Home
Class 11
MATHS
IF f(x) =x^(2) + alpha for x ge 0 ...

IF `f(x) =x^(2) + alpha ` for ` x ge 0` ` and 2 sqrt(x^(2) +1) + beta ` for ` x lt 0` is continuous at ` x=0 and f((1)/(2))=2,` then `alpha ^(2) + beta ^(2)` is

A

3

B

`(8)/(25)`

C

`(25)/(8)`

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2017

    MARVEL PUBLICATION|Exercise QUESTION|50 Videos

  • SEQUENCES AND SERIES

    MARVEL PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|81 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:(x^(2)+alpha," for "xge0),(2sqrt(x^(2)+1)+beta," for "xlt0):} is continuous at x=0 and f((1)/(2))=2 , then alpha^(2)+beta^(2) is

If {:(f(x),=x^(2)+alpha,",","for"x ge 0),(,=2sqrt(x^(2)+1)+beta, ",","for"x lt 0):} is continuous at x = 0 and f((1)/(2))=2 then alpha^(2)+beta^(2) is

If f(x) is continuous at x=0 , where f(x)={:{(x^(2)+alpha", for " x ge 0),(2sqrt(x^(2)+1)+ beta", for " x lt 0):} and f(1/2)=2 , then

If alpha and beta are the roots of x^(2) - (a+1)x + 1/2 (a^(2) + a+1) = 0 then alpha^(2) + beta^(2) = "_____" .

If f(x)=alpha x+beta and f(0)=f^(1)(0)=1 then f(2) =

If f(x)= alpha x+beta and f(0)=f^(')(0)=1 then f(2) =

If f(x) is continuous at x=0 , where f(x)={:{(x^(2)+1", for " x ge 0),(2sqrt(x^(2)+1)+k ", for " x lt 0):} , then k=

If alpha,beta are the roots of x^(2)+7x+3=0 ,then (alpha-1)^(2)+(beta-1)^(2)=

If alpha and beta are the roots of 2x^(2) - x - 2 = 0 , then (alpha^(3) + beta^(-3) + 2alpha^(-1) beta^(-1)) is equal to

Consider f(x)=x^(2)-3x+a+(1)/(a),a in R-{0} such that f(3)>0 and f(2)<=0. If alpha and beta are the roots of equation f(x)=0 then the value of alpha^(2)+beta^(2) is equlal to

MARVEL PUBLICATION-QUESTION PAPER 2018-QUESTION
  1. IF log (10)""((x^(3)-y^(3))/(x^(3)+y^(3)))=2 then (dy)/(dx)=

    Text Solution

    |

  2. IF f :R -{2} to R is a function defined by f(x) =(x^(2)-4)/(...

    Text Solution

    |

  3. IF f(x) =x^(2) + alpha for x ge 0 and 2 sqrt(x^(2) +1) + beta...

    Text Solution

    |

  4. IF y= ( tan ^(-1) x)^(2) " then " (x^(2) +1)^(2) (d^(2)y)/(dx^(2))...

    Text Solution

    |

  5. The line 5x +y-1=0 coincides with one of the lines given by ...

    Text Solution

    |

  6. IF A =[(1,2,3),(-1,1,2),( 1,2,4)]"then " (A^(2) -5A) A^(-1)=

    Text Solution

    |

  7. The equation of line passing throufh (3,-1,2) and perpendicular ...

    Text Solution

    |

  8. Letters in the word HULULULU are rearranged . The probability o...

    Text Solution

    |

  9. The sum of the first 10 terms of the series 9+99+999 +….., is

    Text Solution

    |

  10. If A,B ,C are the angle of Delta ABC then cot A .cot B + c...

    Text Solution

    |

  11. IF (dx)/(sqrt(16-9x^(2)))=A sin^(-1) (bx )+c then A+B=

    Text Solution

    |

  12. int e^(x) [(2+sin 2x)/( 1+cos 2x )]dx =

    Text Solution

    |

  13. A coin is tossed three times .If X denotes the absolute diffe...

    Text Solution

    |

  14. IF 2 sin ( theta +(pi)/(3)) = cos (theta -(pi)/(6)), then ta...

    Text Solution

    |

  15. The area of the region bounded by x^(2) = 4y , y=1, y=4 and the...

    Text Solution

    |

  16. If f(x) =(e^(x^(2))-cos x)/(x^(2)), for x ne 0 is continous at ...

    Text Solution

    |

  17. The maximum value of 2x +y subject to 3x +5y le 26 and 5x +...

    Text Solution

    |

  18. IF bar a , bar b , bar c are mutually perpendicular vectors hav...

    Text Solution

    |

  19. IF points p( 4,5,x),Q (3,y,4) and R (5,8,0) are collinear , then ...

    Text Solution

    |

  20. IF the slope of one of the lines given by ax^(2) +2hxy + by...

    Text Solution

    |