The area enclosed by the curve y = \(\frac { { x }^{ 2 } }{ 2 } \) , the x - axis and the lines x = 1, x = 3 is __________

If u = log (x³ + y³ + z³ - 3xyz) then \(\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z } \) = _____________

The least value of a when f f(x) = x² + ax + 1 is increasing on (1, 2) is __________

.If a = 3+i and z = 2-3i, then the points on the Argand diagram representing az, 3az and - az are _________

The work done by the force \(\overset { \rightarrow }{ F } =\overset { \wedge }{ i } +\overset { \wedge }{ j } +\overset { \wedge }{ k } \) acting on a particle, if the particle is displaced from A(3, 3, 3) to the point B(4, 4, 4) is _________ units

If \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) are two unit vectors, then the vectors \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right) \) is parallel to the vector ___________

The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is ____________

If tan^-1(3) + tan^-1(x) = tan^-1(8) then x = ____________ 

The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has ____________

The system of linear equations x + y + z = 2, 2x + y - z = 3, 3x + 2y + kz = has a unique solution if __________