GATE ME 2001

Question 1
The divergence of vector \vec{r}=x\vec{i}+y\vec{j}+z\vec{k} is
A
\vec{i}+\vec{j}+\vec{k}
B
3
C
0
D
1
Engineering Mathematics   Calculus
Question 2
Consider the system of equations given below:
x+y=2
2x+2y=5
This system has
A
one solution
B
no solution
C
infinite solutions
D
four solutions
Engineering Mathematics   Linear Algebra
Question 3
What is the derivative of f(z)=\left | x\right | at x=0?
A
1
B
-1
C
0
D
Does not exist
Engineering Mathematics   Calculus
Question 4
The Gauss divergence theorem relates certain
A
surface integrals to volume integrals
B
surface integrals to line integrals
C
vector quantities to other vector quantities
D
line integrals to volume integrals
Engineering Mathematics   Calculus
Question 5
For a spring-loaded roller-follower driven with a disc cam,
A
the pressure angle should be larger during rise than that during return for ease of transmitting motion
B
the pressure angle should be smaller during rise than that during return for ease of transmitting motion
C
the pressure angle should be large during rise as well as during return for ease of transmitting motion
D
the pressure angle does not affect the ease of transmitting motion
   
Question 6
The shape of the bending moment diagram for a uniform cantilever beam carrying a uniformly distributed load over its length is
A
a straight line
B
a hyperbola
C
a ellipse
D
a parabola
Strength of Materials   Bending of Beams
Question 7
In the figure shown, the spring deflects by \delta to position A ( the equilibrium position) when a mass m is kept on it. During free vibration, the mass is at position B at some instant. The change in potential energy of the spring-mass system from position A to position B is
A
\frac{1}{2}kx^{2}
B
\frac{1}{2}kx^{2}-mgx
C
\frac{1}{2}k(x+\delta )^{2}
D
\frac{1}{2}kx^{2}+mgx
Theory of Machine   Vibration
Question 7 Explanation: 
\begin{aligned} \Delta(P E) &=(P E)_{B}-(P E)_{A} \\ &=\frac{1}{2} k(x+\delta)^{2}+0-\left[\frac{1}{2} k \delta^{2}+m g x\right] \end{aligned}
Taking reference datum at position B.
At equilibrium position i.e., at A.
\begin{array}{c} m g=\mathrm{k} \delta \\ \Delta(P E)=\frac{1}{2} k x^{2}+\frac{1}{2} k \delta^{2}+x k \delta-\frac{1}{2} k \delta^{2}-m g x\\ \text{as }\quad m g=k \delta\\ \Delta(P E)=\frac{1}{2} k x^{2}+\frac{1}{2} k \delta^{2}+m g x-\frac{1}{2} k \delta^{2}-m g x\\ =\frac{1}{2} k x^{2} \end{array}
Question 8
A particle P is projected from the earth surface at latitude 45^{\circ} with escape velocity v=11.19 km/s. The velocity direction makes an angle \alphawith the local vertical. The particle will escape the earth's gravitational field
A
only when \alpha= 0
B
only when \alpha= 45^{\circ}
C
only when \alpha= 90^{\circ}
D
irrespective of the value of \alpha
   
Question 9
Bars AB and BC, each of negligible mass, support load P as shown in the figure. In this arrangement,
A
bar AB is subjected to bending but bar BC is not subjected to bending
B
bar AB is not subjected to bending but bar BC is subjected to bending
C
neither bar AB nor bar BC is subjected to bending
D
both bars AB and BC are subjected to bending
   
Question 10
The area moment of inertia of a square of size 1 unit about its diagonal is
A
\frac{1}{3}
B
\frac{1}{4}
C
\frac{1}{12}
D
\frac{1}{6}
Strength of Materials   Bending of Beams
There are 10 questions to complete.

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