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A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied simultaneously, then the net ... $\sigma \left ( 1+1/\sqrt{2} \right )$ $\sigma /2$ $\sigma \left ( 1-1/\sqrt{2} \right )$
The lengths of members $\text{BC}$ and $\text{CE}$ in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints is negligible. Two forces of magnitude $Q> 0$ are applied as shown, each at the mid-length of the respective ... or more of the following members do not carry any load (force)? $\text{AB}$ $\text{CD}$ $\text{EF}$ $\text{GH}$
$A$ is a $3 \times 5$ real matrix of rank $2$. For the set ot homogeneous equations $Ax = 0$, where $0$ is a zero vector and $x$ is a vector of unknown variables, which of the following is/are true? The given set of equations will have ... of appropriate size. The given set of equations will have infinitely many solutions. The given set of equations will have many but a finite number of solutions.
The velocity field in a fluid is given to be $\vec{V} = \left ( 4xy \right )\hat{i} + 2\left ( x^{2} - y^{2} \right )\hat{j}$. Which of the following statement$(s)$ is/are correct? The velocity field is one-dimensional. The flow is incompressible. The flow is irrotational. The acceleration experienced by a fluid particle is zero at $(x = 0,y = 0)$.
Which of these processes involve$(s)$ melting in metallic workpieces? Electrochemical machining Electric discharge machining Laser beam machining Electron beam machining
Consider sand casting of a cube of edge length $a$. A cylindrical riser is placed at the top of the casting. Assume solidification time, $t_{s} \:\alpha\: V/A$, where $V$ is the volume and $A$ is the total surface area dissipating heat. If the top of the riser is insulated, which of the following radius/radii of riser is/are acceptable? $\dfrac{a}{3}$ $\dfrac{a}{2}$ $\dfrac{a}{4}$ $\dfrac{a}{6}$
A square plate is supported in four different ways (configurations $(P)$ to $(S)$ as shown in the figure). A couple moment $C$ is applied on the plate. Assume all the members to be rigid and mass-less, and all joints to be frictionless. All support ... for which one or more of the following support configurations? Configuration $(P)$ Configuration $(Q)$ Configuration $(R)$ Configuration $(S)$
The system of linear equations in real $\left ( x,y \right )$ given by $\left ( x \: y \right )\begin{bmatrix} 2 &5 - 2 \alpha \\ \alpha & 1 \end{bmatrix} = \left ( 0\:0 \right )$ involves a real parameter $\alpha$ and has infinitely many non-trivial solutions for special value(s) of $\alpha$. Which one or ... value(s) of $\alpha$? $x = 2, y = -2$ $x = -1, y = 4$ $x = 1, y = 1$ $x = 4, y = -2$
The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure ... Mass flow rate through the nozzle will increase. Mach number at the exit plane of the nozzle will become more than unity.
Which of the following methods can improve the fatigue strength of a circular mild steel $\text{(MS)}$ shaft? Enhancing surface finish Shot peening of the shaft Increasing relative humidity Reducing relative humidity
Which of the following additive manufacturing technique(s) can use a wire as a feedstock material? Stereolithography Fused deposition modeling Selective laser sintering Directed energy deposition processes
Which of the following heat treatment processes is/are used for surface hardening of steels? Carburizing Cyaniding Annealing Carbonitriding
Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE? A body subjected to hydrostatic pressure has no shear stress. If a ... a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.
1 vote
​​​​ A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above. Which one of the following is the correct drawing of the view of the $\text{3D}$ object as viewed in the direction indicated by an arrow in the above figure?
1 vote
In a $12$-hour clock that runs correctly, how many times do the second, minute, and hour hands of the clock coincide, in a $12$-hour duration from $3$ PM in a day to $3$ AM the next day? $11$ $12$ $144$ $2$
1 vote
Four cities $\text{P, Q, R}$ and $\text{S}$ are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of ... the minimum time required? $6$ hours $30$ minutes $3$ hours $45$ minutes $4$ hours $30$ minutes $5$ hours $15$ minutes
1 vote
Equal sized circular regions are shaded in a square sheet of paper of $1$ cm side length. Two cases, case $\text{M}$ and case $\text{N}$, are considered as shown in the figures below. In the case $\text{M}$, four circles are shaded in the square sheet and in the case $\text{N}$, nine circles are ... of unshaded regions of case $\text{M}$ to that of case $\text{N}$? $2 : 3$ $1 : 1$ $3 : 2$ $2 : 1$
1 vote
A person was born on the fifth Monday of February in a particular year. Which one of the following statements is correct based on the above information? The $2^{\text{nd}}$ February of that year is a Tuesday There will be five Sundays in the month of February in that year The $1^{\text{st}}$ February of that year is a Sunday All Mondays of February in that year have even dates
1 vote
Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other? (rotation and translation operations may be used).
