Home
Class 12
MATHS
Let am (m = 1, 2, ,p) be the possible in...

Let `a_m (m = 1, 2, ,p)` be the possible integral values of a for which the graphs of `f(x) =ax^2+2bx +b` and `g(x) =5x^2-3bx-a`meets at some poin for which the graphs o t for all real values of b Let `t_r = prod_(m=1)^p(r-a_m )` and `S_n =sum_(r=1)^n t_r. n in N` The minimum possible value of a i

A

`1/5`

B

`5/26`

C

`3/28`

D

`2/43`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos
  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|6 Videos
  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

Let a_(m)(m=1,2, p) be the possible integral values of a for which the graphs of f(x)=ax^(2)+2bx+b and g(x)=5x^(2)-3bx- ameets at some poin for which the graphs o t for all real values of b Let t_(r)=prod_(m=1)^(m=1)(r-a_(m)) and S_(n)=sum_(r=1)^(n)t_(r).n in N The minimum possible value of a

The number of integral values of m for which f : R to R ,f (x) = (x ^(2))/(3) + (m -1) x ^(2) + (m +5) x+n is bijective is :

sum_(r=1)^(n)r^(2)-sum_(m=1)^(n)sum_(r=1)^(m)r is equal to

Let t_(r)=r! and S_(n)=sum_(r=1)^(n)t_(r), (n>10) then remainder when S_(n) is divided by 24 is:

If sum_(r=1)^(n) r(sqrt(10))/(3)sum_(r=1)^(n)r^(2),sum_(r=1)^(n) r^(3) are in G.P., then the value of n, is

Let the rth term t_(r) of a series is given by t_(r)=r/(1+r^(2)+r^(4)) , the value of lim_(ntooo)sum_(r=1)^(n)t_(r) is

Let f(x)=(mx^2+3x+4)/(x^(2)+3x+4) , m in R . If f(x) lt 5 for all x in R then the possible set of values of m is :

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let am (m = 1, 2, ,p) be the possible integral values of a for which t...

    Text Solution

    |

  2. If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x), then the value...

    Text Solution

    |

  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

    Text Solution

    |

  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

    Text Solution

    |

  5. Let fk(x) = 1/k(sin^k x + cos^k x) where x in RR and k gt= 1. Then f4(...

    Text Solution

    |

  6. The function f:[0,3] to [1,29], defined by f(x)=2x^(3)-15x^(2)+36x+1 i...

    Text Solution

    |

  7. Let f(x)=x^2a n dg(x)=sinxfora l lx in Rdot Then the set of all x sat...

    Text Solution

    |

  8. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  9. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  10. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  11. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, wh...

    Text Solution

    |

  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g{f(x)} is invertible in the dom...

    Text Solution

    |

  13. Domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) fo...

    Text Solution

    |

  14. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (1,oo)...

    Text Solution

    |

  15. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

  16. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  17. Let E={1,2,3,4}a n dF-{1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  18. Suppose f(x)=(x+1)^2forxgeq-1. If g(x) is the function whose graph is ...

    Text Solution

    |

  19. If f:[1,infty) rarr [2,infty) is given by f(x)=x+1/x, " then " f^(-1)(...

    Text Solution

    |

  20. Let f(x0=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f(x...

    Text Solution

    |

  21. The domain of definition of function of f(x)=(log(2)(x+3))/(x^(2)+3x+2...

    Text Solution

    |