GATE 2018 Mechanical Engineering

From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the s...

“Her _______ should not be confused with miserliness; she is ever willing to assist those in need.” The word that best fills the blank in the above sentence is

A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

Consider the following three statements: (i) Some roses are red. (ii) All red flowers fade quickly. (iii) Some roses fade quickly. Which of the following statements can be logicall...

For integers a, b and c, what would be the minimum and maximum values respectively of a + b + c if log |a| + log |b| + log |c| = 0?

“Going by the _________ that many hands make light work, the school _______ involved all the students in the task.” The words that best fill the blanks in the above sentence are

Given that a and b are integers and a + a 2 b 3 is odd, which one of the following statements is correct?

Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m 2 of area. What is the area of th...

“The dress _________ her so well that they all immediately _________ her on her appearance.” The words that best fill the blanks in the above sentence are

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many...

The value of the expression $${1 \over {1 + \log _u^{vw}}} + {1 \over {1 + \log _v^{wu}}} + {1 \over {1 + \log _w^{uv}}}$$ is

An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, th...

The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

A wire would enclose an area of 1936 m 2 , if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the s...

“The judge’s standing in the legal community, though shaken by false allegations of wrongdoing, remained _________.” The word that best fills the blank in the above sentence is

Find the missing group of letters in the following series: BC, FGH, LMNO, _____

"The dress ________ her so well that they all immediately ________ her on her appearance." The words that best fill the blanks in the above sentence are

The product of eigenvalues of the matrix P is P = [[2, 0, 1], [4, -3, 3], [0, 2, -1]]

Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is

The Fourier cosine series for an even function $f(x)$ is given by $f(x) = a_0 + \sum_{n=1}^{\infty} a_n \cos(nx)$. The value of the coefficient $a_2$ for the function $f(x) = \cos^...

Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that a...

"Going by the ________ that many hands make light work, the school ________ involved all the students in the task." The words that best fill the blanks in the above sentence are

The divergence of the vector -yi+x j is

The rank of the matrix $\begin{bmatrix} -4 & 1 & -1 \\ -1 & -1 & -1 \\ 7 & -3 & 1 \end{bmatrix}$ is

"Her ________ should not be confused with miserliness; she is ever willing to assist those in need." The word that best fills the blank in the above sentence is

The divergence of the vector field $\vec{u} = e^x (\cos y\hat{i} + \sin y \hat{j})$ is

The value of lim_{x\to 0} \frac{x^3 - \sin(x)}{x} is

"The judge's standing in the legal community, though shaken by false allegations of wrongdoing, remained ________." The word that best fills the blank in the above sentence is

Find the missing group of letters in the following series: BC, FGH, LMNO, ________

The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is

Consider a function $u$ which depends on position $x$ and time $t$. The partial differential equation $\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}$ is known a...

Consider the following partial differential equation for u(x, y) with the constant c > 1: \frac{\partial u}{\partial y} + c \frac{\partial u}{\partial x} = 0 Solution of this equat...

Seven machines take 7 minutes to make 7 identical toys. At the same rate, how many minutes would it take for 100 machines to make 100 toys?

According to the Mean Value Theorem, for a continuous function $f(x)$ in the interval $[a,b]$, there exists a value $\xi$ in this interval such that $\int_{a}^{b} f(x)dx =$

A sample of 15 data is as follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. The mode of the data is

The differential equation \frac{d^2y}{dx^2} + 16y = 0 for y(x) with the two boundary conditions \frac{dy}{dx}|_{x=0} = 1 and \frac{dy}{dx}|_{x=\frac{\pi}{2}} = -1 has

If $y$ is the solution of the differential equation $y^3 \frac{dy}{dx} + x^3 = 0$, $y(0)=1$, the value of $y(-1)$ is

The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

$F(z)$ is a function of the complex variable $z = x+iy$ given by $F(z) = i z + k Re(z) + i Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equations?

A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m² of area. What is the area of the...

