Home
Class 11
MATHS
Match the following: List - I, List -...

Match the following: List - I, List - II Let `y(x)=cos(3cos^(-1)x)` `x in [-1,1],x!=+-(sqrt(3))/2` Then `1/(y(x)){(x^2-1)(d^2y(x))/(dx^2)+(dy(x))/(dx)}` equals, 1 Let `A_1,A_2, A_n(n >2)` be the vertices of a regular polygon of `n` sides with its centre at the origin. Let ` vec a_k` be the position vector of the point `A_k ,k=1,2, ndot` If `|sum_(k=1)^(n-1)( vec a_k x vec a_(k+1))|=|sum_(k=1)^(n-1)( vec a_kdot vec a_(k+1))|,` then the minimum value of `n` is, 2 If the normal from the point `P(h ,1)` on the ellipse `(x^2)/6+(y^2)/3=1` is perpendicular to the line `x+y=8` , then the value of `h` is, 8 Number of positive solutions satisfying the equation `tan^(-1)(1/(2x)+1)+tan^(-1)(1/(4x+1))=tan^(-1)(2/(x^2))` is, 9

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Let A_(1) , A_(2) ,…..,A_(n) ( n lt 2) be the vertices of regular polygon of n sides with its centre at he origin. Let veca_(k) be the position vector of the point A_(k) ,k = 1,2,….,n if |sum_(k=1)^(n-1) (veca_(k) xx veca_(k) +1)|=|sum_(k=1)^(n-1) (vecak.vecak+1)| then the minimum value of n is

A_1,A_2,..., A_n are the vertices of a regular plane polygon with n sides and O as its centre. Show that sum_(i=1)^n vec (OA)_i xx vec(OA)_(i+1)=(1-n)(vec (OA)_2 xx vec(OA)_1)

A_(1),A_(2), …. A_(n) are the vertices of a regular plane polygon with n sides and O ars its centre. Show that sum_(i=1)^(n-1) (vec(OA_(i))xxvec(OA)_(i+1))=(n-1) (vec(OA)_1 xx vec(OA)_(2))

Value of L = lim_(n->oo) 1/n^4 [1 sum_(k=1)^n k + 2sum_(k=1)^(n-1) k + 3 sum_(k=1)^(n-2) k +.....+n.1] is

Let f(n)=sum_(k=-n)^(n)(cot^(-1)((1)/(k))-tan^(-1)(k)) such that sum_(n=2)^(10)(f(n)+f(n-1))=a pi then find the value of (a+1) .

Prove that sum_(k=1)^(n-1) ""^(n)C_(k)[cos k x. cos (n+k)x+sin(n-k)x.sin(2n-k)x]=(2^(n)-2)cos nx .

If f(x) = sum_(k=2)^(n) (x-(1)/(k-1))(x-(1)/(k)) , then the product of root of f(x) = 0 as n rarr oo , is

Let (1 + x^(2))^(2) (1 + x)^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … if a_(1),a_(2) " and " a_(3) are in A.P , the value of n is

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . If sum_(k=1)^(n)f(a+k)=16(2^(n)-1) , then a=

If S_n=sum_(k=1)^n a_k and lim_(n->oo)a_n=a , then lim_(n->oo)(S_(n+1)-S_n)/sqrt(sum_(k=1)^n k) is equal to

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the equation of the locus of the middle points of the chords of ...

    Text Solution

    |

  2. Find the angle between the asymptotes of the hyperbola (x^2)/(16)-(y^2...

    Text Solution

    |

  3. Match the following: List - I, List - II Let y(x)=cos(3cos^(-1)x) ...

    Text Solution

    |

  4. If a hyperbola passing through the origin has 3x-4y-1=0 and 4x-3y-6=0 ...

    Text Solution

    |

  5. Let E1 and E2 be two ellipse whose centers are at the origin. The maj...

    Text Solution

    |

  6. A triangle has its vertices on a rectangular hyperbola. Prove that the...

    Text Solution

    |

  7. From any point on any directrix of the ellipse (x^2)/(a^2)+(y^2)/(b^2)...

    Text Solution

    |

  8. Find the equation of the asymptotes of the hyperbola 3x^2+10 x y+9y^2+...

    Text Solution

    |

  9. A tangent is drawn to the ellipse to cut the ellipse x^2/a^2+y^2/b^2=1...

    Text Solution

    |

  10. P Q and R S are two perpendicular chords of the rectangular hyperbola ...

    Text Solution

    |

  11. Ois the origin & also the centre of two concentric circles having radi...

    Text Solution

    |

  12. If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)...

    Text Solution

    |

  13. The tangent at a point P on an ellipse intersects the major axis at T ...

    Text Solution

    |

  14. If (asectheta, btantheta) and (asecphi, btanphi) be two coordinate of ...

    Text Solution

    |

  15. Find the area of the triangle formed by any tangent to the hyperbola (...

    Text Solution

    |

  16. If a triangle is inscribed in an ellipse and two of its sides are pa...

    Text Solution

    |

  17. Normal are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at point t...

    Text Solution

    |

  18. The tangent at a point P(acosvarphi,bsinvarphi) of the ellipse (x^2)/(...

    Text Solution

    |

  19. Find the product of the length of perpendiculars drawn from any point ...

    Text Solution

    |

  20. Tangents are drawn to the ellipse from the point ((a^2)/(sqrt(a^2-b^2)...

    Text Solution

    |