x|| , is

The number of real solutions of 1+|e^(x)-1|=e^(x)(e^(x)-2)

Find the number of solutions of 3^(|x|)=|2-|x||

The number of solutions of |x-1|-|x-2|=k when -3

Find the number of solution |x|*3^(|x|)=1

The number of solution (s) of |x-1|-|x+2|=k, when -3

The number of solution of the equation e^(|x|)+|x|+e^(|x|)=4

Let alpha and beta respectively be the number of solutions of e^(x)=x^(2) and e^(x)=x^(3) .Then, the numerical value of 2 alpha+3 beta is

Let alpha and beta respectively be the number of solutions of e^(x)=x^(2) and e^(x)=x^(3) . Then, the numerical value of 2alpha+3beta , is

RESONANCE-TEST SERIES-MATHEMATICS
  1. A function is defined as f(x)=lim(x->oo)[cos^(2n) x , if x<0) , ...

    Text Solution

    |

  2. If [.] denotes the greatest integer function and x,yepsilonRr,"n" epsi...

    Text Solution

    |

  3. The number of solutions to |e^(|x|)-3|=K is

    Text Solution

    |

  4. Let f(x)={(x+1, -1lexle0),(-x,0ltxle1):} then

    Text Solution

    |

  5. Angle bisector of angles subtended by the chord of a circle in the sam...

    Text Solution

    |

  6. Let f(x)={(xsin((pi)/x), "at" xgt0),(0,"at"x=0):}

    Text Solution

    |

  7. Which of the following is True?

    Text Solution

    |

  8. lim(xrarrc)f(x) does not exist for wher [.] represent greatest integ...

    Text Solution

    |

  9. f(x)is defined for xge0 & has a continuous derivative. It satisfies f(...

    Text Solution

    |

  10. Let A*B=A^(T)B^(-1) where A^(T) represents transpose of matrix A and B...

    Text Solution

    |

  11. Let A*B=A^(T)B^(-1) where A^(T) represents transpose of matrix A and B...

    Text Solution

    |

  12. A curve is represented parametrically by the equations x = e^t cos t a...

    Text Solution

    |

  13. A curve is represented paramtrically by the equations x=e^(t)cost and ...

    Text Solution

    |

  14. Find the locus of the point of intersection of the perpendicular ta...

    Text Solution

    |

  15. The coplanar points A,B,C,D are (2-x,2,2),(2,2-y,2),(2,2,2-z) and (1,1...

    Text Solution

    |

  16. cot^(-1)(-1/2)+cot^(-1)(-1/3) is equal to

    Text Solution

    |

  17. If the focus of a parabola is (3,3) and its directrix is 3x-4y=2 then ...

    Text Solution

    |

  18. If a(1),a(2),a(3),…a(n+1) are in arithmetic progression, then sum(k=0)...

    Text Solution

    |

  19. A line makes an angel theta with each of the x-and z-axes. If the a...

    Text Solution

    |

  20. The range of the function f(x)=2+x-[x-3] is, (where [.] denotes greate...

    Text Solution

    |