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  • Question 1
    4 / -1

    If \(x^{m+1} y^{n+1}=c^{m+n+2}\), then what is \(\frac{d y}{d x}\) equal to:

  • Question 2
    4 / -1

    Find the distance between the straight line x - 2 = y = z + 1 and the plane x + y - 2z + 3 = 0?

  • Question 3
    4 / -1

    The function \(f(x)=\sqrt{\cos (\sin x)}+\sin ^{-1}\left(\frac{1+x^{2}}{2 x}\right)\) is defined for:

  • Question 4
    4 / -1

    Let \(\Delta=\left|\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right|\), the \(\Delta\) lies in the interval:

  • Question 5
    4 / -1

    If \({ }^{\mathrm{n}} \mathrm{P}_{\mathrm{r}}=2760,{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=23\), then the value of \(\mathrm{r}\) is

  • Question 6
    4 / -1

    The distance of the point (2,3,5) from the line \(\frac{\mathrm{x}+2}{-3}=\frac{\mathrm{y}-2}{4}=\frac{\mathrm{z}+2}{1}\) is

  • Question 7
    4 / -1

    If the group \((z, *)\) of all integers, where \(a * b=a+b+1\) for all \(a, b \in z\), the inverse of \(-2\) is:

  • Question 8
    4 / -1

    If the focus of a parabola is \((-8,-2)\) and the directrix is \(y=2 x-9\), then the equation of the parabola is:

  • Question 9
    4 / -1

    If the constraints in a linear programming problem are changed _______________.

  • Question 10
    4 / -1

    If \(f(x)=\tan ^{-1}\left[\frac{\sin x}{1+\cos x}\right]\), then what is first term derivative of \(f(x)\)?

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