Home
Class 12
MATHS
Number of ordered pair (a,b) the set A =...

Number of ordered pair (a,b) the set `A = {1,2,3,4,5}` so that the functon `f(x)=(x^(3))/(3)+a/2 x ^(2)+ bx+10` is an injective mapping `AA x in R:`

A

`13

B

14

C

15

D

16

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise ONE OR MORE THAN ONE ANSWE IS/ARE CORRECT|23 Videos

  • FUNCTION

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise COMPREHENSION TYPE PROBLEMS|13 Videos

  • ELLIPSE

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|2 Videos

  • HYPERBOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-4 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

Consider the function f(x)=(x^(3)-x)|x^(2)-6x+5|, AA x in R , then f(x) is

Find the values of a and b so that the function f(x)={(x^2+3x+a ,, ifxlt=1), (bx+2 ,, ifx >1):} is differentiable at each x∈R

The number of ordered pairs (a,b) where a,b are integers satisfying the inequality min (x ^(2) +(a-b) x + (1-a-b)) gtmax (-x ^(2) +(a+b)x-(1+a+b)AA x in R, is :

A function f : R to R is defined by f(x) = 2x^(3) + 3 . Show that f is a bijective mapping .

Show that f: R->R defined by f(x)=(x-1)(x-2)(x-3) is surjective but not injective.

The value of x, AA x in R which satisfy the equation (x-1)|x^(2)-4x+3|+2x^(2)+3x-5=0 is

The number of integral values of a for which f(x) = x^3 + (a + 2)x^2 + 3ax + 5 is monotonic in AA x in R

If f:R to R be the function defined by f(x) = sin(3x+2) AA x in R. Then, f is invertible.

The function f:R rarr R defined as f(x)=(3x^2+3x-4)/(3+3x-4x^2) is :

VIKAS GUPTA (BLACK BOOK) ENGLISH-FUNCTION -SUBJECTIVE TYPE PROBLEMS
  1. Number of ordered pair (a,b) the set A = {1,2,3,4,5} so that the funct...

    Text Solution

    |

  2. Let f (x) be a polynomial of degree 6 with leading coefficient 2009, S...

    Text Solution

    |

  3. Let f(x)=x^(3)-3x+1. Then number of different real solutions of f(f(x)...

    Text Solution

    |

  4. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

    Text Solution

    |

  5. If the domain of f(x) = sqrt (12-3^(x)-3^(3-x))+ sin ^(-1) ((2x)/(3 ...

    Text Solution

    |

  6. The number of elements in the range of the function : y =sin ^(-1) [...

    Text Solution

    |

  7. The number of integers in the range of function f(x)= [sinx] + [cosx] ...

    Text Solution

    |

  8. If P (x) is polynomial of degree 4 such than P (-1)=P (1) =5 and P (-2...

    Text Solution

    |

  9. The number of integral vlaue (s) of k for which the curve y = sqrt ( ...

    Text Solution

    |

  10. Let the solution set of the equation sqrt([x+[x/2]])+[sqrt({x})+[x/3]]...

    Text Solution

    |

  11. For the real number x, let f (x)=(1)/( ""^(2011sqrt(1-x^(2011)))). Fi...

    Text Solution

    |

  12. Find the number of elements contained in the range of the function f (...

    Text Solution

    |

  13. Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -...

    Text Solution

    |

  14. Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral va...

    Text Solution

    |

  15. The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x...

    Text Solution

    |

  16. Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=...

    Text Solution

    |

  17. Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x...

    Text Solution

    |

  18. If x=10 sum(r=3) ^(100) (1)/((r ^(2) -4)), then [x]= (where [.] deno...

    Text Solution

    |

  19. Let f(x)= cx+d/ax+b ​ . Then fof(x) = x provided that.

    Text Solution

    |

  20. Let A = {x|x ^(2) -4x+ 3 lt 0 , x in R} B={x|2^(1-x)+p le 0;x^2-2(p+7...

    Text Solution

    |

  21. Let the maximum value of expression y= (x ^(4)-x ^(2))/(x ^(6) + 2x ^(...

    Text Solution

    |