1
GATE PI 2009
MCQ (Single Correct Answer)
+1
-0.3
The line integral of the vector function $$\overrightarrow F = 2x\widehat i + {x^2}\widehat j\,\,$$ along the $$x$$ - axis from $$x=1$$ to $$x=2$$ is
A
$$0$$
B
$$2.33$$
C
$$3$$
D
$$5.33$$
2
GATE PI 2009
MCQ (Single Correct Answer)
+2
-0.6
The solution of the differential equation $${{{d^2}y} \over {d{x^2}}} = 0$$ with boundary conditions
(i) $${{dy} \over {dx}} = 1$$ at $$x=0$$
(ii) $${{dy} \over {dx}} = 1$$ at $$x=1$$
A
$$y=1$$
B
$$y=x$$
C
$$y=x+c$$ where $$c$$ is an arbitrary constant.
D
$$\,y = {C_1}x + {C_2}$$ where $${C_1},\,{C_2}$$ are arbitrary constants
3
GATE PI 2009
MCQ (Single Correct Answer)
+1
-0.3
The homogeneous part of the differential equation $$\,{{{d^2}y} \over {d{x^2}}} + p{{dy} \over {dx}} + qy = r\,\,$$ ( $$p, q, r$$ are constants) has real distinct roots if
A
$${p^2} - 4q > 0$$
B
$${p^2} - 4q < 0$$
C
$${p^2} - 4q = 0$$
D
$${p^2} - 4q = r$$
4
GATE PI 2009
MCQ (Single Correct Answer)
+1
-0.3
During the numerical solution of a first order differential equation using the Euler (also known as Euler Cauchy) method with step size $$h,$$ the local truncation error is of the order of
A
$${h^2}$$
B
$${h^3}$$
C
$${h^4}$$
D
$${h^5}$$
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