1
GATE CE 2010
+1
-0.3
Two coins are simultaneously tossed. The probability of two heads simultaneously appearing
A
$$1/8$$
B
$$1/6$$
C
$$1/4$$
D
$$1/2$$
2
GATE CE 2010
+1
-0.3
The order and degree of a differential equation $${{{d^3}y} \over {d{x^3}}} + 4\sqrt {{{\left( {{{dy} \over {dx}}} \right)}^3} + {y^2}} = 0$$ are respectively
A
$$3$$ and $$2$$
B
$$2$$ and $$3$$
C
$$3$$ and $$3$$
D
$$3$$ and $$1$$
3
GATE CE 2010
+2
-0.6
The solution to the ordinary differential equation $${{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}} - 6y = 0\,\,\,$$ is
A
$$y = {C_1}\,{e^{3x}} + {C_2}\,{e^{ - 2x}}$$
B
$$y = {C_1}\,{e^{3x}} + {C_2}\,{e^{2x}}$$
C
$$y = {C_1}\,{e^{ - 3x}} + {C_2}\,{e^{2x}}$$
D
$$y = {C_1}\,{e^{ - 3x}} + {C_2}\,{e^{ - 2x}}$$
4
GATE CE 2010
+1
-0.3
The partial differential equation that can be formed from $$z=ax+by+ab$$ has the form $$\,\,\left( {p = {{\partial z} \over {\partial x}},q = {{\partial z} \over {\partial y}}} \right)\,\,$$
A
$$z=px+qy$$
B
$$z=px-qy$$
C
$$z=px+qy+pq$$
D
$$z=qy+pq$$
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