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  • Question 1
    1 / -0

    Sum to the infinity of the series \(\frac{3}{4}-\frac{5}{4^{2}}+\frac{3}{4^{3}}-\frac{5}{4^{4}}+\frac{3}{4^{5}}-\frac{5}{4^{6}}+\ldots .\) is

  • Question 2
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    Two vertical poles AL and BM of heights 20 m and 80 m respectively stand apart on a horizontal plane. If A and B be the feet of the poles and AM and BL intersect at P, then the height of P is equal to

  • Question 3
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    Two tangents are drawn from a point P to the parabola y2 = 4x such that the slope of one tangent is 5 times the slope of the other. The locus of P is-

  • Question 4
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    If the sides of a triangle are in the ratio \(1: \sqrt{3}: 2,\) then the angles of the triangle are in the ratio:

  • Question 5
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    \begin{equation}\lim _{x \rightarrow 0}\left(\frac{a^{x}+b^{x}+c^{x}}{3}\right)^{\frac{2}{z}}(a>0, b>0, c>0) \text { is }\end{equation}

  • Question 6
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    The area of the region bounded by the curves y=x2, y=|2-x2 |, which lies to the right of the line x = 1/2, is

  • Question 7
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    Find the solution of the differential equation \(\frac{d y}{d x}=\frac{y}{2 y \ln y+y-x}\)
    given that \(y=4\) at \(x=3\)

  • Question 8
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    \begin{equation}\text { The value of } \sum_{r=1}^{89} \log _{10} . \tan \frac{\pi r}{180} \quad \text { is equal to }\end{equation}

  • Question 9
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    \begin{equation}If (4)^{\log _{9} 3}+(9)^{\log _{2} 4}=(10)^{\log _{ x } 83}, \text { then the value of } x \text { is equal to }\end{equation}

  • Question 10
    1 / -0

    \begin{equation}\text { If } \sqrt{\log _{2} x}-0.5=\log _{2} \sqrt{x} \quad \text { , then } x \text { is equal to }\end{equation}

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