# 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 $\alpha$with 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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