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  • Question 1
    4 / -1

    Evaluate \(\int e^x\left(\frac{1}{x}-\frac{1}{x^2}\right) d x\)

  • Question 2
    4 / -1

    The angle between the vectors \(\hat{i}-\hat{j}\) and \(\hat{j}-\hat{k}\) is:

  • Question 3
    4 / -1

    Find the coefficient of \(x^{4}\) in the expansion of \(\left(1+x+x^{2}+x^{3}\right)^{11}\).

  • Question 4
    4 / -1

    There are \(12\) points in a plane out of which \(5\) are collinear. The number of triangles formed by the points as vertices is:

  • Question 5
    4 / -1

    The distance between two parallel tangents of a circle of radius \(4\) cm is:

  • Question 6
    4 / -1

    Solve \((2 y+x) \frac{d y}{d x}=1\).

  • Question 7
    4 / -1

    Find the set of value of x for which f(x) = cos x − x is decreasing in

  • Question 8
    4 / -1

    If \(a \cot \theta+b \operatorname{cosec} \theta=p\) and \(b \cot \theta+a\) \(\operatorname{cosec} \theta=q\), then \(p^2-q^2=\)

  • Question 9
    4 / -1

    \(\left|\begin{array}{lll}a+b & a & b \\ a & a+c & c \\ b & c & b+c\end{array}\right|=\)

  • Question 10
    4 / -1

    The vector equation of the plane passing through \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{c}}\), is \(\overrightarrow{\mathrm{r}}=\alpha \overrightarrow{\mathrm{a}}+\beta \overrightarrow{\mathrm{b}}+\gamma \overrightarrow{\mathrm{c}}\), provided that,

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