41. The polynomial p(x) = x5 + x + 2 has
42. A function y = 5x2 + 10x is defined over an open interval x = (1, 2). At least at one point in this interval, $$\frac{{{\text{dy}}}}{{{\text{dx}}}}$$ is exactly
43. Let x and y be two vectors in a 3 dimensional space and <x, y> denote their dot product. Then the determinant det \[\left[ {\begin{array}{*{20}{c}}
{ < {\text{x}},{\text{x}} > }&{ < {\text{x}},{\text{y}} > } \\
{ < {\text{y}},{\text{x}} > }&{ < {\text{y}},{\text{y}} > }
\end{array}} \right].\]
44. $$\mathop {{\text{Lim}}}\limits_{{\text{x}} \to \infty } \left( {\frac{{{\text{x}} + \sin {\text{x}}}}{{\text{x}}}} \right)$$ equal to
45. For a vector E, which one of the following statements is NOT TRUE?
46. Which one of the following functions is continuous at x = 3?
47. If A(0, 4, 3), B(0, 0, 0) and C(3, 0, 4) are three points defined in x, y, zeo-ordinate system, then which of the following vector is perpendicular to both vectors \[\overrightarrow {{\text{AB}}} \] and \[\overrightarrow {{\rm{BC}}} .\]
48. A function f(x) is defined as
\[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}}
{{{\text{e}}^x}}&{{\text{x}} < 1} \\
{\ln {\text{x}} + {\text{a}}{{\text{x}}^2} + {\text{bx}},}&{{\text{x}} \geqslant 1}
\end{array}} \right.\]
where x\[ \in \] R which one of the following statements is TRUE?
\[{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {{{\text{e}}^x}}&{{\text{x}} < 1} \\ {\ln {\text{x}} + {\text{a}}{{\text{x}}^2} + {\text{bx}},}&{{\text{x}} \geqslant 1} \end{array}} \right.\]
where x\[ \in \] R which one of the following statements is TRUE?
49. The inner (dot) product of two non zero vectors \[\overrightarrow {\text{P}} \] and \[\overrightarrow {\text{Q}} \] is zero. The angle (degrees) between the two vectors is
50. Let f(x) = ex + x2 for real x. From among the following, choose the Taylor series approximation of f(x) around x = 0, which includes all powers of x less than or equal to 3,
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