A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

The Laplace transform of $te^t$ is

The value of the expression $\frac{1}{1+\log_u vw} + \frac{1}{1+\log_v wu} + \frac{1}{1+\log_w uv}$ is

The minimum axial compressive load, $P$, required to initiate buckling for a pinned-pinned slender column with bending stiffness $EI$ and length $L$ is

A six-face fair dice is rolled a large number of times. The mean value of the outcomes is _________

A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure. The tensions in the strings are

A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency $\omega$ of this single degree of freedom system is

A frictionless gear train is shown in the figure. The leftmost 12-teeth gear is given a torque of 100 N-m. The output torque from the 60-teeth gear on the right in N-m is

For integers a, b and c, what would be the minimum and maximum values respectively of a + b + c if log |a| + log |b| + log |c| = 0?

If σ₁ and σ₃ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and n...

For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the fol...

The state of stress at a point is $\sigma_x = \sigma_y = \sigma_z = \tau_{xz} = \tau_{zx} = \tau_{yz} = \tau_{zy} = 0$ and $\tau_{xy} = \tau_{yx} = 50$ MPa. The maximum normal stre...

In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped...

The equation of motion for a spring-mass system excited by a harmonic force is $M\ddot{x}+Kx= F \cos(\omega t)$, where M is the mass, K is the spring stiffness, F is the force ampl...

Given that a and b are integers and a + a² b³ is odd, which one of the following statements is correct?

A wire would enclose an area of 1936 m², if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the sho...

Consider the two-dimensional velocity field given by $\vec{V} = (5 + a_1x + b_1y)\hat{i} + (4 + a_2x + b_2y)\hat{j}$, where $a_1, b_1, a_2$ and $b_2$ are constants. Which one of th...

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many...

For a loaded cantilever beam of uniform cross-section, the bending moment (in N·mm) along the length is $M(x) = 5x^2 + 10x$, where x is the distance (in mm) measured from the free...

Pre-tensioning of a bolted joint is used to

From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of 54 km/h. At the s...

For an Oldham coupling used between two shafts, which among the following statements are correct? I. Torsional load is transferred along shaft axis. II. A velocity ratio of 1:2 bet...

Water (density = 1000 kg/m³) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of 1 kg/s. If the pressure drop across the pipe is 100 kPa,...

Which of the following functions describe the graph shown in the below figure?

A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transv...

A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number. i. If the house number is a multiple of 3...

For a two-dimensional incompressible flow field given by $\vec{u} = A(x\hat{i} - y \hat{j})$, where A > 0, which one of the following statements is FALSE?

The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 µm. If the peak wavelength of emitted radiation changes to 2.90 µm, then the temperature...

Which one of the following is NOT a rotating machine?

Saturated steam at 100°C condenses on the outside of a tube. Cold fluid enters the tube at 20 °C and exits at 50 °C. The value of the Log Mean Temperature Difference (LMTD) is ____...

For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy (Δs) from state 1 to 2?

An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, th...

Consider the following three statements: (i) Some roses are red. (ii) All red flowers fade quickly. (iii) Some roses fade quickly. Which of the following statements can be logicall...

Which one of the following statements is correct for a superheated vapour?

A steel bar is held by two fixed supports as shown in the figure and is subjected to an increase of temperature ΔT=100 °C. If the coefficient of thermal expansion and Young's modul...

In a linearly hardening plastic material, the true stress beyond initial yielding

A machine component made of a ductile material is subjected to a variable loading with σ_min = -50 MPa and σ_max = 50 MPa. If the corrected endurance limit and the yield strength f...

Select the correct statement for 50% reaction stage in a steam turbine.

The molar specific heat at constant volume of an ideal gas is equal to 2.5 times the universal gas constant (8.314 J/mol-K). When the temperature increases by 100 K, the change in...

In a slider-crank mechanism, the lengths of the crank and the connecting rod are 100 mm and 160 mm, respectively. The crank is rotating with an angular velocity of 10 radian/s coun...

