1. \[\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin \frac{\theta }{2}}}{\theta }\] is
2. At x = 0, the function f(x) = x3 + 1 has
3. If T(x, y, z) = x2 + y2 + 2z2 defines the temperatures at any location (x, y, z) then magnitude of temperature gradient at P(1, 1, 1) is
4. The value of \[\mathop {\lim }\limits_{{\text{x}} \to 0} \frac{{{{\text{x}}^3} - \sin \left( {\text{x}} \right)}}{{\text{x}}}\] is
5. The divergence of the vector field \[\left( {{\rm{x}} - {\rm{y}}} \right){\rm{\hat i}} + \left( {{\rm{y}} - {\rm{x}}} \right){\rm{\hat j}} + \left( {{\rm{x}} + {\rm{y}} + {\rm{z}}} \right){\rm{\hat k}}\] is
6. The solution of \[\int\limits_1^{\text{a}} {\int\limits_1^{\text{b}} {\frac{{{\text{dxdy}}}}{{{\text{xy}}}}} } \] is
7. The line integral \[\int {\overrightarrow {\text{V}} .{\text{d}}\overrightarrow {\text{r}} } \] of the vector \[\overrightarrow {\rm{V}} .\left( {\overrightarrow {\rm{r}} } \right) = 2{\rm{xyz\hat i}} + {{\rm{x}}^2}{\rm{z\hat j}} + {{\rm{x}}^2}{\rm{y\hat k}}\] from the origin to the point P(1, 1, 1)
8. Given a vector \[\overline {\rm{u}} = \frac{1}{3}\left( { - {{\rm{y}}^3}{\rm{\hat i}} + {{\rm{x}}^3}{\rm{\hat j}} + {{\rm{z}}^3}{\rm{\hat k}}} \right)\] and \[{{\rm{\hat n}}}\] as the unit normal vector to the surface of the hemisphere (x2 + y2 + z2 = 1; z ≥ 0), the value of integral \[\int {\left( {\nabla \times \overline {\rm{u}} } \right) \cdot {\rm{\hat n}}} {\rm{dS}}\] evaluated on the curved surface of the hemisphere S is
9. The minimum value of function y = x2 in the interval [1, 5] is
10. Let f(x) = \[{{\rm{x}}^{ - \frac{1}{3}}}\] and A denote the area of the region bounded by f(x) and the X-axis, when x varies from -1 to 1. Which of the following statements is/are True?
1. f is continuous in [-1, 1]
2. f is not bounded in [-1, 1]
3. A is nonzero and finite
1. f is continuous in [-1, 1]
2. f is not bounded in [-1, 1]
3. A is nonzero and finite
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