Home
Class 12
MATHS
The number of roots of the equation, (...

The number of roots of the equation,
`(81) ^( sin ^(2)x) + (81) ^( cos ^(2)x) x = 30`
in the interval [0, `pi`] is equal to :

A

3

B

4

C

8

D

2

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS (SECTION B)|30 Videos
  • JEE MAIN 2021

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS SECTION A|40 Videos
  • JEE MAIN 2021

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

    JEE MAINS PREVIOUS YEAR|Exercise QUESTION|1 Videos
  • JEE MAIN 2022

    JEE MAINS PREVIOUS YEAR|Exercise Question|454 Videos

Similar Questions

Explore conceptually related problems

The number of solution of the equation sin^(3)x cos x+sin^(2)x cos^(2)x+cos^(3)x sin x+1=0 in the interval [0, 2pi] is equal to

The number of solutions of the equation 16(sin^(5)x +cos^(5)x)=11(sin x + cos x) in the interval [0,2pi] is

The number of solutions to the equations cos^(4)x+(1)/(cos^(2)x)=sin^(4)x+(1)/(sin^(2)x) in the interval [0,2pi] 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]

If x in[0,2 pi] then the number of solution of the equation 81^(sin^(2)x)+81^(cos^(2)x)=30

The number of roots of the equation x^(3)+x^(2)+2x+sin x=0 in (-2 pi,2 pi)

Number of solutions of the equation 27^(sin^(2)x)+27^(cos^(2)x)=12 in the interval [-pi,pi] is

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

Number of solutions to the equation 2^(sin^(2)x)+5.2^(cos^(2)x)=7, in the interval [-pi,pi], is

JEE MAINS PREVIOUS YEAR-JEE MAIN 2021-MATHEMATICS (SECTION A)
  1. Let a vector a hati + beta hatj be obtained by rotating the vector s...

    Text Solution

    |

  2. Let A = [{:(i, -i), (-i , i):}], i sqrt (-i) Then, the system of line...

    Text Solution

    |

  3. The number of roots of the equation, (81) ^( sin ^(2)x) + (81) ^( co...

    Text Solution

    |

  4. Let the functions f: R toR and g: R to R be defined as : f (x) = {{:...

    Text Solution

    |

  5. If y=yır) is the solution of the differential equation, (dy)/(dx) + 2 ...

    Text Solution

    |

  6. Let a complex number z|z| =1,. satisfy log ((1)/(sqrt2)) ((|z| +11)/(...

    Text Solution

    |

  7. Let S (K) = sum (r=1) ^(k) tan ^(-1) (( 6 ^r)/( 2 ^( 2 r + 1) + 3 ^( 2...

    Text Solution

    |

  8. The range of a R for which the function f (x) = (4a -3) (x + log (e)...

    Text Solution

    |

  9. If "log"(10) sin x+"log"(10)cos x=-1 and "log"(10)(sin x+cosx)=(("log"...

    Text Solution

    |

  10. If for x in (0, (pi)/(2) ) , log (10) sin x + log (10) cos x =-1 and ...

    Text Solution

    |

  11. Let the position vectors of two points P and Q be 3 hati - hatj + 2 ha...

    Text Solution

    |

  12. If for a gt 0, the feet of perpendiculars from the points A(a, - 2a, ...

    Text Solution

    |

  13. Let P be a plane Ix+my+nz=0 containing the line, (1-x)/(1) = (y+4)/(2)...

    Text Solution

    |

  14. If n is the number of irrational terms in the expansion of (3 ^(1//4) ...

    Text Solution

    |

  15. Which of the following Boolean expression is a tautology ?

    Text Solution

    |

  16. The system of equations kx + y + z =1, x + ky + z = k and x + y + zk ...

    Text Solution

    |

  17. If the fourth term in the expansion of ( x + x^(log(2) x ))^(7) is 44...

    Text Solution

    |

  18. If the Boolean expression ( p rArr q ) hArr ( ~q ** p ) is a tautology...

    Text Solution

    |

  19. Which of the following is true for y(x) that satisfies the differentia...

    Text Solution

    |

  20. Choose the incorrect statement about the two circles whose equations a...

    Text Solution

    |