The type of weld represented by the shaded region in the figure is

A heat pump absorbs 10 kW of heat from outside environment at 250 K while absorbing 15 kW of work. It delivers the heat to a room that must be kept warm at 300 K. The Coefficient o...

Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing different phases, a eutectoid reaction is described by

Which one of the following statements is TRUE?

Using the Taylor's tool life equation with exponent n = 0.5, if the cutting speed is reduced by 50%, the ratio of new tool life to original tool life is

The Poisson's ratio for a perfectly incompressible linear elastic material is

During solidification of a pure molten metal, the grains in the casting near the mould wall are

Match the following products with the suitable manufacturing process

A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t) = t^2, θ(t) = t, where t is time. The kinetic energy of the particle at time t...

A grinding ratio of 200 implies that the

A mass m of a perfect gas at pressure p₁ and volume V₁ undergoes an isothermal process. The final pressure is p₂ and volume is V₂. The work done on the system is considered positiv...

Interpolator in a CNC machine

Feed rate in slab milling operation is equal to

If a mass of moist air contained in a closed metallic vessel is heated, then its

A motor driving a solid circular steel shaft transmits 40 kW of power at 500 rpm. If the diameter of the shaft is 40 mm, the maximum shear stress in the shaft is ________ MPa.

For the stability of a floating body the

Consider a beam with circular cross-section of diameter d. The ratio of the second moment of area about the neutral axis to the section modulus of the area is

Metal removal in electric discharge machining takes place through

The time series forecasting method that gives equal weightage to each of the m most recent observations is

The following figure shows the velocity-time plot for a particle traveling along a straight line. The distance covered by the particle from $t = 0$ to $t = 5$ s is ________ m.

Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is denoted by $\tau_w$. The axial positions $x_1$ and $x_2$ on the plate are measured from...

The number of atoms per unit cell and the number of slip systems, respectively, for a face-centered cubic (FCC) crystal are

The preferred option for holding an odd-shaped workpiece in a centre lathe is

A six-faced fair dice is rolled five times. The probability (in %) of obtaining "ONE" at least four times is

The heat loss from a fin is 6 W. The effectiveness and efficiency of the fin are 3 and 0.75, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base...

The damping ratio for a viscously damped spring mass system, governed by the relationship $m\frac{d^2x}{dt^2} + c\frac{dx}{dt} + kx = F(t)$, is given by

A local tyre distributor expects to sell approximately 9600 steel belted radial tyres next year. Annual carrying cost is Rs. 16 per tyre and ordering cost is Rs. 75. The economic o...

A steel column of rectangular section (15 mm × 10 mm) and length 1.5 m is simply supported at both ends. Assuming modulus of elasticity, E = 200 GPa for steel, the critical axial l...

Consider the schematic of a riveted lap joint subjected to tensile load F, as shown below. Let d be the diameter of the rivets, and S_f be the maximum permissible tensile stress in...

The emissive power of a blackbody is P. If its absolute temperature is doubled, the emissive power becomes

If A = $\begin{bmatrix} 1 & 2 & 3 \ 0 & 4 & 5 \ 0 & 0 & 1 \end{bmatrix}$ then det(A$^{-1}$) is ________ (correct to two decimal places).

Cylindrical pins of diameter $15\pm0.020$ mm are being produced on a machine. Statistical quality control tests show a mean of 14.995 mm and standard deviation of 0.004 mm. The pro...

A four bar mechanism is made up of links of length 100, 200, 300 and 350 mm. If the 350 mm link is fixed, the number of links that can rotate fully is ________.

A hollow circular shaft of inner radius 10 mm, outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa,...

Which one of the following statements is TRUE for the ultrasonic machining (USM) process?

In a metal forming operation when the material has just started yielding, the principal stresses are $\sigma_1 = +180$ MPa, $\sigma_2 = -100$ MPa, $\sigma_3 = 0$. Following von Mis...

The crystal structure of aluminium is

If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in %) is ________ (correct to two decimal places).

Fatigue life of a material for a fully reversed loading condition is estimated from $\sigma_a = 1100N^{-0.15}$, where $\sigma_a$ is the stress amplitude in MPa and N is the failure...

