Question 1 |
The divergence of vector \vec{r}=x\vec{i}+y\vec{j}+z\vec{k} is
\vec{i}+\vec{j}+\vec{k} | |
3 | |
0 | |
1 |
Question 2 |
Consider the system of equations given below:
x+y=2
2x+2y=5
This system has
x+y=2
2x+2y=5
This system has
one solution | |
no solution | |
infinite solutions | |
four solutions |
Question 3 |
What is the derivative of f(z)=\left | x\right |
at x=0?
1 | |
-1 | |
0 | |
Does not exist |
Question 4 |
The Gauss divergence theorem relates certain
surface integrals to volume integrals | |
surface integrals to line integrals | |
vector quantities to other vector quantities | |
line integrals to volume integrals |
Question 5 |
For a spring-loaded roller-follower driven with a disc cam,
the pressure angle should be larger during rise than that during return for ease of transmitting motion | |
the pressure angle should be smaller during rise than that during return for ease of transmitting motion | |
the pressure angle should be large during rise as well as during return for ease of transmitting motion | |
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 straight line | |
a hyperbola | |
a ellipse | |
a parabola |
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
\frac{1}{2}kx^{2} | |
\frac{1}{2}kx^{2}-mgx | |
\frac{1}{2}k(x+\delta )^{2} | |
\frac{1}{2}kx^{2}+mgx |
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}
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
only when \alpha= 0 | |
only when \alpha= 45^{\circ} | |
only when \alpha= 90^{\circ} | |
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,
bar AB is subjected to bending but bar BC is not subjected to bending | |
bar AB is not subjected to bending but bar BC is subjected to bending | |
neither bar AB nor bar BC is subjected to bending | |
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
\frac{1}{3} | |
\frac{1}{4} | |
\frac{1}{12} | |
\frac{1}{6} |
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