Consider a steady flow through a horizontal divergent channel, as shown in the figure, with supersonic flow at the inlet. The direction of flow is from left to right. Pressure at location $B$ is observed to be higher than that at an upstream location $A$. ... ? Since volume flow rate is constant, velocity at $B$ is lower than velocity at $A$ Normal shock Viscous effect Boundary layer separation
Match the additive manufacturing technique in Column $\text{I}$ with its corresponding input material in Column $\text{II}$. Additive manufacturing technique (Column $\text{I}$) Input material (Column $\text{II}$) $P$ Fused deposition modelling $1$ Photo sensitive liquid resin $Q$ Laminated object manufacturing $2$ Heat fusible ... $P -1, Q -2, R -4$ $P -2, Q -3, R -1$ $P -4, Q -1, R -4$
A shaft of diameter $25_{-0.07}^{-0.04}$ $\text{mm}$ is assembled in a hole of diameter $25_{-0.00}^{+0.02}$ $\text{mm}$. Match the allowance and limit parameter in Column $\text{I}$ with its corresponding quantitative value in Column $\text{II}$ ... $P -1, Q -3, R -2$ $P -1, Q -3 R -4$ $P -3, Q -1, R -2$
Fluidity of a molten alloy during sand casting depends on its solidification range. The phase diagram of a hypothetical binary alloy of components $A$ and $B$ is shown in the figure with its eutectic composition and temperature. All the lines in this phase diagram, including the solidus and liquidus ... $400^{\circ}C$ $250^{\circ}C$ $800^{\circ}C$ $150^{\circ}C$
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end $E$ of a massive uniform rigid shaft $\text{AE}$ which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings $\text{AB}$ ... to $\omega$) about the positive $y$-axis direction rotate slowly (compared to $\omega$) about the negative $y$-axis direction
Consider a cube of unit edge length and sides parallel to co-ordinate axes, with its centroid at the point $(1, 2, 3)$. The surface integral $\int _{A} \vec{F}.d\vec{A}$ of a vector field $\vec{F} = 3x\hat{i} + 5y\hat{j} + 6z\hat{k}$ over the entire surface $A$ of the cube is _____________. $14$ $27$ $28$ $31$
$F(t)$ is a periodic square wave function as shown. It takes only two values, $4$ and $0$, and stays at each of these values for $1$ second before changing. What is the constant term in the Fourier series expansion of $F(t)$? $1$ $2$ $3$ $4$
1 vote
Consider the following for non-zero positive integers, $p$ and $q$. $f\left ( p, q \right ) = \frac{p\times p\times p\times \cdots\: \cdots\: \cdots \times p \:= \:p^{q}}{q\:{terms}}; f\left ( p, 1 \right )=p$ ... $g\left ( 2,1 \right ) \neq f\left ( 2,1 \right )$ $f\left ( 3,2 \right )> g\left ( 3,2 \right )$
1 vote
For the past $m$ days, the average daily production at a company was $100$ units per day. If today’s production of $180$ units changes the average to $110$ units per day, What is the value of $m$? $18$ $10$ $7$ $5$
Fish belonging to species $S$ in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black pigment results in lower ... and disadvantages to species $S$ Having ultra-black skin is only disadvantageous to species $S$ but advantageous only to their predators
1 vote
If $f\left ( x \right ) = 2 \:\ln \left ( \sqrt{e^{x}} \right )$, what is the area bounded by $f\left ( x \right )$ for the interval $\left [ 0,2 \right ]$ on the $x$ – axis? $\frac{1}{2}$ $1$ $2$ $4$
1 vote
Which one of the following is a representation (not to scale and in bold) of all values of $x$ satisfying the inequality $2 - 5x \leq - \dfrac{6x - 5}{3}$ on the real number line?
1 vote
Writing too many things on the ___________ while teaching could make the students get _____________. bored / board board / bored board / board bored / bored
Consider the definite integral $\int_{1}^{2} \left ( 4x^{2} + 2x + 6 \right )dx.$ Let $I_{e}$ be the exact value of the integral. If the same integral is estimated using Simpson’s rule with $10$ equal subintervals, the value is $I_{S}$. The percentage error is defined as $e = 100\times \left ( I_{e} - I_{S}\right )/I_{e}$. The value of $e$ is $2.5$ $3.5$ $1.2$ $0$
Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$ If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________. $\sqrt{\pi a}$ $\sqrt{\frac{\pi }{a}}$ $b\sqrt{\pi a}$ $b\sqrt{\frac{\pi }{a}}$
A polynomial $\varphi \left ( s \right ) = a_{n}s^{n} + a_{n-1}s^{n-1} + \cdots + a_{1}s+a_{0}$ of degree $n>3$ with constant real coefficients $a_{n}, a_{n-1}, \:\dots a_{0}$ has triple roots at $s = -\sigma$ ... $\varphi \left ( s \right ) = 0,$ and $\frac{d^{3}\varphi \left ( s \right )}{ds^{3}} = 0$ at $s = -\sigma$
Which one of the following is the definition of ultimate tensile strength $\text{(UTS)}$ obtained from a stress-strain test on a metal specimen? Stress value where the stress-strain curve transitions from elastic to plastic behavior The ... original cross-sectional area The maximum load attained divided by the corresponding instantaneous cross-sectional area Stress where the specimen fractures
A structural member under loading has a uniform state of plane stress which is usual notations is given by $\sigma _{x} = 3P, \sigma _{y} = -2P$ and $\tau_{xy} = \sqrt{2}P$, where $P>0$. The yield strength of the material is $350$ $\text{MPa}$. If the member is ... (according to the maximum distortion energy theory) is $70$ $\text{MPa}$ $90$ $\text{MPa}$ $120$ $\text{MPa}$ $75$ $\text{MPa}$
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine? Linear motor Ball screw Lead screw Chain and sprocket