Home
Class 12
MATHS
Number of solutions to the equation 2^(s...

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

A

zero

B

1

C

finitely many

D

infinitely many

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Exercise ( Level 2 (single correct answer type questions))|20 Videos
  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Exercise ( Level 2 (Numerical answer type questions))|19 Videos
  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Exercise (Concept-based single correct answer type questions)|20 Videos
  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|25 Videos
  • SETS, RELATIONS AND FUNCTIONS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEAR.S B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|19 Videos

Similar Questions

Explore conceptually related problems

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 3"sin"^(2) x - 7"sin" x +2 = 0 in the interval [0, 5 pi] , is

Find the number of solutions of the equation sin^(8)x+cos^(8)x=1 in the interval [-2 pi,2 pi]

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 of the equation log_(sqrt2sin x)(1+cosx)=2 in the interval [0, 5pi] is

Number of solutions of the equation tan x+sec x=2cos x lying in the interval [0,2 pi] is

The number of solutions of the equation 2 "tan" x + x = (12 pi)/(5) " in the interval " [0, 2 pi] , is

MCGROW HILL PUBLICATION-QUADRATIC EQUATIONS-Exercise ( Level 1 (single correct answer type questions))
  1. The integral values of a for which the quadratic equation (x - a) (x -...

    Text Solution

    |

  2. The number of real solution fo 4^(x + 1.5) + 9^(x + 0.5) = (10)/ (6^(x...

    Text Solution

    |

  3. Number of solutions to the equation 2^(sin^2 x) +5.2^(cos^2 x) = 7, in...

    Text Solution

    |

  4. The number of values of k for which the equation x^(2) - 2x + k = 0 ha...

    Text Solution

    |

  5. If roots of the equation ax^2 + bx + c = 0 are alpha/(alpha-1) and (a...

    Text Solution

    |

  6. Let x be an integer and x^2 + x + 1 is divisible by 3. When is x divid...

    Text Solution

    |

  7. If alpha, beta are roots of the equation x^(2) + ax + b = 0, then max...

    Text Solution

    |

  8. If both the roots of the equation x^(2) + bx + c = 0 lie in the interv...

    Text Solution

    |

  9. Let a, b, c in R be such that a + b + c lt 0, a - b + c lt 0 and c g...

    Text Solution

    |

  10. Find the valuesof m for which exactly one root of the equation x^(2)-2...

    Text Solution

    |

  11. The value of sqrt(8 + 2 sqrt(8 + 2 sqrt(8 + 2 sqrt(8 + . . . . )))) i...

    Text Solution

    |

  12. The number of solutions of the equation sin((pix)/(2sqrt3))=x^2-2sqrt3...

    Text Solution

    |

  13. The number of solutions of |x+2| = 2(3 - x) is

    Text Solution

    |

  14. If the equation ax^(2)+bx+c=0 (a lt 0) has two roots alpha and beta su...

    Text Solution

    |

  15. Two non-integer roots of (x^(2) - 5x)^(2) - 7 (x^(2) - 5x) + 6 = 0 are

    Text Solution

    |

  16. The number of real roots of ((x - 1)/( x + 1))^(4) - 13 ((x - 1)/( x +...

    Text Solution

    |

  17. The number of negative roots of 9^(x +2) - 6 (3^(x +1)) + 1 = 0 is

    Text Solution

    |

  18. The number of roots of 81 ((2x - 5)/( 3x +1))^(4) - 45 ((2x - 5)/(3x ...

    Text Solution

    |

  19. (x^2+3x+2)^2 - 8(x^2+3x) -4 =0

    Text Solution

    |

  20. The number of roots of the equation sqrt((x)/(x - 3)) + sqrt((x - 3)/(...

    Text Solution

    |