# Recent questions in Others $F(t)$ 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 $F(t)$? $1$ $2$ $3$ $4$
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 _____________. $14$ $27$ $28$ $31$
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 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
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 $70$ $\text{MPa}$ $90$ $\text{MPa}$ $120$ $\text{MPa}$ $75$ $\text{MPa}$
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 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 $\text{II}$ ... $P -1, Q -3, R -2$ $P -1, Q -3 R -4$ $P -3, Q -1, R -2$
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 ... $P -1, Q -2, R -4$ $P -2, Q -3, R -1$ $P -4, Q -1, R -4$
Which one of the following $\text{CANNOT}$ impart linear motion in a $\text{CNC}$ machine? Linear motor Ball screw Lead screw Chain and sprocket
Which one of the following is an intensive property of a thermodynamic system? Mass Density Energy Volume
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
Which of the following non-dimensional terms is an estimate of Nusselt number? Ratio of internal thermal resistance of a solid to the boundary layer thermal resistance Ratio of the rate at which internal energy is advected to the rate of conduction heat transfer Non-dimensional temperature gradient Non-dimensional velocity gradient multiplied by Prandtl number
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 $(S)$
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? $\dfrac{a}{3}$ $\dfrac{a}{2}$ $\dfrac{a}{4}$ $\dfrac{a}{6}$
Which of these processes involve$(s)$ melting in metallic workpieces? Electrochemical machining Electric discharge machining Laser beam machining Electron beam machining
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 $(x = 0,y = 0)$.
A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each can be placed on the platforms. The number of discs placed on the left side platform ... refer to part $\text{(ii)}$ of the figure) required to prevent downward motion of the left side platform is _____________________(in integer).
For a dynamical system governed by the equation. $\ddot{x}\left ( t \right ) + 2\zeta \omega _{n}\dot{x}\left ( t \right )+\omega _{n}^{2}x\left ( t \right ) = 0$ the damping ratio $\zeta$ ... . Neglecting higher powers $(>1)$ of the damping ratio, the displacement at the next peak in the positive direction will be __________________ $\text{mm}$ (in integer).
An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing method with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is ____________ units (in integer).
The demand of a certain part is $1000$ parts/year and its cost is ₹$1000$/part. The orders are placed based on the economic order quantity $\text{(EOQ)}$. The cost of ordering is ₹$100$/order and the lead time for receiving the orders is $5$ days. If the holding cost is ₹$20$/part/year, the inventory level for placing the orders is ________________ parts (round off to the nearest integer).
Consider $1$ $\text{kg}$ of an ideal gas at $1$ bar and $300$ $K$ contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume $c_{v}$ is equal to $750 \:J \cdot kg^{-1}\cdot K^{-1}$. A ... work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be _____________ bar (in integer).
Wien's law is stated as follows: $\lambda _{m}T = C$, where $C$ is $2898$ $\mu m \cdot K$ and $\lambda_{m}$ is the wavelength at which the emissive power of a black body is maximum for a given temperature $T$. The spectral hemispherical ... $K$ (round off to the nearest integer).
For the exact differential equation, $\frac{du}{dx}= \frac{-xu^{2}}{2+x^{2}u},$ which one of the following is the solution? $u^{2} + 2x^{2} =$ constant $xu^{2} + u =$ constant $\frac{1}{2}x^{2}u^{2} + 2u =$ constant $\frac{1}{2}ux^{2} + 2x =$ constant
A rigid homogeneous uniform block of mass $1$ $\text{kg}$, height $h = 0.4 \:m$ and width $b = 0.3\: m$ is pinned at one corner and placed upright in a uniform gravitational field $(g = 9.81 m/s^{2})$, supported by a roller in the configuration shown in the figure. A short duration ... required to topple the block is $0.953$ $\text{Ns}$ $1.403$ $\text{Ns}$ $0.814$ $\text{Ns}$ $1.172$ $\text{Ns}$
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 ... $\sigma \left ( 1+1/\sqrt{2} \right )$ $\sigma /2$ $\sigma \left ( 1-1/\sqrt{2} \right )$
A rigid body in the $\text{X-Y}$ plane consists of two point masses ($1$ $\text{kg}$ each) attached to the ends of two massless rods, each of $1$ $\text{cm}$ length, as shown in the figure. It rotates at $30$ $\text{RPM}$ counter-clockwise about the $Z$-axis passing through point ... to point $O$. The length of the third rod is _______________ $\text{cm}$. $1$ $\sqrt{2}$ $1/\sqrt{2}$ $1/2\sqrt{2}$
A spring mass damper system (mass $m$, stiffness $k$, and damping coefficient $c$) excited by a force $F(t) = B \sin w t$, where $B$, $w$ and $t$ ... $(P) \rightarrow \text{(iii)}, (Q) \rightarrow \text{(iv)}, (R) \rightarrow \text{(ii)}, (S) \rightarrow \text{(i)}$
Parts $P1 - P7$ are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required tor carrying out both the operations for all $7$ ... $31$ $33$ $30$ $32$
A manufacturing unit produces two products $P1$ and $P2$. For each piece of $P1$ and $P2$, the table below provides quantities of materials $\text{M1, M2}$ and $M3$ required, and also the profit earned. The maximum quantity available per day for $\text{M1, M2}$ and $M3$ is also ... $5000$ $4000$ $3000$ $6000$
A tube of uniform diameter $D$ is immersed in a steady flowing inviscid liquid stream of velocity $V$, as shown in the figure. Gravitational acceleration is represented by $g$. The volume flow rate through the tube is __________________. $\dfrac{\pi}{4}D^{2}V$ $\dfrac{\pi}{4}D^{2}\sqrt{2gh_{2}}$ $\dfrac{\pi}{4}D^{2}\sqrt{2g\left ( h_{1} + h_{2}\right )}$ $\dfrac{\pi}{4}D^{2}\sqrt{V^{2} - 2gh_{2}}$
The steady velocity field in an inviscid fluid of density $1.5$ is given to be $\vec{V} = \left ( y^{2}-x^{2} \right )\hat{i} + \left ( 2xy \right )\hat{j}.$ Neglecting body forces, the pressure gradient at $(x = 1, y = 1)$ is _________________. $10\hat{j}$ $20\hat{i}$ $-6\hat{i} - 6\hat{j}$ $-4\hat{i} - 4\hat{j}$
In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to $250$ $\text{kJ/kg}$ ... the dryness fraction of the refrigerant at entry to evaporator is _______________. $0.2$ $0.25$ $0.3$ $0.35$
$A$ 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 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)? $\text{AB}$ $\text{CD}$ $\text{EF}$ $\text{GH}$
If the sum and product of eigenvalues of a $2 \times 2$ real matrix $\begin{bmatrix} 3 & p\\ p & q \end{bmatrix}$ are $4$ and $-1$ respectively, then $\left | p \right |$ is ______________ (in integer).
Given $z = x + iy, i = \sqrt{-1}$. $C$ is a circle of radius $2$ with the centre at the origin. If the contour $C$ is traversed anticlockwise, then the value of the integral $\dfrac{1}{2\pi}\int _{C}\dfrac{1}{\left ( z-i \right )\left ( z+4i \right )}dz$ is __________________ (round off to one decimal place).
A shaft of length $L$ is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is $d_{i}$ and the ... range and stress-strain relations are linear. Then the ratio $\tau_{i}/ \tau_{o}$ is ______________ (round off to $2$ decimal places).