Home
Class 12
MATHS
Let f(x) = sin(x/3) + cos((3x)/10) for a...

Let `f(x) = sin(x/3) + cos((3x)/10)` for all real x. Find the least natural number n such that `f(npi + x) = f(x)` for all real x.

Text Solution

Verified by Experts

The correct Answer is:
6
Promotional Banner

Topper's Solved these Questions

  • NTA JEE MOCK TEST 28

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

  • NTA JEE MOCK TEST 30

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=sin((x)/(3))+cos((3x)/(10)) for all real x.Find the least natural number n such that f(n pi+x)=f(x) for all real x.

If f is real-valued differentiable function such that f(x)f'(x)<0 for all real x, then

Let f(x)=(x)/(1+x) and let g(x)=(rx)/(1-x) Let S be the set off all real numbers r such that f(g(x))=g(f(x)) for infinitely many real number x. The number of elements in set s is

Let f(x)=x sin pi x,x>0 Then for all natural numbers n,f(x) vanishes at

If f(x)=|x|^(3), show that f(x) exists for all real x and find it.

Given that f is a real valued differentiable function such that f(x) f'(x) lt 0 for all real x, it follows that

Let f(sin x)+2f(cos x)=3 for all x in R Fird f(x)

Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

Let h(x)=f(x)-(f(x))^(2)+(f(x))^(3) for every real x. Then,

NTA MOCK TESTS-NTA JEE MOCK TEST 29-MATHEMATICS
  1. A closed cylindrical can has to be made with 100m^(2) of plastic. If i...

    Text Solution

    |

  2. If A and B are non- singular square matrix of same order 3xx3, then wh...

    Text Solution

    |

  3. The area (in sq. units) enclosed by the graphs of |x+y|=2 and |x|=1 is

    Text Solution

    |

  4. The sum to n terms of [(1)/(1.3)+(2)/(13.5)+(3)/(1.3.5.7)+(4)/(1.3.5...

    Text Solution

    |

  5. The value of P for which both the roots of the equation 4x^2-20Px + (2...

    Text Solution

    |

  6. Let g(x)=|x-2| and h(x)=g(g(x)) be two functions, then the value of h'...

    Text Solution

    |

  7. A card is lost from a pack of 52 playing cards. From remainder of the ...

    Text Solution

    |

  8. Suppose S and S' are foci of the ellipse (x^(2))/(25)+(y^(2))/(16)=1. ...

    Text Solution

    |

  9. If cot (alpha + beta) = 0, then sin (alpha + 2 beta) is equal to

    Text Solution

    |

  10. The value of Delta=|(1,sin 3theta, sin^(3)theta),(2cos theta, sin 6 th...

    Text Solution

    |

  11. lim(x to 0) ((1-cos 2x)(3+cosx))/(x tan 4x) is equal to

    Text Solution

    |

  12. The number of 7 digit integers abcdefg, where a lt b lt c lt d gt e gt...

    Text Solution

    |

  13. If int((-1)/(sqrt3))^(1//sqrt3)(x^(4))/(1-x^(4))cos^(-1)((2x)/(1+x^(2)...

    Text Solution

    |

  14. If (9a, 6a) is a point bounded in the region formed by parabola y^(2)=...

    Text Solution

    |

  15. Let P(1):x-2y+3z=5 and P(2):2x-3y+z+4=0 be two planes. The equation of...

    Text Solution

    |

  16. If the 6th term in the expansion of [1/x^(8/3)+x^2 log10 x]^8 is 5600...

    Text Solution

    |

  17. If f(x) is the antidervative of (1+2 tanx(tanx+secx)^((1)/(2))) and f(...

    Text Solution

    |

  18. Let f(x) = sin(x/3) + cos((3x)/10) for all real x. Find the least natu...

    Text Solution

    |

  19. If x + (1)/(x) = 1 " and" p = x^(4000) + (1)/(x^(4000)) and q is the...

    Text Solution

    |

  20. If variance of first n natural number is 10 and variance of first m ev...

    Text Solution

    |