Home
Class 12
MATHS
Column I contain rational algebraic expr...

Column I contain rational algebraic expressions and ColumnII contains possible integers which lie in their range. Match the entries of Column I with one or more entries of the elements of Column II.

Text Solution

Verified by Experts

`(A)to(p),(B)to(p,q,r,s),(C)t(p,q,s)`
(A)`y=(x^(2)-2x+9)/(x^(2)+2x+9)impliesx^(2)y+2xy+9y=x^(2)-2x+9`
`implies(y-1)x^(2)+2x(y+1)+9(y-1)=0`
`:' x epsilonR`
`:.4(y+1)^(2)-4.9.(y-1)^(2)ge0`
`=(y+1)^(2)-(3y-3)^(2)ge0`
`implies(4y-2)(-2y+4)ge0`
`implies(2y-1)(y-2)le0`
`:.1/2leyle2impliesy=1,2(p)`
(B)`:'y=(x^(2)-3x-2)/(2x-3)implies2xy-3y=x^(2)-3x-2`
`impliesx^(2)-x(3+2y)+3y-2=0 :'x epsioonR`
`:.(3+2y)^(2)-4.1.(3y-2)ge0`
`implies4y^(2)+17ge0`
`:.y epsilon R(p,q,r,s)`
(C)`:' y=(2x^(2)-2x+4)/(x^(2)-4x+3)`
`impliesx^(2)y-4xy+3y=2x^(2)-2x+4`
`impliesx^(2)(y-2)+2x(1-2y)+3y-4=0`
`:'x epsionR`
`:.4(1-2y)^(2)-4(y-2)(3y-4)ge0`
`implies(4y^(2)-4y+1)-(3y^(2)-10y+8)ge0`
`impliesy^(2)+6y-7ge0`
`implies(y+7)(y-1)ge0`
`:.yle-7` or `yge1(p,q,s)`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|11 Videos
  • THEORY OF EQUATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|10 Videos
  • THE STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|17 Videos
  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS ENGLISH|Exercise Three Dimensional Coordinate System Exercise 12 : Question Asked in Previous Years Exam|2 Videos

Similar Questions

Explore conceptually related problems

Column I contains rational algebraic expressions and Column II contains possible integers which lie in their ragne. Match the entries of Column I with one or more entries of the elements of Column II.

Column I contains rational algebraic expressions and Column II contains possible integers.

Match the entries of Column I with those of Column-II

Match the entries of Column I with those of Column-II

Match the entries in column I with the correctly related quantum number(s) in column II.

Match all the entries in column-I to all the entries in column-II

Match the entries in column II with the statements given in column I.

Match the entry in colum-I with the entry in column-II

Match the entries in Column - I with those of Column - II and chosse the correct answer

ARIHANT MATHS ENGLISH-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Column I contain rational algebraic expressions and ColumnII contains ...

    Text Solution

    |

  2. In the quadratic equation ax^2 + bx + c = 0. if delta = b^2-4ac and al...

    Text Solution

    |

  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

    Text Solution

    |

  4. If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c ...

    Text Solution

    |

  5. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

    Text Solution

    |

  6. If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are ...

    Text Solution

    |

  7. Let aa n db be the roots of the equation x^2-10 c x-11 d=0 and those o...

    Text Solution

    |

  8. Let a,b,c be the sides of a triangle. No two of them are equal and lam...

    Text Solution

    |

  9. All the values of m for whilch both the roots of the equation x^2-2m x...

    Text Solution

    |

  10. If the roots of the quadratic equation x^2+p x+q=0 are tan30^0a n dtan...

    Text Solution

    |

  11. Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2...

    Text Solution

    |

  12. If the difference between the roots of the equation x^2+a x+1=0 is les...

    Text Solution

    |

  13. Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots o...

    Text Solution

    |

  14. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

    Text Solution

    |

  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

    Text Solution

    |

  16. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

    Text Solution

    |

  17. The smallest value of k, for which both the roots of the equation, x^2...

    Text Solution

    |

  18. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

    Text Solution

    |

  19. Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...

    Text Solution

    |

  20. solve 0=1+2x+3x^2

    Text Solution

    |

  21. Find the roots of x^2-6x-2=0

    Text Solution

    |