Home
Class 12
MATHS
If each ai > 0, then the shortest dista...

If each `a_i > 0`, then the shortest distance between the points `(0,-3)` and the curve `y=1+a_1x^2+a_2 x^4+.......+a_n x^(2n)` is

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • TIPS

    FIITJEE|Exercise ASSIGNMENT (SECTION (I): MCQ (SINGLE CORRECT)|125 Videos

  • TIPS

    FIITJEE|Exercise OBJECTIVE|84 Videos

  • TEST PAPERS

    FIITJEE|Exercise MATHEMATICS|328 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    FIITJEE|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

If each a_(i)>0, then the shortest distance between the points (0,-3) and the curve y=1+a_(1)x^(2)+a_(2)x^(4)+......+a_(n)x^(2n) is

The shortest distance between the line x-y=1 and the curve id x^2=2y

Find the shortest distance between the line x-y+1=0 and the curve y^(2)=x

The shortest distance between the line x - y = 1 and the curve x^2 = 2y is :

The shortest distance between the point (0, 1/2) and the curve x = sqrt(y) , (y gt 0 ) , is:

The shortest distance between the point ((3)/(2),0) and the curve y=sqrt(x),(x gt 0) , is

The shortest distance between the curve y=x^(2)+7x+2 and the line y=3x-3 is

The shortest distance between the line " 2x-3y+1=0 " and the parabola " y^(2)=4x " ,is

The shortest distance between the lines 2x+y+z-1=0=3x+y+2z-2 and x=y=z, is

The distance between the point (1 1) and the normal to the curve y=e^(2x)+x^(3) at x=0 is

FIITJEE-TIPS-NUERICAL DECIMAL BASED QUATIONS
  1. If each ai > 0, then the shortest distance between the points (0,-3) ...

    Text Solution

    |

  2. If {x} denotes the fractiona part of x, then {(4^(2n))/(15)}, n in N, ...

    Text Solution

    |

  3. Period of sin.(pi)/(4)[x]+sin.(pix)/(2)+tan.(pi)/(3)+sin.(pit)/(4) is

    Text Solution

    |

  4. The period of the function f(t)=sin.(pit)/(3)+sin.(pit)/(4) is

    Text Solution

    |

  5. The value of lim(xrarroo)(x^(3)sin(1//x)-2x^(2))/(1+3x^(2)) is

    Text Solution

    |

  6. Let fp(alpha)=(cos(alpha/p^2)+i sin(alpha/p^2))+((cos)(2alpha)/p^2+isi...

    Text Solution

    |

  7. Evaluate underset(xto0)lim(1-cos(1-cosx))/(x^(4)).

    Text Solution

    |

  8. The value of int(-1)^(1)g(x)-g-(-x)+[x]dx where [.] is the greatest fu...

    Text Solution

    |

  9. Tet alpha, beta and gamma be the roots of f(x) = x^3 + x^2 - 5x - 1 = ...

    Text Solution

    |

  10. If a, b, c, d, e and f are non negative real numbers such that a +b+...

    Text Solution

    |

  11. Let f(x)=cospix+10x+3x^2+x^3,-2lt=xlt=3. The absolute minimum value of...

    Text Solution

    |

  12. If int(sqrt(cotx))/(cosx cos x)dx=a sqrt(cotx)+b, then

    Text Solution

    |

  13. If f(x+1)+f(x+7)=0, x in R , then possible value of t for which inta^(...

    Text Solution

    |

  14. f(x)={{:(3[x]-5(|x|)/(x)",",x ne0),(2",", x=0):}, then int(-3//2)^(2)f...

    Text Solution

    |

  15. If f(x)=x(x-1), 0 le x le 1, and f(x+1)=f(x) AA x in R, then |int(2)^(...

    Text Solution

    |

  16. int2^3(x^2dx)/(2x^2-10 x+25)

    Text Solution

    |

  17. Let f(x) = x-[x], for every real number x, where [x] is integral part ...

    Text Solution

    |

  18. Let f:(0, oo) rarr R and F(x^(2))=int(0)^(x^(2))f(t)dt. " If "F(x^(2))...

    Text Solution

    |

  19. intx^6sin(5x^7)dx=k/5cos(5x^7)+c ,then k=

    Text Solution

    |

  20. If int(sqrt(cotx))/(sinx cos x)dx=A sqrt(cotx)+B, then A is equal to

    Text Solution

    |

  21. If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h...

    Text Solution

    |