Home
Class 12
MATHS
The least positive vlaue of the paramete...

The least positive vlaue of the parameter 'a' for which there exist atleast one line that is tangent to the graph of the curve `y= x ^(3)-ax,` at one point and normal to the graph at another point is `p/q,` where p and q ar relatively prime positive integers. Find product pq.

Text Solution

Verified by Experts

The correct Answer is:
12
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|5 Videos

  • AREA UNDER CURVES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

The least positive integral value of 'k' for which there exists at least one line that the tangent to the graph of the curve y=x^(3)-kx at one point and normal to the graph at another point is

If sum _( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relatively prime positive integers. Find the value of (p-q),

If sum _( k =1) ^(oo) (k^(2))/(3 ^(k))=p/q, where p and q are relatively prime positive integers. Find the value of (p+q),

The set of points (x,y) in the plane satisfying x ^(2//5)+ |y| =1 form a curve enclosing a region of area p/q square units, when p and q are relatively prime positive intergers. Find p-q.

Find the point on the curve 9y^2=x^3, where the normal to the curve makes equal intercepts on the axes.

India and Australia play a series of 7 one-day matches. Each team has equal probability of winning a match. No match ends in a draw. If the probability that India wins atleast three consecutive matches can be expressed as (p)/(q) where p and q are relatively prime positive integers. Find the unit digit of p.

Three different numbers are selected at random from the set A={1,2,3,……..,10} . Then the probability that the product of two numbers equal to the third number is (p)/(q) , where p and q are relatively prime positive integers then the value of (p+q) is :

For the parabola y=-x^(2) , let a lt 0 and b gt 0,P(a, -a^(2)) and Q(b, -b^(2)) . Let M be the mid-point of PQ and R be the point of intersection of the vertical line through M, with the parabola. If the ratio of the area of the region bounded by the parabola and the line segment PQ to the area of the triangle PQR be (lambda)/(mu) , where lambda and mu are relatively prime positive integers, then find the value of (lambda+mu) :

Find the points on the curve 9y^2=x^3 where normal to the curve makes equal intercepts with the axes.

Find the points on the curve 9y^2=x^3 where normal to the curve makes equal intercepts with the axes.

VK JAISWAL ENGLISH-APPLICATION OF DERIVATIVES -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If f (x)= (px)/(e ^(x)) - (x ^(2))/(2) + x is a decreasing function f...

    Text Solution

    |

  2. Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0)...

    Text Solution

    |

  3. Find sum of all possible values of the real parameter 'b' if the diffe...

    Text Solution

    |

  4. Let 'theta' be the angle in radians between the curves (x ^(2))/(36) +...

    Text Solution

    |

  5. Let set of all possible values of lamda such that f (x)= e ^(2x) - (la...

    Text Solution

    |

  6. Let a,b,c and d be non-negative real number such that a ^(5)+b^(5) le ...

    Text Solution

    |

  7. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

    Text Solution

    |

  8. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

    Text Solution

    |

  9. Let f (x) = int (0)^(x) ((a -1) (t ^(2)+t+1)^(2) -(a+1)(t^(4)+t ^(2) +...

    Text Solution

    |

  10. The numbr of real roots of the equation x ^(2013)+ e ^(20144x) =0 is

    Text Solution

    |

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

    Text Solution

    |

  12. The least positive vlaue of the parameter 'a' for which there exist at...

    Text Solution

    |

  13. Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and b...

    Text Solution

    |

  14. A tank contains 100 litres of fresh water. S solution containg 1 gm/li...

    Text Solution

    |

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

    Text Solution

    |

  16. It is given that f (x) is defined on R satisfying f (1)=1 and for AA ...

    Text Solution

    |

  17. The number of normals to the curve 3y ^(3) =4x which passes through th...

    Text Solution

    |

  18. Find the number of real root (s) of the equation ae ^(x) =1+ x + (x ^(...

    Text Solution

    |

  19. Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in...

    Text Solution

    |

  20. If p (1) and p(2) are the lengths of the perpendiculars from origin on...

    Text Solution

    |