Home
Class 12
MATHS
Let f be a differentiable function satis...

Let f be a differentiable function satisfying `f '(x) =2 f(x) +10 AA x in R and f (0) =0,` then the number of real roots of the equation `f (x)+ 5 sec ^(2) x=0` ln `(0, 2pi)` is:

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|35 Videos
  • CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION

    VK JAISWAL ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|29 Videos
  • COMPOUND ANGLES

    VK JAISWAL ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos
  • DETERMINANTS

    VK JAISWAL ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

If f(x) is a differentiable function satisfying |f'(x)|le4AA x in [0, 4] and f(0)=0 , then

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

Let f(x) be a function satisfying f(x) + f(x+2) = 10 AA x in R , then

Let f(x)=max{tanx, cotx} . Then the number of roots of the equation f(x)=(1)/(2)" in "(0, 2pi) is

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

If a function satisfies the relation f(x) f''(x)-f(x)f'(x)=(f'(x))^(2) AA x in R and f(0)=f'(0)=1, then Number of roots of the equation f(x)=e^(x) is

If f is a real- valued differentiable function satisfying |f(x) - f(y)| le (x-y)^(2) ,x ,y , in R and f(0) =0 then f(1) equals

Let f(x+y)+f(x-y)=2f(x)f(y) AA x,y in R and f(0)=k , then

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then f(x) is

If f(x) is a differentiable real valued function satisfying f''(x)-3f'(x) gt 3 AA x ge 0 and f'(0)=-1, then f(x)+x AA x gt 0 is

VK JAISWAL ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let f be a differentiable function satisfying f '(x) =2 f(x) +10 AA x ...

    Text Solution

    |

  2. Let f (x)= {{:(ax (x-1)+b,,, x lt 1),( x+2,,, 1 le x le 3),(px ^(2) +q...

    Text Solution

    |

  3. If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...

    Text Solution

    |

  4. If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(2)), where k ...

    Text Solution

    |

  5. The number of values of x , x ∈ [-2,3] where f (x) =[x ^(2)] sin (pix)...

    Text Solution

    |

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

    Text Solution

    |

  7. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  8. Consider f(x) =x^(2)+ax+3 and g(x) =x+band F(x) = lim( n to oo) (f...

    Text Solution

    |

  9. Let f (x)= {{:(2-x"," , -3 le x le 0),( x-2"," , 0 lt x lt 4):} Then f...

    Text Solution

    |

  10. If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable...

    Text Solution

    |

  11. Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number o...

    Text Solution

    |

  12. If (d^(2))/(d x ^(2))((sin ^(4)x+ sin ^(2)x+1)/(sin ^(2)x + si n x+1))...

    Text Solution

    |

  13. f (x) =a cos (pix)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...

    Text Solution

    |

  14. Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...

    Text Solution

    |

  15. Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...

    Text Solution

    |

  16. If y=3^(2 sin ^(-1)) then |((x ^(2) -1) y^('') +xy')/(y)| is equal to

    Text Solution

    |

  17. Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...

    Text Solution

    |

  18. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

    Text Solution

    |

  19. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

    Text Solution

    |

  20. Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th)...

    Text Solution

    |

  21. If x = cos theta and y = sin^(3) theta, then |(yd ^(2)y)/(dx ^(2))+((d...

    Text Solution

    |