GATE CE 2001 | GATE CE Year Wise Previous Years Questions

GATE CE 2001

MCQ (Single Correct Answer)

-0.6

The solution for the following differential equation with boundary conditions $$y(0)=2$$ and $$\,\,{y^1}\left( 1 \right) = - 3$$ is where $${{{d^2}y} \over {d{x^2}}} = 3x - 2$$

$$y = {{{x^3}} \over 3} - {{{x^2}} \over 2} = 3x - 2$$

$$y = 3{x^3} - {{{x^2}} \over 2} - 5x + 2$$

$$y = {{{x^3}} \over 2} - {x^2} - 5{x \over 2} + 2$$

$$y = {x^3} - {{{x^2}} \over 2} + 5x + {3 \over 2}$$

GATE CE 2001

MCQ (Single Correct Answer)

-0.3

The number of boundary conditions required to solve the differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\partial {y^2}}} = 0\,\,$$ is

$$2$$

$$0$$

$$4$$

$$1$$

GATE CE 2001

MCQ (Single Correct Answer)

-0.3

The inverse Laplace transform of $$1/\left( {{s^2} + 2s} \right)$$ is

$$\left( {1 - {e^{ - 2t}}} \right)$$

$$\left( {1 + {e^{2t}}} \right)/2$$

$$\left( {1 - {e^{2t}}} \right)/2$$

$$\left( {1 - {e^{ - 2t}}} \right)/2$$

GATE CE 2001

MCQ (Single Correct Answer)

-0.6

A 15 cm length of steel rod with relative density of 7.4 is submerged in a two layer fluid. The bottom layer is mercury and the top layer is water. The height of top surface of the rod above the liquid interface in 'cm' is

8.24

7.82

7.64

7.38

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2018