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11 . Limit of the following series as x approaches is
 A. 1 B. Π / 2 C. Π / 3 D. 2Π / 3

12 . Directional derivative of f ( x, y, z ) = x² + y² + z² at the point (1, 1, 1) in the direction i - k is
 A. 0 B. 2 C. √2 D. 2√2

13 . Minimum point of the function f(x)=x ³/x is at
 A. x = 0 B. x = -1 C. x = 1 D. x = 1/√3

14 . If f (0) = 2 and f (x) = 1 / (5-x2), then lower and upper bound of f(1) estimated by the mean value theorem are
 A. 1.9,2.2 B. 2.25,2.5 C. 2.2,2.25 D. None of these

15 . The unit normal to the plane 2x +y + 2z = 6 can be expressed in the vector form as
 A. B. C. D. None of these

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