Home
Class 12
MATHS
If n is the number of solutions of the e...

If n is the number of solutions of the equation `2 cos x (4 sin ((pi)/4 + x ) sin ((pi)/4 - x) - 1) = 1, x in [ 0, pi]` and S is the sum of all these solutions, then the ordered pair (n, S) is :

A

`(3, 5pi //3)`

B

`(3, 13 pi//9)`

C

`(2, 8pi//9)`

D

`(2, 2pi //3)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematics Section B|20 Videos

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematics (Section A)|80 Videos

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION-B)|40 Videos

  • JEE MAINS 2020

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS|250 Videos

  • JEE MAINS 2022

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION - B)|10 Videos

Similar Questions

Explore conceptually related problems

the number of solution of the equation 1+sin x*sin^(2)((x)/(2))=0, in [-pi,pi], is

The number of solutions of the equation (3+cos x)^(2)=4-2sin^(8)x" in "[0, 9pi) is equal to

If x in[0,(pi)/(2)] then the number of solutions of the equation sin7x+sin4x+sin x=0 is

The number of solution (s) of the equation sin^(-1)(1-x)-2sin^(-1)x=(pi)/(2) is/are

The number of solution of the equation 2 "sin"^(3) x + 2 "cos"^(3) x - 3 "sin" 2x + 2 = 0 "in" [0, 4pi] , is

Find the number of solutions of the equation sin^(4)x+cos^(4)x-2sin^(2)x+(3)/(4)sin^(2)2x=0 in the interval [0,2 pi]

Number of solution of the equation sin 2x + cos 2x + sin x + cos x + 1 = 0 In the interval, (0, pi//2) is

JEE MAINS PREVIOUS YEAR-JEE MAINS 2021-Mathematics Section A
  1. Let the acute angle bisector of the two planes x - 2y - 2z + 1 = 0 an...

    Text Solution

    |

  2. cos^(-1) (cos (-5)) + sin^(-1) (sin(6)) - tan^(-1)(tan (12)) is equal...

    Text Solution

    |

  3. If n is the number of solutions of the equation 2 cos x (4 sin ((pi)/4...

    Text Solution

    |

  4. Which of the following is equivalent to the Boolean expression P^^~q ?

    Text Solution

    |

  5. Let J(n,m) = int0^(1//2) x^n/(x^m-1), AA ngt mand n, m in N. Consider ...

    Text Solution

    |

  6. Consider the system of linear equations - x + y + 2z = 0 3x - ay...

    Text Solution

    |

  7. The number of pairs (a, b) of real numbers, such that whenever a is a ...

    Text Solution

    |

  8. If y = y (x) is the solution curve of the differential equation x^2d...

    Text Solution

    |

  9. The function f(x), that satisfies the condition f(x) = x + int0^(pi//...

    Text Solution

    |

  10. Let theta be the acute angle between the tangents to the ellipse x^2/...

    Text Solution

    |

  11. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

    Text Solution

    |

  12. Let a1, a2, …, a21 be an AP such that sum(n=1)^20 1/(an a(n+1)) = 4/9...

    Text Solution

    |

  13. Let P1, P2…, P15 be 15 points on a circle. The number of distinct tria...

    Text Solution

    |

  14. Two squares are chosen at random on a chessboard (see figure). The pro...

    Text Solution

    |

  15. Let f: R to R be a continuous function. Then lim(x to pi//4) (pi/4 in...

    Text Solution

    |

  16. The distance of line 3y - 2z - 1 = 0 = 3x - z + 4 from the point (2, -...

    Text Solution

    |

  17. Let f be any continuous function on [0, 2] and twice differentiable on...

    Text Solution

    |

  18. Let f : N rarr N be a function such that f(m + n) = f(m) + f(n) for ev...

    Text Solution

    |

  19. If alpha = lim(x rarr pi//4)""(tan^(3)x - tan x)/(cos (x + (pi)/(4))) ...

    Text Solution

    |

  20. Let vec(a), vec(b), vec(c) be three vectors mutually perpendicular to ...

    Text Solution

    |