Home
Class 12
MATHS
Which of the following is/are correct? ...

Which of the following is/are correct?
(A) Between any two roots of `e^xcosx=1,` there exists at least one root of `tanx=1.`
(B) Between any two roots of `e^xsinx=1,` there exists at least one root of `tanx=-1.`
(C) Between any two roots of `e^xcosx=1,` there exists at least one root of `e^xsinx=1.`
(D) Between any two roots of `e^xsinx=1,` there exists at least one root of `e^xcosx=1.`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

Show that between any two roots of e^(-x)-cosx=0, there exists at least one root of sinx-e^(-x)=0

Between any two real roots of the equation e^xsinx-1=0 , the equation e^xcosx+1=0 has :

If f(x) is a polynomial, show that between two roots of the polynomial equation f(x)=0, there lies at least one root of the polynomial f'(x)=0.

One root of the equation x+(1)/(x)=-2 is

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

For what real 'p' do the roots of x^2-2x-p^2+1=0 lie between the roots of x^2-(p+1)x+(p-1)=0 ?

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^2+2bx+c=0 has (a) at least one root in [0, 1] (b) at least one root in [1,2] (c) at least one root in [3/2, 2] (d) none of these

Find the number of roots of the equation xlog_(e)x= 1 .

The number of roots of x^2-2=[sinx],w h e r e[dot] stands for the greatest integer function is 0 (b) 1 (c) 2 (d) 3.

Let a ,b , c in R such that no two of them are equal and satisfy |(2a, b, c),( b, c,2a), (c, 2a, b)|=0, then equation 24 a x^2+8b x+4c=0 has (a) at least one root in [0,1] (b) at least one root in [-1/2,1/2] (c) at least one root in [-1,0] (d) at least two roots in [0,2]

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. If the line a x+b y+c=0 is a normal to the curve x y=1, then (a)a >0,...

    Text Solution

    |

  2. Which one of the following curves cut the parabola y^2 =4ax ...

    Text Solution

    |

  3. Which of the following is/are correct? (A) Between any two roots of ...

    Text Solution

    |

  4. Which of the following pairs(s) of curves is/are orthogonal? (a) y^2 ...

    Text Solution

    |

  5. find all the tangents to the curve y=cos(x+y),-2pilexle2pithat are par...

    Text Solution

    |

  6. Find the equation of the normal to the curve y=(1+x)^y+sin^(-1)(sin^2x...

    Text Solution

    |

  7. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0)=0,f(1)=6 ...

    Text Solution

    |

  8. Find the shortest distance of the point (0, c) from the parabola y=...

    Text Solution

    |

  9. The distance between the origin and the normal to the curve y=e^(2x)+x...

    Text Solution

    |

  10. Let f(x)={-x^2,for x<0; x^2+8,for xgeq0 Find x intercept of the common...

    Text Solution

    |

  11. The curve y=a x^3+b x^2+c x+5 touches the x-axis at P(-2,0) and cuts t...

    Text Solution

    |

  12. If the function f:[0,4]->R is differentiable, the show that for a , b ...

    Text Solution

    |

  13. The slope of the tangent to the curve y=sqrt(4-x^2) at the point where...

    Text Solution

    |

  14. If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined...

    Text Solution

    |

  15. If the line joining the points (0,3) and (5,-2) is a tangent to the c...

    Text Solution

    |

  16. The curve given by x+y=e^(x y) has a tangent parallel to the y-axis at...

    Text Solution

    |

  17. The number of tangents to the curve x^(3/2)+y^(3/2)=2a^(3/2),a >0, whi...

    Text Solution

    |

  18. Show that the square roots of two successive natural numbers greater ...

    Text Solution

    |

  19. If m is the slope of a tangent to the curve e^y=1+x^2, then (a)|m|>1 ...

    Text Solution

    |

  20. The angle made by the tangent of the curve x = a (t + sint cost), y = ...

    Text Solution

    |