Home
Class 12
MATHS
Consider the statements : P : There ex...

Consider the statements : P : There exists some x IR such that f(x) + 2x = 2(1+x2) Q : There exists some x IR such that 2f(x) +1 = 2x(1+x) Then (A) both P and Q are true (B) P is true and Q is false (C) P is false and Q is true (D) both P and Q are false.

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos

Similar Questions

Explore conceptually related problems

p ^^ q is true when : ( a) p and q are both true (b) p and q are both false ( c ) p is true and q is false ( d) p is false and q is true.

If p and q are two statements then (p

If p and q are two statement then (p

Let f(x)=(1-x)^(2)sin^(2)x+x^(2) for all x in IR, and let g(x)=int_(1)^(x)((2(t-1))/(t-1)-ln t)f(t) dt for all x,in(1,oo). Consider the statements: P: There exists some x in IR such that f(x)+2x=2(1+x^(2)) Q: There exists some x in IR such that 2f(x)+1=2x(1+x) Then

If P (x) = (x ^(3) - 8) (x +1) and Q (x) = (x ^(3) +1) (x - 2), then find the LCM of P (x) and Q (x).

Find p and q so that (x + 2)" and "(x – 1) may be factors of the polynomial f(x) = x^(3) + 10x^(2) + px + q .

If P (x) = (x^(3) + 1) (x-1) and Q (x) = (x^(2) -x +1) (x^(2) -3x +2) , then find HCF of P (x) and Q (x) .

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Let f be a real-valued function defined on interval (0,oo),by f(x)=lnx...

    Text Solution

    |

  2. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  3. Consider the statements : P : There exists some x IR such that f(x)...

    Text Solution

    |

  4. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is 6 (b)...

    Text Solution

    |

  5. Let f(x)=xsinpix ,x > 0. Then for all natural numbers n ,f^(prime)(x) ...

    Text Solution

    |

  6. Given P(x)""=""x^4+""a x^3+""c x""+""d such that x""=""0 is the only ...

    Text Solution

    |

  7. The real number k for which the equation, 2x^3+""3x""+""k""=""0 has tw...

    Text Solution

    |

  8. If f(x)={x^2,xlt=0 2sinx ,x >0'in v e s t iga t et h e function at x=...

    Text Solution

    |

  9. The function y=(a x+b)/((x-1)(x-4)) has turning point at P(2,1)dot The...

    Text Solution

    |

  10. Find the points of maxima and minima of the function. f(x)=12 x^5-4...

    Text Solution

    |

  11. Discuss the extremum of f(x)=x^2+1/(x^2)

    Text Solution

    |

  12. The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N, has a local minimum...

    Text Solution

    |

  13. Q. Let f (x)=sin^3x+ lambdasin^2x where (pi)/2 ltxlt (pi)/2. The inte...

    Text Solution

    |

  14. f(x)={cos(pix)/2,x >0x+a ,xlt=0 Find the values of a if x=0 is a poin...

    Text Solution

    |

  15. Investigate for the maxima and minima of the function f(x)=int1^x[2(t...

    Text Solution

    |

  16. Leg f(x) be a cubic polynomial which has local maximum at x=-1a n df(x...

    Text Solution

    |

  17. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=pa n dx=q ...

    Text Solution

    |

  18. Find the maximum value of f(x)=(1/x)^x

    Text Solution

    |

  19. Let f(x)=2x^3=9x^2+12 x+6. Discuss the global maxima and minima of f(x...

    Text Solution

    |

  20. Find the greatest and least values of function f(x)=3x^4-8x^3-18 x^...

    Text Solution

    |