Home
Class 12
MATHS
The function f(x)=(4sin^2x-1)^n(x^2-x+1)...

The function `f(x)=(4sin^2x-1)^n(x^2-x+1),n in N ,` has a local minimum at `x=pi/6` . Then `n` is any even number n is an odd number n is odd prime number `n` is any natural number

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

The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N , has a local minimum at x=pi/6 . Then (a) n is any even number (b) n is an odd number (c) n is odd prime number (d) n is any natural number

The function f(x)=(x^2-4)^n(x^2-x+1),n in N , assumes a local minimum value at x=2. Then find the possible values of n

The function f(x)=(x^2-4)^n(x^2-x+1),n in N , assumes a local minimum value at x=2. Then find the possible values of n

The sum of n odd natural numbers is

The number of natural numbers n for which (15n^2+8n+6)/n is a natural number is:

Let f(x)=(x-2)^2x^n, n in N Then f(x) has a minimum at

Let f(x)=(x^2-1)^n(x^2+x+1) then f(x) has local extremum at x=1 when (a) n=2 (b) n=3 (c) n=4 (d) n=6

If A={x:x in N and x is an odd prime number less than 17}, then the cardinal number of A is

Let f(x)=(sin 2n x)/(1+cos^(2)nx), n in N has (pi)/(6) as its fundamental period , then n=

If the number of terms in (x +1+ 1/x)^n n being a natural number is 301 the n=

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. For each positive integer n , let f(n+1)=n(-1)^(n+1)-2f(n) and f(1)=(2...

    Text Solution

    |

  2. Solve the following equations : (i) |x^(2)-2| = 2 |x-3| (ii) |x^(2...

    Text Solution

    |

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

    Text Solution

    |

  4. The value of ("lim")(nvec0)[1/n+(e^(1/n))/n+(e^(2/n))/n++(e^((n-1)/n))...

    Text Solution

    |

  5. The number of roots of the equation 2sqrt(2x+1)=2x-1 is equal to

    Text Solution

    |

  6. The functionf(x)=|ax-b|+ax-b|+c|x| forallx in(-00,00) where agt0, bt0,...

    Text Solution

    |

  7. Let f(0) and int(0)^(2) f'(2t)e^(f(2t))dt=5 . Then the value of f(4) i...

    Text Solution

    |

  8. The value of c in Rolle's theorem for the function f(x)=(x(x+1))/(e^(x...

    Text Solution

    |

  9. Maximum value of |z+1+i|, where z in S is (a)sqrt(2) (b) 2 (c)...

    Text Solution

    |

  10. If f(x)=x^3-x^2+100x+2002 ,t h e n f(1000)>f(1001) f(1/(2000))>f(1...

    Text Solution

    |

  11. If ("log"a)/(b-c) = ("log"b)/(c-a) = ("log"c)/(a-b), "then" a^(a)b^(b)...

    Text Solution

    |

  12. Value of 'alpha' for which system of equations x+y+z=1,x+2y+4z=alpha a...

    Text Solution

    |

  13. if alpha,beta be the roots of the equation (x-a)(x-b)+x=0(c ne0), then...

    Text Solution

    |

  14. Let f(x) be a function such that f''(x) = f'(x) + e^x and f'(0) =1 ,f(...

    Text Solution

    |

  15. If |(x^2-5x+3, 2x-5, 3) (3x^2+x+4, 6x+1, 9) (7x^2-6x+9, 14 x-6, 21)| =...

    Text Solution

    |

  16. Draw the graph of y=|x^(2)-3|x|+2|.

    Text Solution

    |

  17. The equation of a line which is parallel to the line common to the pai...

    Text Solution

    |

  18. Draw the graph of y=|x^(2)-3|x|+2|.

    Text Solution

    |

  19. If point (a ,a) lies in between the lines |x+y|=6 , then ' a ' may sat...

    Text Solution

    |

  20. If sintheta+costheta=1/5a n d0lt=theta<pi, then tantheta is -4/3 (b) ...

    Text Solution

    |