Home
Class 12
MATHS
The number of all possible positive inte...

The number of all possible positive integral values of `alpha` for which the roots of the quadratic equation `6x^2-11x+alpha=0` are rational numbers is : (a) 3 (b) 2 (c) 4 (d) 5

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise MATH|21 Videos

  • LIMITS AND DERIVATIVES

    JEE MAINS PREVIOUS YEAR ENGLISH|Exercise All Questions|5 Videos

Similar Questions

Explore conceptually related problems

Number of non-negative integral values of 'k' for which roots of the equation x^(2)+6x+k=0 are rational is-

Find all the integral values of a for which the quadratic equation (x - a) (x - 10) + 1 = 0 has integral roots.

If alpha and beta are the roots of the quadratic equation x^(2) - 4x - 6 = 0 , find the values of alpha^(2) + beta^(2) .

Number of possible value(s) of integer 'a' for which the quadratic equation x^(2) + ax + 16 = 0 has integral roots, is

The number of integral values of a for which the quadratic equation (x+a)(x+1991)+1=0 has integral roots are a. 3 b. 0 c. 1 d. 2

Two different real numbers alpha and beta are the roots of the quadratic equation ax ^(2) + c=0 a,c ne 0, then alpha ^(3) + beta ^(3) is:

If [x] denotes the integral part of x and k=sin^-1 ((1+t^2)/(2t))gt0 then integral valueof alpha for which the equation (x-[k])(x+alpha)-1=0 has integral roots is (A) 1 (B) 2 (C) 4 (D) none of these

If alpha and beta are roots of the quadratic equation x ^(2) + 4x +3=0, then the equation whose roots are 2 alpha + beta and alpha + 2 beta is :

If alpha , beta , gamma are the roots of the equation x^3 -6x^2 +11 x +6=0 then sum alpha^2 beta =

The minimum integral value of alpha for which the quadratic equation (cot^(-1)alpha)x^(2)-(tan^(-1)alpha)^(3//2)x+2(cot^(-1)alpha)^(2)=0 has both positive roots

JEE MAINS PREVIOUS YEAR ENGLISH-JEE MAINS-All Questions
  1. The area (in sq. units) bounded by the parabola y=x^2-1, the tangent a...

    Text Solution

    |

  2. int(5x^8+7x^6)/(x^2+1+2x^7)^2dx is equal to (a) x/(x^2+1+2x^7)+C (b) ...

    Text Solution

    |

  3. The number of all possible positive integral values of alpha for whic...

    Text Solution

    |

  4. The coeficient of t^(4) in the expansion of ((1-t^(6))/(1-t))^(3) is

    Text Solution

    |

  5. If sum(i=1)^n(xi+1)^2=9n and sum(i=1)^n(xi-1)^2=5n, then standard devi...

    Text Solution

    |

  6. The number of natural numbers less than 7,000 which can be formed by u...

    Text Solution

    |

  7. An urn contains 5 red and 2 green balls, one ball is chosen from urn. ...

    Text Solution

    |

  8. Find sum of first 15 term of series 1+6+(9(1^2+2^2+3^2))/7+(12(1^2+2^2...

    Text Solution

    |

  9. Let z(0) be a root of the quadratic equation x^(2) + x + 1 = 0. If z =...

    Text Solution

    |

  10. let veca=hati+hatj+sqrt2hatk vecb=b1hati+b2hatJ+sqrt2hatk vecc=5hati+...

    Text Solution

    |

  11. int(0)^((pi)/(3))(tanx)/(sqrt(2ksecx))dx=1-(1)/(sqrt2), then value of ...

    Text Solution

    |

  12. Find number of solution of equation sinx-sin2x+sin3x=0 in 0lexle(pi)/(...

    Text Solution

    |

  13. Find area enclosed by curve 0leylex|x|+1 between -1lexle1 (a) ...

    Text Solution

    |

  14. Find the value of lim(xrarr0)(x(([x]+|x|)sin[x]))/(|x|). (a) -...

    Text Solution

    |

  15. Let y=y(x) is a solution of (dy)/(dx)=f(x) where f(xy)=f(x)f(y) AA x,y...

    Text Solution

    |

  16. If A(4,-4) and B(9,6) lies on y^2=4x and a point C on arc AOB(O= ori...

    Text Solution

    |

  17. If the circles x^2+y^2-16x-20y+164=r^2 and (x-4)^2+(y-7)^2=36 intersec...

    Text Solution

    |

  18. Find the eccetricity of hyperbola through (4,2) whose centre is (0,0)...

    Text Solution

    |

  19. If x=3tant and y=3sect then find (d^2y)/(dx^2) at x=(pi)/(4) (...

    Text Solution

    |

  20. Let A={x:xepsilonR-{1}}f is defined from ArarrR as f(x)=(2x)/(x-1) the...

    Text Solution

    |