1
GATE CE 2010
MCQ (Single Correct Answer)
+2
-0.6
A parabolic cable is held between two supports at the same level. The horizontal span between the supports is $$L.$$ The sag at the mid-span is $$h.$$ The equation of the parabola is $$y = 4h{{{x^2}} \over {{L^2}}},\,\,$$ where $$x$$ is the horizontal coordinate and $$y$$ is the vertical coordinate with the origin at the centre of the cable. The expanssion for the total length of the cable is
A
$$\int\limits_0^L {\sqrt {1 + 64{{{h^2}{x^2}} \over {{L^4}}}} dx} $$
B
$$2\int\limits_0^{L/2} {\sqrt {1 + 64{{{h^3}{x^2}} \over {{L^4}}}} dx} $$
C
$$\int\limits_0^{L/2} {\sqrt {1 + 64{{{h^2}{x^2}} \over {{L^4}}}} dx} $$
D
$$2\int\limits_0^{L/2} {\sqrt {1 + 64{{{h^2}{x^2}} \over {{L^4}}}} dx} $$
2
GATE CE 2010
MCQ (Single Correct Answer)
+1
-0.3
The $$\mathop {Lim}\limits_{x \to 0} {{\sin \left( {{2 \over 3}x} \right)} \over x}\,\,\,$$ is
A
$${{2 \over 3}}$$
B
$$1$$
C
$${{3 \over 2}}$$
D
$$ \propto $$
3
GATE CE 2010
MCQ (Single Correct Answer)
+2
-0.6
Given a function $$f\left( {x,y} \right) = 4{x^2} + 6{y^2} - 8x - 4y + 8,$$ the optimal values of $$f(x,y)$$ is
A
a minimum equal to $${{10} \over 3}$$
B
a maximum equal to $${{10} \over 3}$$
C
a minimum equal to $${{8} \over 3}$$
D
a maximum equal to $${{8} \over 3}$$
4
GATE CE 2010
MCQ (Single Correct Answer)
+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
$$1/2$$
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