Match the processes with their characteristics. Process P: Electrical Discharge Machining Q: Ultrasonic machining R: Chemical machining S: Ion Beam Machining Characteristics 1. No...

Given the atomic weight of Fe is 56 and that of C is 12, the weight percentage of carbon in cementite (Fe3C) is _________

A flat plate of width L = 1 m is pushed down with a velocity U = 0.01 m/s towards a wall resulting in the drainage of the fluid between the plate and the wall as shown in the figur...

The viscous laminar flow of air over a flat plate results in the formation of a boundary layer. The boundary layer thickness at the end of the plate of length L is δ. When the plat...

For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite...

In an arc welding process, welding speed is doubled. Assuming all other process parameters to be constant, the cross sectional area of the weld bead will

An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in kJ/cycle) is ________ (correct to two decimal places).

An ideal gas undergoes a process from state 1 ($T_1$= 300 K, $P_1$ = 100 kPa) to state 2 ($T_2$ = 600 K, $P_2$ = 500 kPa). The specific heats of the ideal gas are : $C_p$ = 1 kJ/kg...

For a Pelton wheel with a given water jet velocity, the maximum output power from the Pelton wheel is obtained when the ratio of the bucket speed to the water jet speed is ________...

The standard deviation of linear dimensions P and Q are 3 µm and 4 µm, respectively. When assembled, the standard deviation (in µm) of the resulting linear dimension (P+Q) is _____...

Metric thread of 0.8 mm pitch is to be cut on a lathe. Pitch of the lead screw is 1.5 mm. If the spindle rotates at 1500 rpm, the speed of rotation of the lead screw (rpm) will be

The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive cu...

A ball is dropped from rest from a height of 1 m in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring the curved porti...

It is desired to make a product having T-shaped cross-section from a rectangular aluminium block. Which one of the following processes is expected to provide the highest strength o...

In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers to

The height (in mm) for a 125 mm sine bar to measure a taper of 27°32′ on a flat work piece is ____________ (correct to three decimal places).

The surface integral $\iint_S \mathbf{F} \cdot \mathbf{n}\,dS$ over the surface $S$ of the sphere $x^2 + y^2 + z^2 = 9$, where $\mathbf{F}=(x+y)\mathbf{i}+(x+z)\mathbf{j}+(y+z)\mat...

Let z be a complex variable. For a counter-clockwise integration around a unit circle C, centred at origin, $\oint_C \frac{1}{5z-4} dz = A\pi i$, the value of A is

Consider the matrix P = $\begin{bmatrix} \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\ 0 & 1 & 0 \\ -\frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \end{bmatrix}$. Which one of the f...

Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2, respectively. Consider Y = X1 – X2; μ1 = μ2 =1, σ1 = 1, σ2 = 2. Then,

For the vector $\vec{V} = 2yz \hat{i} + 3xz \hat{j} + 4xy \hat{k}$, the value of $\vec{V} \cdot (\nabla \times \vec{V})$ is _________

Consider the differential equation $3y''(x)+27y(x)=0$ with initial conditions $y(0)=0$ and $y'(0)=2000$. The value of y at x = 1 is _________.

Let X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X1, X2) is

The value of the integral $\oiint_S \vec{r} \cdot \vec{n} \, dS$ over the closed surface S bounding a volume V, where $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ is the position vec...

For a position vector $\vec{r} = x\hat{i}+y\hat{j}+z\hat{k}$ the norm of the vector can be defined as $|\vec{r}| = \sqrt{x^2 + y^2 + z^2}$. Given a function $\phi = \ln|\vec{r}|$,...

Consider the matrix A = $\begin{bmatrix} 50 & 70 \\ 70 & 80 \end{bmatrix}$ whose eigenvectors corresponding to eigenvalues $\lambda_1$ and $\lambda_2$ are $\mathbf{x}_1 = \begin{bm...

