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  • Question 1
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    If the two pairs of lines x2 – 2mxy – y2 = 0 and x2 – 2nxy – y2 = 0 are such that one of them represents the bisector of the angles between the other, then

  • Question 2
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    For any positive integer \(n, \int \frac{d x}{x^{n+1}+x}\) is equal to :

  • Question 3
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    If \(\overrightarrow{ a }\) is perpendicular to \(\vec{b}\) and \(\vec{c},|\vec{a}|=2,|\vec{b}|=3,|\vec{c}|=4\) and the angle between \(\vec{b}\) and \(\vec{c}\) is \(\frac{2 \pi}{3},\) then \([\overrightarrow{ a } \overrightarrow{ b } \overrightarrow{ c }]\) is equal to :

  • Question 4
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    If f(x) = (x – 2)(x – 4)(x – 6)….(x – 2n), then f'(2) is equal to :

  • Question 5
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    The solution of the differential equation \(x \frac{d y}{d x}+2 y=x^{2}\) is :

  • Question 6
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    The differential equation of all non - horizontal lines in a plane is :

  • Question 7
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    The equation of the sphere concentric with the sphere 2x2 + 2y2 + 2z2 - 6x + 2y - 4z = 1 and double its radius is :

  • Question 8
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    Let f : R be a differentiable function and f(1) = 4. Find the value of
    \begin{equation}\lim _{x \rightarrow 1} \int_{4}^{f(x)} \frac{2 t}{x-1} d t, \text { if } f^{\prime}(1)=2\end{equation}

  • Question 9
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    If three natural numbers between 1 and 100 are selected randomly, then the probability that all are divisible by both 2 and 3 is :

  • Question 10
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    The sum to \(n\) terms of the series \(\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots \ldots .\) is :

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