Home
Class 12
MATHS
If f (x) ={{:( px^(2) +q,"for " xle 1),...

If f (x) ` ={{:( px^(2) +q,"for " xle 1),( qx^(2) +px +r ,"for " xlgt 1 ):}` where `q ne 0` is derivable at x =1 ,then

A

p=q,r=0

B

p=q ,r`ne ` 0

C

p=2q,r=0

D

p=2q ,`rne 0`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • Differential Equation

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTION|277 Videos

  • INTEGRATION

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS|582 Videos

Similar Questions

Explore conceptually related problems

If f(x) {:(=px-q", if " x le 1 ),(= 3x ", if " 1 lt x lt 2 ), (= qx^(2)-p ", if " x ge 2 ):} is continuous at x = 1 and dicontinuous at x = 2 , then

Let p and q be real numbers such that the function f(x)={{:(p^(2)+qx","xge1),(-5px^(2)-6","xlt1):} is derivable for all x in R . Then sum of all possible values of p is

If f(x) = {:{(px^(2)-q, x in [0,1)), ( x+1 , x in (1,2]):} and f(1) =2 , then the value of the pair ( p,q) for which f(x) cannot be contiinuous at x =1 is

If the function g(x) {{:((e^(px) + log _(e) (1+4x)+q)/(x^(3))","x ne 0),(r"," x=0):} continuous at x=0 , then find the values of p,q and r.

The equation x^(2) + px +q =0 has two roots alpha, beta then Choose the correct answer : (1) The equation qx^(2) +(2q -p^(2))x +q has roots (1) alpha /beta , beta/alpha (2) 1/alpha ,1/beta (3) alpha^(2), beta^(2) (4) None of these (2) The equation whose roots are 1/alpha , 1/beta is (1) px^(2) + qx + 1 =0 (2) qx^(2) +px +1 =0 (3) x^(2) + qx + p =0 (4) qx^(2) +x+ p =0 3. the values of p and q when roots are -1,2 (1) p = -1 , q = -2 (2) p =-1 , q =2 (3) p=1 , q = -2 (4) None of these

If x^(2)-2x-1 is a factor of px^(3)+qx^(2)+1 , (where p , q are integers) then find the value of p +q.

Let f(x)=x^(2)+2px+2q^(2) and g(x)=-x^(2)-2px+p^(2) (where q ne0 ). If x in R and the minimum value of f(x) is equal to the maximum value of g(x) , then the value of (p^(2))/(q^(2)) is equal to

If 3 - 4i is a root of x^(2) - px + q = 0 where p, q in R . then value (2 p - q)/( p + q) is

NIKITA PUBLICATION-DIFFERENTIATION -MCQ
  1. If the function g(x)={{:(,k sqrt(x+1),0 le x le3),(,mx+2,3lt xle5):...

    Text Solution

    |

  2. The value of m which the function f(x) {{:( mx^(2), "for " xle 1 ),( ...

    Text Solution

    |

  3. If f (x) ={{:( px^(2) +q,"for " xle 1),( qx^(2) +px +r ,"for " xlgt 1...

    Text Solution

    |

  4. Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):} Then f(x) is conti...

    Text Solution

    |

  5. If f(x) = {{:( e^(x) +ax ,"for " x lt 0 ),( b(x-1) ^(2) ,"for " xge 0...

    Text Solution

    |

  6. If f (x)= ae^(|x|)+b |x|^(2) ,a ,b in R and f(x) is differentiable...

    Text Solution

    |

  7. If lim( xto 2 ) (f(x) -f(2))/( x-2) exist ,then

    Text Solution

    |

  8. If f is derivable at x =a,then lim(xto a )( (xf(a) -af( x))/(x-a) )

    Text Solution

    |

  9. If the relation f'(a+b) =f'( a)+ f '(b) and (d)/(dx)(f(x))=f'(x) ,the...

    Text Solution

    |

  10. Derivative of even function is

    Text Solution

    |

  11. Derivative of odd function is

    Text Solution

    |

  12. If f (x) is polynomial of degree two and f(0) =4 f'(0) =3,f''(0) =4,th...

    Text Solution

    |

  13. If f (x) is a polynomial of degree two and f(0) =4 f'(0) =3,f'' (0) 4 ...

    Text Solution

    |

  14. let f(x) be a polynomial function of second degree. If f(1)=f(-1)and a...

    Text Solution

    |

  15. For x in R, f(x) = | log 2- sin x| and g(x) = f(f(x)), then

    Text Solution

    |

  16. y=(5x^3-4x^2-8x)^9,f i n d(dy)/(dx)

    Text Solution

    |

  17. If y = (1)/( (x^(2) +3)) , then (dy)/(dx) =

    Text Solution

    |

  18. If y= sqrt (x+(1)/( x) ),then (dy)/(dx) =

    Text Solution

    |

  19. If y= (sqrt( x) +(1)/(sqrt(x)) ) ^(5) , then (dy)/(dx) =

    Text Solution

    |

  20. If y= 3sqrt ((2x^(2) -7x -4) ^(5) ) ,then (dy)/(dx) =

    Text Solution

    |