Home
Class 12
MATHS
If alpha is the only positive root of (2...

If `alpha` is the only positive root of `(2^(2014)-1)x^2+(2-2^(2014))x-1=0` . Then the value of `(alpha^(2014)-1)p^2+(1-alpha^(2015))p q+1` is equal to (a) 1 (b) 0 (c) pq (d) `p^2+p q+1`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP ENGLISH|Exercise All Questions|15 Videos
  • MATRICES

    RESONANCE DPP ENGLISH|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta be the roots of x^(2)-a(x-1)+b=0 , then the value of (1)/(alpha^(2)-a alpha)+(1)/(beta^(2)-a beta)+(2)/(a+b) is

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

The value of lim_(x to1)(p/(1-x^p)-q/(1-x^q)),p ,q , in N , equal (a) (p+q)/2 (b) (p q)/2 (c) (p-q)/2 (d) sqrt(p/q)

If alpha and beta are the roots of x^2 - p (x+1) - c = 0 , then the value of (alpha^2 + 2alpha+1)/(alpha^2 +2 alpha + c) + (beta^2 + 2beta + 1)/(beta^2 + 2beta + c)

If alpha and beta are the roots of x^2 - p (x+1) - c = 0 , then the value of (alpha^2 + 2alpha+1)/(alpha^2 +2 alpha + c) + (beta^2 + 2beta + 1)/(beta^2 + 2beta + c)

If alpha , beta gamma are the roots of the equation x^3+px^2+qx+r=0 , then (1-alpha^2)(1-beta^2)(1-gamma^2) is equal to (a) (1+q)^2-(p+r)^2 (b) (1+q)^2+(p+r)^2 (c) (1-q)^2+(p-r)^2 (d) none of these

If p >1 and q >1 are such that log(p+q)=logp+logq , then the value of log(p-1)+log(q-1) is equal to (a) 0 (b) 1 (c) 2 (d) none of these

If alpha , beta , gamma are the roots of x^3 -px^2 +qx -r=0 and r ne 0 then find (1)/( alpha^2) +(1)/( beta^2) +(1)/( gamma ^2) in terms of p,q ,r

If alpha and beta are roots of x^2+px+2=0 and 1/alpha,1/beta are the roots of 2x^2+2qx+1=0 . Find the value of (alpha-1/alpha)(beta-1/beta)(alpha+1/beta)(beta+1/alpha)

If alpha,beta, gamma re the roots of the equations x^3+px^2+2x+p=0 then the general value of tan^-1 alpha+tan^-1 beta+tan^-1 gamma is (A) npi (B) (npi)/2 (C) (2n+1) pi/2 (D) dependent upon the value of p.

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. If function y=f(x) has only two points of discontinuity say x1,x2, whe...

    Text Solution

    |

  2. Number of solutions of the equation e(k-xlnx)=1 for kepsilon(0,(1)/(e)...

    Text Solution

    |

  3. If alpha is the only positive root of (2^(2014)-1)x^2+(2-2^(2014))x-1=...

    Text Solution

    |

  4. The coefficient of x^(49) in the product (x-1)(x-3)(x-99)i s a. -99^...

    Text Solution

    |

  5. Find the principal argument of the complex number sin(6pi)/5+i(1+cos(6...

    Text Solution

    |

  6. In an equilateral triangle, the inradius and the circumradius are c...

    Text Solution

    |

  7. If cos x=t a n x , then which of the following is true? (a)1/(sinx)+...

    Text Solution

    |

  8. a(1),a(2),a(3)…………,a(n) are in A.P. and a(1)+a(3)+a(5)+a(7)+a(9)= 20 t...

    Text Solution

    |

  9. f(x)=cos^(-1)((-2-x^2)/(x^2+2x+2)),then (a)f(-1/2)=2tan^(-1)(1/2) ...

    Text Solution

    |

  10. Let A ,B ,C are three sets such that n(A)=25 ,n(B)=20 ,n(C)=27 ,n(AnnB...

    Text Solution

    |

  11. If statements p and q take truth values as T T ,T F ,F T ,F F in order...

    Text Solution

    |

  12. All letters of the word 'RACHIT' are permuted in all possible ways ...

    Text Solution

    |

  13. The sum of the series 1+4+3+6+5+8+ upto n term when n is an even numbe...

    Text Solution

    |

  14. The positive integers p ,q and r are all primes if p^2 − q^2 = r , t...

    Text Solution

    |

  15. The marks of some students were listed out of a maximum 75. The SD ...

    Text Solution

    |

  16. If angles A,B, and C of a triangle ABC are in A.P. and if (b)/(c) = (s...

    Text Solution

    |

  17. If (x1, y1) be the centroid of the triangle formed by a line L and c...

    Text Solution

    |

  18. The value of sin^(-1) (cot(sin^(-1) sqrt((2 -sqrt3)/(4)) + cos^(-1)....

    Text Solution

    |

  19. Let I=int(kpi)^((k+1)pi)(|sin2x|)/(|sinx|+|cosx|)dx,(kepsilonN) and J=...

    Text Solution

    |

  20. The greatest integral value of m for which the point of intersection...

    Text Solution

    |