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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