GATE CE 2002 | GATE CE Year Wise Previous Years Questions

GATE CE 2002

MCQ (Single Correct Answer)

-0.6

The directional derivative of the following function at $$(1, 2)$$ in the direction of $$(4i+3j)$$ is : $$f\left( {x,y} \right) = {x^2} + {y^2}$$

$$4/5$$

$$4$$

$$2/5$$

$$1$$

GATE CE 2002

MCQ (Single Correct Answer)

-0.6

The Laplace transform of the following function is $$$f\left( t \right) = \left\{ {\matrix{ {\sin t} & {for\,\,0 \le t \le \pi } \cr 0 & {for\,\,t > \pi } \cr } } \right.$$$

$$1/\left( {1 + {s^2}} \right)\,$$ for all $$\,s > 0$$

$$1/\left( {1 + {s^2}} \right)\,$$ for all $$\,s < \pi $$

$$\left( {1 + {e^{ - \pi s}}} \right)/\left( {1 + {s^2}} \right)$$ for all $$s>0$$

$${e^{ - \pi s}}/\left( {1 + {s^2}} \right)$$ for all $$s > 0$$

GATE CE 2002

Subjective

-0

Using Laplace transforms, solve $${a \over {{s^2} - {a^2}}}\,\,\left( {{d^2}y/d{t^2}} \right) + 4y = 12t\,\,$$
given that $$y=0$$ and $$dy/dt=9$$ at $$t=0$$

GATE CE 2002

MCQ (Single Correct Answer)

-0.3

In natural water, hardness is mainly caused by

$$Ca^{++}$$ and $$Mn^{++}$$

$$Ca^{++}$$ and $$Fe^{++}$$

$$Na^{+}$$ and $$K^{+}$$

$$Ca^{++}$$ and $$Mg^{++}$$

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GATE CE Papers

2018