A parametric curve defined by $x = \cos\left(\frac{\pi u}{2}\right)$, $y = \sin\left(\frac{\pi u}{2}\right)$ in the range $0 \le u \le 1$ is rotated about the X- axis by 360 degree...

A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming tha...

The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is 10 kPa, then the normal stress $\sigma_y$ (in kPa) is

In a rigid body in plane motion, the point R is accelerating with respect to point P at $10\angle180^\circ$ m/s². If the instantaneous acceleration of point Q is zero, the accelera...

P (0, 3), Q (0.5, 4), and R (1, 5) are three points on the curve defined by $f(x)$. Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limit...

If $f(z) = (x^2 + ay^2) + ibxy$ is a complex analytic function of $z = x + iy$, where $i = \sqrt{-1}$, then

The velocity profile inside the boundary layer for flow over a flat plate is given as $\frac{u}{U_{\infty}} = \sin \left(\frac{\pi y}{2 \delta}\right)$, where $U_{\infty}$ is the f...

A rigid rod of length 1 m is resting at an angle $\theta = 45^\circ$ as shown in the figure. The end P is dragged with a velocity of $U = 5$ m/s to the right. At the instant shown,...

An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are 20, 30 and 20, respectively. Gear C has 80 teeth on the inner surface and 100...

Block 2 slides outward on link 1 at a uniform velocity of 6 m/s as shown in the figure. Link 1 is rotating at a constant angular velocity of 20 radian/s counterclockwise. The magni...

The radius of gyration of a compound pendulum about the point of suspension is 100 mm. The distance between the point of suspension and the centre of mass is 250 mm. Considering th...

A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $\theta = 30^{\circ}$ as shown in the figure. The glue used at the interface fails if...

A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment $T = 150$ Nm is applied at a distance of 100 mm from end P. The torsional reac...

Consider steady flow of an incompressible fluid through two long and straight pipes of diameters $d_1$ and $d_2$ arranged in series. Both pipes are of equal length and the flow is...

For a steady flow, the velocity field is $\vec{V} = (-x^2 + 3y)\hat{i} + (2xy)\hat{j}$. The magnitude of the acceleration of a particle at $(1,-1)$ is

A gear train shown in the figure consists of gears P, Q, R and S. Gear Q and gear R are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of te...

A self-aligning ball bearing has a basic dynamic load rating (C10, for $10^6$ revolutions) of 35 kN. If the equivalent radial load on the bearing is 45 kN, the expected life (in $1...

In a cam-follower, the follower rises by h as the cam rotates by δ (radians) at constant angular velocity ω (radians/s). The follower is uniformly accelerating during the first hal...

One kg of an ideal gas (gas constant, $R = 400$ J/kg. K; specific heat at constant volume, $C_v = 1000$ J/kg. K) at 1 bar, and 300 K is contained in a sealed rigid cylinder. During...

A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MP...

A bimetallic cylindrical bar of cross sectional area 1 m² is made by bonding Steel (Young's modulus = 210 GPa) and Aluminium (Young's modulus = 70 GPa) as shown in the figure. To m...

A tank open at the top with a water level of 1 m, as shown in the figure, has a hole at a height of 0.5 m. A free jet leaves horizontally from the smooth hole. The distance X (in m...

The pressure ratio across a gas turbine (for air, specific heat at constant pressure, $C_p = 1040$ J/kg. K and ratio of specific heats, $\gamma = 1.4$) is 10. If the inlet temperat...

Air flows at the rate of 1.5 m³/s through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have diameters of 400...

Three masses are connected to a rotating shaft supported on bearings A and B as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the...

In a Lagrangian system, the position of a fluid particle in a flow is described as $x = x_0e^{-kt}$ and $y = y_0e^{kt}$ where $t$ is the time while $x_0, y_0$, and $k$ are constant...

The problem of maximizing z = x₁-x₂ subject to constraints x₁ + x₂ ≤10, x₁ ≥ 0, x₂ ≥ 0 and x₂ ≤5 has

The maximum reduction in cross-sectional area per pass ($R$) of a cold wire drawing process is $R=1-e^{-(n+1)}$, where $n$ represents the strain hardening coefficient. For the case...

A steel plate, connected to a fixed channel using three identical bolts A, B and C, carries a load of 6 kN as shown in the figure. Considering the effect of direct load and moment,...

Moist air is treated as an ideal gas mixture of water vapor and dry air (molecular weight of air = 28.84 and molecular weight of water = 18). At a location, the total pressure is 1...

Given the ordinary differential equation $\frac{d^2y}{dx^2} + \frac{dy}{dx} -6y=0$ with y(0) = 0 and $\frac{dy}{dx}(0) = 1$, the value of y(1) is ________ (correct to two decimal p...

The percentage scrap in a sheet metal blanking operation of a continuous strip of sheet metal as shown in the figure is ________ (correct to two decimal places).

Air contains 79% N₂ and 21% O₂ on a molar basis. Methane (CH₄) is burned with 50% excess air than required stoichiometrically. Assuming complete combustion of methane, the molar pe...

A single-plate clutch has a friction disc with inner and outer radii of 20 mm and 40 mm, respectively. The friction lining in the disc is made in such a way that the coefficient of...

An explicit forward Euler method is used to numerically integrate the differential equation $\frac{dy}{dt} = y$ using a time step of 0.1. With the initial condition $y(0) = 1$, the...

A thin-walled cylindrical can with rigid end caps has a mean radius R = 100 mm and a wall thickness of t=5 mm. The can is pressurized and an additional tensile stress of 50 MPa is...

The principal stresses at a point in a critical section of a machine component are σ₁ = 60 MPa, σ₂ = 5 MPa and σ₃ = -40 MPa. For the material of the component, the tensile yield st...

Two black surfaces, AB and BC, of lengths 5 m and 6 m, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor F₁₂ = 0...

The rod PQ of length L = √2 m. and uniformly distributed mass of M = 10 kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces O...

A bar is subjected to a combination of a steady load of 60 kN and a load fluctuating between -10 kN and 90 kN. The corrected endurance limit of the bar is 150 MPa, the yield streng...

$F(s)$ is the Laplace transform of the function $f(t) = 2t^2e^{-t}$. $F(1)$ is ________ (correct to two decimal places).

Heat is generated uniformly in a long solid cylindrical rod (diameter = 10 mm) at the rate of 4 × 10^7 W/m³. The thermal conductivity of the rod material is 25 W/m.K. Under steady...

A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam...

The arrangement shown in the figure measures the velocity V of a gas of density 1 kg/m³ flowing through a pipe. The acceleration due to gravity is 9.81 m/s². If the manometric flui...

A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure. If the disc rolls without slipping on the flo...

An initially stress-free massless elastic beam of length L and circular cross-section with diameter d (d <<< L) is held fixed between two walls as shown. The beam material has Youn...

A machine of mass m = 200 kg is supported on two mounts, each of stiffness k = 10 kN/m. The machine is subjected to an external force (in N) F(t) = 50 cos 5t. Assuming only vertica...

A 60 mm-diameter water jet strikes a plate containing a hole of 40 mm diameter as shown in the figure. Part of the jet passes through the hole horizontally, and the remaining is de...

A point mass of 100 kg is dropped onto a massless elastic bar (cross-sectional area = 100 mm², length = 1 m, Young's modulus = 100 GPa) from a height H of 10 mm as shown (Figure is...

A frictionless circular piston of area 10⁻² m² and mass 100 kg sinks into a cylindrical container of the same area filled with water of density 1000 kg/m³ as shown in the figure. T...

Two disks A and B with identical mass (m) and radius (R) are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk A has all of its mas...

A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45° and a force of 40 N is acting towards the left on the slider. The length of the crank is 30...

A 0.2 m thick infinite black plate having a thermal conductivity of 3.96 W/m-K is exposed to two infinite black surfaces at 300 K and 400 K as shown in the figure. At steady state,...

A rectangular region in a solid is in a state of plane strain. The (x,y) coordinates of the corners of the undeformed rectangle are given by P(0,0), Q(4,0), R(4,3), S(0,3). The rec...

A sprinkler shown in the figure rotates about its hinge point in a horizontal plane due to water flow discharged through its two exit nozzles. The total flow rate Q through the spr...

Air is held inside a non-insulated cylinder using a piston (mass M=25 kg and area A=100 cm²) and stoppers (of negligible area), as shown in the figure. The initial pressure Pᵢ and...

A standard vapor compression refrigeration cycle operating with a condensing temperature of 35°C and an evaporating temperature of -10°C develops 15 kW of cooling. The p-h diagram...

A machine element has an ultimate strength ($\sigma_u$) of 600 N/mm², and endurance limit ($\sigma_{en}$) of 250 N/mm². The fatigue curve for the element on a log-log plot is shown...

A solid block of 2.0 kg mass slides steadily at a velocity V along a vertical wall as shown in the figure below. A thin oil film of thickness h = 0.15 mm provides lubrication betwe...

A horizontal bar, fixed at one end (x = 0), has a length of 1 m, and cross-sectional area of 100 mm². Its elastic modulus varies along its length as given by E(x) = 100 e⁻ˣ GPa, wh...

Ambient air is at a pressure of 100 kPa, dry bulb temperature of 30°C and 60% relative humidity. The saturation pressure of water at 30°C is 4.24 kPa. The specific humidity of air...

A tank of volume 0.05 m³ contains a mixture of saturated water and saturated steam at 200°C. The mass of the liquid present is 8 kg. The entropy (in kJ/kg K) of the mixture is ____...

Steam flows through a nozzle at a mass flow rate of m = 0.1kg/s with a heat loss of 5 kW. The enthalpies at inlet and exit are 2500kJ/kg and 2350 kJ/kg, respectively. Assuming negl...

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at 100 rpm. Let the number of teeth on the sun, planet an...

A test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m and volumetric flow rate of 1 m³/s at 450 rpm. Take the water density and the acceleration d...

An engine working on air standard Otto cycle is supplied with air at 0.1 MPa and 35°C. The compression ratio is 8. The heat supplied is 500 kJ/kg. Property data for air: cₚ = 1.005...

The true stress (in MPa) versus true strain relationship for a metal is given by $\sigma = 1020 \varepsilon^{0.4}$. The cross-sectional area at the start of a test (when the stress...

A thin uniform rigid bar of length L and mass M is hinged at point O, located at a distance of L/3 from one of its ends. The bar is further supported using springs, each of stiffne...

A plane slab of thickness L and thermal conductivity k is heated with a fluid on one side (P), and the other side (Q) is maintained at a constant temperature, TQ of 25°C, as shown...

For an inline slider-crank mechanism, the lengths of the crank and connecting rod are 3 m and 4 m, respectively. At the instant when the connecting rod is perpendicular to the cran...

A steel wire is drawn from an initial diameter ($d_i$) of 10 mm to a final diameter ($d_f$) of 7.5 mm. The half cone angle ($\alpha$) of the die is 5º and the coefficient of fricti...

A 10 mm deep cylindrical cup with diameter of 15 mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto 2 decimal points accuracy) o...

Following data correspond to an orthogonal turning of a 100 mm diameter rod on a lathe. Rake angle: +15°; Uncut chip thickness: 0.5 mm; nominal chip thickness after the cut: 1.25 m...

The true stress (σ) - true strain (ε) diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of 500 MPa and strain of...

Taylor's tool life equation is used to estimate the life of a batch of identical HSS twist drills by drilling through holes at constant feed in 20 mm thick mild steel plates. In te...

An orthogonal cutting operation is being carried out in which uncut thickness is 0.010 mm, cutting speed is 130 m/min, rake angle is 15° and width of cut is 6 mm. It is observed th...

Circular arc on a part profile is being machined on a vertical CNC milling machine. CNC part program using metric units with absolute dimensions is listed below: N60 G01 X 30 Y 55...

A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is ________ (correct to two decimal places).

