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If 0 le x le 2pi and 2^(cosec^(2)x)sqrt(...

If `0 le x le 2pi` and `2^(cosec^(2)x)sqrt(1/2y^(2)-y+1)lesqrt(2)` then the number of ordered pairs of (x,y) is

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Knowledge Check

  • If x, y in [0, 2 pi] , then the total number of ordered pairs (x, y) satisfying the equation sinx cos y = 1 is

    A
    1
    B
    2
    C
    3
    D
    4

  • f(x)={:{(x+1,x le 1),(2x+1,1 lt x le 2):} and g(x)={:{(x^(2)",",-1le x lt2),(x+2",",2 le x le 3):} The domain of the function f(g(x)) is

    A
    `[0, sqrt(2)]`
    B
    `[-1, 2]`
    C
    `[-1, sqrt(2)]`
    D
    `[sqrt(2), 2]`

  • If x ge 0, y ge 0, 2x le x +y le 8, 2x+y le 10 , then the minimum value of F=5x+7y is

    A
    10
    B
    14
    C
    6
    D
    5

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    Number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^(-1)(sinx) where -pi le x le pi

    If Sec^(-1)sqrt(1-x^(2))+Cosec^(-1)(sqrt(1+y^(2)))/y+"Cot"^(-1)1/z=3pi then

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    If x ge 0, y ge 0, 2x+3y le 10 and x+2y ge 10 then the minimum value of f=2x+3y is

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