Home
Class 12
MATHS
We are given the curvers y=int(- infty)^...

We are given the curvers `y=int_(- infty)^(x) f(t) dt` through the point `(0,(1)/(2))` any `y=f(x)`, where `f(x) gt 0 and f(x)` is differentiable ,`AA x in ` R through `(0,1)` Tangents drawn to both the curves at the points with equal abscissae intersect on the same point on the X- axists
The number of solutions `f(x) =2ex ` is equal to

A

0

B

1

C

2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise EXAMPLE|35 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

We are given the curvers y=int_(- infty)^(x) f(t) dt through the point (0,(1)/(2)) any y=f(x) , where f(x) gt 0 and f(x) is differentiable , AA x in R through (0,1) Tangents drawn to both the curves at the points with equal abscissae intersect on the same point on the X- axists The function f(x) is

We are given the curves y=int_(-oo)^(x)f(t) dt through the point (0,(1)/(2)) and y=f(X), where f(x)gt0 and f(x) is differentiable, AAx in R through (0,1). If tangents drawn to both the curves at the point wiht equal abscissae intersect on the point on the X-axis, then int_(x to oo)(f(x))^f(-x) is

Given two curves: y=f(x) passing through the point (0,1) and g(x)=int_(-oo)^xf(t)dt passing through the point (0,1/n)dot The tangents drawn to both the curves at the points with equal abscissas intersect on the x-axis. Find the curve y=f(x)dot

Area bounded by y=f^(-1)(x) and tangent and normal drawn to it at points with abscissae pi and 2pi , where f(x)=sin x-x is

If f(x) be such that f(x) = max (|3 - x|, 3 - x^(3)) , then (a) f(x) is continuous AA x in R (b) f(x) is differentiable AA x in R (c) f(x) is non-differentiable at three points only (d) f(x) is non-differentiable at four points only

Let f((x+y)/(2))=(f(x)+f(y))/(2) and f(0)=b. Find f''(x) (where y is independent of x), when f(x) is differentiable.

Find the equation of the curve through the point (1,0) if the slope of the tangent to the curve at any point (x,y) is (y-1)/(x^2+x) .

Given f'(1)=1and f(2x)=f(x)AAxgt0.If f'(x) is differentiable, then there exists a number c in (2,4) such that f''(c ) equal

If f(x)= int_(0)^(x)(f(t))^(2) dt, f:R rarr R be differentiable function and f(g(x)) is differentiable at x=a , then

If a curve y=f(x) passes through the point (1,-1) and satisfies the differential equation ,y(1+x y)dx""=x""dy , then f(-1/2) is equal to:

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. We are given the curvers y=int(- infty)^(x) f(t) dt through the point ...

    Text Solution

    |

  2. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

    Text Solution

    |

  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo) to vec R be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , ...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a loca...

    Text Solution

    |

  7. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  8. A vertical line passing through the point (h,0) intersects th ellipse ...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  10. The total number of local maxima and local minima of the function f(x)...

    Text Solution

    |

  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  13. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  14. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  15. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  16. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  17. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  19. If f(x) is a cubic polynomil which has local maximum at x=-1 . If f(2)...

    Text Solution

    |

  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  21. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |