GATE 2022 Mechanical Engineering (ME) Slot - 2 Question Paper with Solutions Pdfs can be downloaded from this page. GATE 2022 ME Slot 2 was conducted by IIT Kharagpur on 13th February 2022, from 2:30 PM to 5:30 PM. The overall difficulty level of the exam stands at moderate to tough. Sections such as Engineering Mechanics, SOM, Industrial, Manufacturing & HMT were accountable for carrying the highest weightage in the exam.
GATE 2022 Mechanical Engineering (ME) Slot - 2 Question Paper with Solutions
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Writing too many things on the ____ while teaching could make the students get ____ .
Which one of the following is a representation (not to scale and in bold) of all values of \( x \) satisfying the inequality \( 2 - 5x \leq \frac{-6x - 5}{3} \) on the real number line?
If \( f(x) = 2 \ln(\sqrt{e^x}) \), what is the area bounded by \( f(x) \) for the interval \([0, 2]\) on the x-axis?
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?
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).
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 collagen on their skin, making their skin more fragile.
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 \( m \)?
Consider the following functions for non-zero positive integers, \( p \) and \( q \):
\[ f(p, q) = p \times p \times p \times \cdots \times p = p^q \quad ; \quad f(p, 1) = p \] \[ g(p, q) = ppppp\cdots (up to q terms) \quad ; \quad g(p, 1) = p \]
Which one of the following options is correct based on the above?
Four cities P, Q, R, and 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 the first train of the day and their frequency of operation. For example, from city P, the first trains of the day start at 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train.
If the person starts from R at 7 AM and is required to visit S and return to R, what is the minimum time required?
Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.
What is the ratio of the areas of unshaded regions of case M to that of case N?
\(F(t)\) 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 \(F(t)\)?
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 \[ \int_A \vec{F} \cdot d\vec{A} \]
of the vector field \[ \vec{F} = 3x\,\hat{i} + 5y\,\hat{j} + 6z\,\hat{k} \]
over the entire surface A of the cube is ________.
Consider the definite integral \[ \int_{1}^{2} (4x^2 + 2x + 6)\, dx. \]
Let I_e be the exact value. Using Simpson’s rule with 10 equal subintervals, the estimate is I_s.
The percentage error \[ e = 100 \times \frac{(I_e - I_s)}{I_e} \]
is ________.
Given \[ \int_{-\infty}^{\infty} e^{-x^2}\, dx = \sqrt{\pi}. \]
If \(a\) and \(b\) are positive integers, the value of \[ \int_{-\infty}^{\infty} e^{-a(x+b)^2}\, dx is \_\_\_\_\_\_\_\_. \]
A polynomial \[ \varphi(s) = a_n s^n + a_{n-1} s^{n-1} + \cdots + a_1 s + a_0 \]
of degree \(n>3\) with constant real coefficients has triple roots at \( s = -\sigma \).
Which one of the following conditions must be satisfied?
Which one of the following is the definition of ultimate tensile strength (UTS) obtained from a stress-strain test on a metal specimen?
A massive uniform rigid circular disc is mounted on a frictionless bearing at the end E of a massive uniform rigid shaft AE which is suspended horizontally in a uniform gravitational field by two identical light inextensible strings AB and CD as shown, where G is the center of mass of the shaft-disc assembly and g is the acceleration due to gravity. The disc is then given a rapid spin \(\omega\) about its axis in the positive x-axis direction as shown, while the shaft remains at rest. The direction of rotation is defined using the right-hand thumb rule. If the string AB is suddenly cut, assuming negligible energy dissipation, the shaft AE will
A structural member under loading has a uniform state of plane stress which in 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 MPa. If the member is designed using the maximum distortion energy theory, then the value of \(P\) at which yielding starts (according to the maximum distortion energy theory) is
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 lines, are straight lines. If this binary alloy with 15 weight % of B is poured into a mould at a pouring temperature of 800\,\(^\circ\)C, then the solidification range is ________.
A shaft of diameter \(25^{-0.04}_{-0.07}\) mm is assembled in a hole of diameter \(25^{+0.02}_{+0.00}\) mm.
Match the allowance and limit parameter in Column I with its corresponding quantitative value in Column II for this shaft–hole assembly.
Match the additive manufacturing technique in Column I with its corresponding input material in Column II.
Which one of the following CANNOT impart linear motion in a CNC machine?
Which one of the following is an intensive property of a thermodynamic system?
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. Which among the following options can be the reason?
Which of the following non-dimensional terms is an estimate of Nusselt 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 links of the plate are identical.
The square plate can remain in equilibrium in its initial state for which one or more of the following support configurations?
Consider sand casting of a cube of edge length \(a\). A cylindrical riser is placed at the top of the casting. Assume solidification time, \(t_s \propto V/A\), 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?
Which of these processes involve(s) melting in metallic workpieces?
The velocity field in a fluid is given to be \[ \vec{V} = (4xy)\,\hat{i} + 2(x^{2} - y^{2})\,\hat{j}. \]
Which of the following statement(s) is/are correct?
A rope with two mass–less platforms passes over a fixed pulley. Each disc weighs 20 N.
For \(n=5\) and \(m=0\), a downward force \(F = 200\) N applied on the right platform (figure (i)) is just sufficient to initiate upward motion of the left platform.
If the force \(F\) is removed (figure (ii)), the minimum value of \(m\) required to prevent downward motion of the left platform is _______ (in integer).
For a dynamical system governed by the equation
\[ \ddot{x}(t) + 2 \zeta \omega_n \dot{x}(t) + \omega_n^2 x(t) = 0, \]
the damping ratio is given as \( \zeta = \frac{1}{2\pi} \log_e 2 \).
A displacement peak in the positive direction is measured as 4 mm.
Neglecting higher powers (\(>1\)) of damping ratio, the displacement at the next peak (positive direction) will be ________ mm (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 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 using EOQ. The ordering cost is ₹100/order and the lead time 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 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container.
The specific heat at constant volume is \( c_v = 750\ J kg^{-1}K^{-1} \).
A stirrer performs 225 kJ of work on the gas.
Assume no heat interaction. The final pressure of the gas will be ________ bar (integer).
Wien's law is stated as \( \lambda_m T = C \), where \( C = 2898\ \mum·K \) 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 emissivity curve shows a maximum at \( \lambda_m \approx 6000\ \AA \).
The temperature at which the total hemispherical emissivity is highest is ________ K (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?
A rigid homogeneous uniform block of mass 1 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 as shown. A short duration impulsive force \(F\), producing an impulse \(I_F\), is applied at a height \(d = 0.3\) m from the bottom. Assume all joints to be frictionless. The minimum value of \(I_F\) required to topple the block is ________.
A linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to these two loadings are shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress \(\sigma_{xx}\) is ________.
A rigid body in the X–Y plane consists of two point masses (1 kg each) attached to the ends of two massless rods, each of 1 cm length, as shown in the figure. It rotates at 30 RPM counter-clockwise about the Z-axis passing through point O. A point mass of \(\sqrt{2}\) kg, attached to one end of a third massless rod, is used for balancing the body by attaching the free end of the rod to point O. The length of the third rod is ________ cm.
A spring–mass–damper system (mass \(m\), stiffness \(k\), damping coefficient \(c\)) excited by a force \(F(t)=B\sin \omega t\) is shown in the figure. Four different responses of the system (marked as (i)–(iv)) are shown. In the figures, \(A\) is the amplitude of the oscillatory response, and the dashed lines show its envelope. The responses represent only qualitative trends. Four different forcing and parameter conditions are also given:
\[ (P)\ c>0,\quad \omega=\sqrt{\frac{k}{m}}, \qquad (Q)\ c<0\ and\ \omega\ne 0, \] \[ (R)\ c=0,\quad \omega=\sqrt{\frac{k}{m}}, \qquad (S)\ c=0,\quad \omega \approx \sqrt{\frac{k}{m}}. \]
Which option correctly matches each condition to its response (i)–(iv)?
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 for carrying out both the operations for all 7 parts is __________ hours.
A manufacturing unit produces two products P1 and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. The maximum possible profit per day is ₹ ________.
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 \(g\). The volume flow rate through the tube is ________.
The steady velocity field in an inviscid fluid of density 1.5 is given to be \(\vec{V} = (y^{2} - x^{2})\hat{i} + (2xy)\hat{j}.\)
Neglecting body forces, the pressure gradient at \((x = 1, y = 1)\) is ________.
In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure with enthalpy 250 kJ/kg. The exit of the compressor is at 300 kJ/kg. COP of the cycle is 3. The refrigerant after condensation is throttled to evaporator pressure. If the enthalpy of saturated liquid at evaporator pressure is 50 kJ/kg, the dryness fraction at entry to evaporator is ________.
\(A\) is a \(3\times 5\) real matrix of rank \(2\). For the set of homogeneous equations \(A x = 0\), where \(0\) is a zero vector and \(x\) is a vector of unknown variables, which of the following is/are true?
The lengths of members BC and 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 member on which it acts. Which one or more of the following members do not carry any load (force)?
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 \(|p|\) is ______ (in integer).
Given \(z = x + iy\), \(i = \sqrt{-1}\). \(C\) is a circle of radius \(2\) centred at the origin and traversed anticlockwise.
The value of \[ \frac{1}{2\pi i} \int_C \frac{1}{(z-i)(z+4i)}\, dz \]
is ______ (round off to one decimal place).
A shaft of length \(L\) is made of two materials—an inner core and an outer rim—perfectly bonded with no slip.
The inner core has diameter \(d_i\), the outer diameter is \(d_o\), and the rigidities are \(G_i\) and \(G_o\) respectively.
Given: \( d_o = 2 d_i \) and \( G_i = 3 G_o \).
Under an applied torque, the maximum shear stresses in the outer rim and inner core are \( \tau_o \) and \( \tau_i \).
Find the ratio \( \tau_i / \tau_o \) (round off to 2 decimals).
A rigid beam AD of length \(3a = 6\) m is hinged at A and supported by two strings as shown.
A force \(F = 9\) kN is applied at C. Assuming small deflection and linear elastic strings,
the tension in the string at C is _____ kN (round off to 2 decimal places).
In the four-bar mechanism shown, the \(2\) cm input link rotates at \(\omega_2 = 5\) rad/s.
Given the geometry, the magnitude of angular velocity \(\omega_4\) of the 4 cm link is _____ rad/s
(round off to 2 decimal places).
A shaft carries a thin pulley of radius \( r = 0.4\ m \) at end C.
Taut and slack belt tensions are \( T_1 = 300\ N \) and \( T_2 = 100\ N \).
Allowable shear stress in the shaft is 80 MPa. The shaft length segments are \( AB = BC = L = 0.5\ m \).
Neglecting shock and fatigue and using maximum shear stress theory, find the minimum shaft diameter (in mm).
A straight–teeth horizontal slab milling cutter has 4 teeth and diameter \(D = 200\) mm.
Rotational speed = 100 rpm,
Feed = 1000 mm/min,
Workpiece width \(w = 100\) mm.
Cutting force/tooth = \(F = K\, t_c\, w\), \(K = 10\) N/mm\(^2\).
Depth of cut is \(d = D/2\), and the maximum cutting force is _____ kN (round off to one decimal place).
In an orthogonal machining operation, the cutting and thrust forces are equal.
Uncut chip thickness = 0.5 mm, shear angle = \(15^\circ\), rake angle = \(0^\circ\), width of cut = 2 mm.
The work material is perfectly plastic with yield shear strength \(500\ MPa\).
Find the cutting force (nearest integer).
The best size wire is fitted in a groove of a metric screw such that the wire touches
the flanks of the thread on the pitch line. The pitch \(p = 4\) mm and the included angle
of the thread is \(60^\circ\). The diameter of the best size wire is ______ mm
(round off to 2 decimal places).
In a DC arc welding process, open-circuit voltage is 100 V and short-circuit current is 1000 A.
Arc voltage varies as \(V = 10 + 5l\), where \(l\) is arc length in mm.
The maximum available arc power during the process is ______ kVA (in integer).
A cylindrical billet of diameter 100 mm and length 100 mm is directly extruded into an L-section.
The extrusion pressure is given by \[ p = K_s\, \sigma_m \left[0.8 + 1.5\ln(r) + \frac{2l}{d_0}\right] \]
where \( \sigma_m = 50\ MPa \), \( K_s = 1.05 \), \( d_0 = 100\ mm \).
Find the maximum force at the start of extrusion (in kN).
A project consists of five activities (A, B, C, D, E).
Each activity duration follows beta distribution.
Three-time estimates are given and expected completion time is _____ weeks (in integer).
A rigid tank (8 m\(^3\)) is filled with air from a pipeline at 600 kPa and 306 K.
Heat loss during filling = 1000 kJ.
Final tank pressure equals pipeline pressure.
Final temperature is _____ K (rounded to nearest integer).
At steady state, 500 kg/s of steam enters a turbine with specific enthalpy \(h_1 = 3500\ kJ/kg\) and entropy \(s_1 = 6.5\ kJ·kg^{-1}K^{-1}\).
It expands reversibly in the turbine at 500 K. Exit properties: \(h_2 = 2500\ kJ/kg\), \(s_2 = 6.3\ kJ·kg^{-1}K^{-1}\).
Find turbine work output (MW, integer).
A uniform wooden rod (specific gravity = 0.6, diameter = 4 cm, length = 8 m) is hinged at A at waterline.
A lead sphere (specific gravity = 11.4) is attached at the free end to keep the rod submerged horizontally.
Find the radius of the lead ball (in cm, round to 2 decimals).
Consider steady one-dimensional heat conduction in a slab of thickness \(2L\) (with \(L=1\) m).
Thermal conductivity varies as \(k = C T\), with \(C = 2\) W·m\(^{-1}\)·K\(^{-2}\), and the slab generates heat at \(1280\) kW/m\(^3\). Both faces are held at 600 K. The temperature at \(x=0\) is _____ K (in integer).
Saturated vapor at 200°C condenses to saturated liquid at 150 kg/s on the shell side of a heat exchanger
(latent heat \(h_{fg} = 2400\) kJ/kg).
A fluid with \(c_p = 4\) kJ·kg\(^{-1}\)·K\(^{-1}\) enters the tube side at 100°C.
Effectiveness = 0.9.
The required tube-side mass flow rate is _____ kg/s (in integer).
A hydrodynamically and thermally fully-developed fluid of 1 kg/s flows in a uniformly heated pipe (diameter 0.1 m, length 40 m).
A constant heat flux of 15000 W/m\(^2\) is applied.
The fluid enters at 200\(^\circ\)C.
Given: Re = 85000, Pr = 5, \(k = 0.08\) W/m·K, \(c_p = 2600\) J/kg·K.
Correlation: \[ Nu = 0.023\, Re^{0.8} Pr^{0.4} \]
Find the pipe surface temperature at the exit (nearest integer).
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GATE 2022 ME Slot 2 Detailed Paper Analysis
The question paper was a combination of 6 MSQs (Multiple Select Questions), 35 MCQs (Multiple Choice Questions), and 24 NATs (Numerical Answer Type) questions. As compared to the previous slot, more MCQs were asked in slot 2. Go through the below-mentioned table in order to get a detailed analysis of the questions as per the sections-
| Sections | 1 Mark Questions | 2 Marks Questions | Total Marks |
|---|---|---|---|
| TOM & Vibrations | 2 | 2 | 6 |
| Manufacturing Engineering and Materials | 7 | 4 | 15 |
| Strength of Materials | 3 | 1 | 5 |
| Machine Design | 0 | 2 | 4 |
| Fluid Mechanics and Machinery | 1 | 2 | 5 |
| Thermodynamics | 1 | 2 | 5 |
| Refrigerating and Air Conditioning | 0 | 3 | 6 |
| Power Plant | 1 | 2 | 5 |
| I C Engine | 0 | 0 | 0 |
| Industrial Engineering | 2 | 3 | 8 |
| Heat Transfer | 2 | 3 | 8 |
| Engineering Mechanics | 2 | 2 | 6 |
| Engineering Mathematics | 4 | 4 | 12 |
| General Aptitude | 5 | 5 | 15 |
| Total | 30 | 35 | 100 |
- There were 30 questions carrying 1 mark, and 35 questions carrying 2 marks
- In slot 2, I C Engine carried zero weightage in the exam
- Machine Design carried the least weightage of only 4% in the exam
- Engineering Mathematics carries 12% of the total weightage and rated moderate in terms of difficulty level
- The General Aptitude section was rated the easiest section
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