Assume that the surface roughness profile is triangular as shown schematically in the figure. If the peak to valley height is 20 µm, the central line average surface roughness Ra (...

For sand-casting a steel rectangular plate with dimensions 80 mm x 120 mm × 20 mm, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The tot...

Two models, P and Q, of a product earn profits of Rs. 100 and Rs. 80 per piece, respectively. Production times for P and Q are 5 hours and 3 hours, respectively, while the total pr...

The minimum value of 3x + 5y such that: 3x + 5y ≤ 15 4x + 9y ≤ 8 13x + 2y ≤ 2 x ≥ 0, y ≥ 0 is ________.

The arc lengths of a directed graph of a project are as shown in the figure. The shortest path length from node 1 to node 6 is _________.

Following data refers to the jobs (P, Q, R, S) which have arrived at a machine for scheduling. The shortest possible average flow time is _________ days.

A circular hole of 25 mm diameter and depth of 20 mm is machined by EDM process. The material removal rate (in mm³/min) is expressed as $4 \times 10^4 IT^{-1.23}$, where I = 300 A...

Processing times (including setup times) and due dates for six jobs waiting to be processed at a work centre are given in the table. The average tardiness (in days) using shortest...

A welding operation is being performed with voltage = 30 V and current = 100 A. The cross-sectional area of the weld bead is 20 mm². The work-piece and filler are of titanium for w...

The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at point X. A for...

A block of length 200 mm is machined by a slab milling cutter 34 mm in diameter. The depth of cut and table feed are set at 2 mm and 18 mm/minute, respectively. Considering the app...

Steam in the condenser of a thermal power plant is to be condensed at a temperature of 30°C with cooling water which enters the tubes of the condenser at 14°C and exits at 22°C. Th...

Block P of mass 2 kg slides down the surface and has a speed 20 m/s at the lowest point, Q, where the local radius of curvature is 2 m as shown in the figure. Assuming g = 10 m/s²,...

A sprue in a sand mould has a top diameter of 20 mm and height of 200 mm. The velocity of the molten metal at the entry of the sprue is 0.5 m/s. Assume acceleration due to gravity...

Two cutting tools with tool life equations given below are being compared: Tool 1: VT^0.1 = 150 Tool 2: VT^0.3 = 300 where V is cutting speed in m/minute and T is tool life in minu...

A vehicle powered by a spark ignition engine follows air standard Otto cycle ($\gamma$=1.4). The engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of f...

An electrochemical machining (ECM) is to be used to cut a through hole into a 12 mm thick aluminum plate. The hole has a rectangular cross-section, 10 mm x 30 mm. The ECM operation...

He was one of my best __________ and I felt his loss __________.

As the two speakers became increasingly agitated, the debate became __________.

A right-angled cone (with base radius 5 cm and height 12 cm), as shown in the figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the...

In a company with 100 employees, 45 earn Rs. 20,000 per month, 25 earn Rs. 30,000, 20 earn Rs. 40,000, 8 earn Rs. 60,000, and 2 earn Rs. 150,000. The median of the salaries is

P, Q, and R talk about S's car collection. P states that S has at least 3 cars. Q believes that S has less than 3 cars. R indicates that to his knowledge, S has at least one car. O...

"Here, throughout the early 1820s, Stuart continued to fight his losing battle to allow his sepoys to wear their caste-marks and their own choice of facial hair on parade, being ag...

What is the sum of the missing digits in the subtraction problem below? 5 -48 89 ----- 1111

Let S₁ be the plane figure consisting of the points (x, y) given by the inequalities |x - 1| ≤ 2 and |y + 2| ≤ 3. Let S₂ be the plane figure given by the inequalities x - y ≥ -2, y...

Two very famous sportsmen Mark and Steve happened to be brothers, and played for country K. Mark teased James, an opponent from country E. "There is no way you are good enough to p...

The growth of bacteria (lactobacillus) in milk leads to curd formation. A minimum bacterial population density of 0.8 (in suitable units) is needed to form curd. In the graph below...