The PYQ practice room

GATE ME 2014 Set 3

All 65 solved GATE ME 2014 Set 3 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

Attempt before revealInstant answer feedbackExplore questions

Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.

Questions

Paper marks

100

Question formats

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 34Medium 26Hard 5

Explore the questions

65 of 65 questions

Question typeDifficultyYour progress

MECHANICAL – ME

11
Q11MCQ1 markEasy
Consider a $3 \times 3$ real symmetric matrix $S$ such that two of its eigenvalues are $a \neq 0, b \neq 0$ with respective eigenvectors…
Think it through. Then check your answer.
Question
$3 \times 3$
Your answer
Choose one option, then check your answer.
A. $a$ B. $b$ C. $ab$ D. $0$
Restoring your progress…
The solution stays hidden until you check.
$a$
Open question page
12
Q12MCQ1 markEasy
If a function is continuous at a point,
Think it through. Then check your answer.
Question
$If a function is continuous at a point,$
Your answer
Choose one option, then check your answer.
A. $the limit of the function may not exist at the point$ B. $the function must be derivable at the point$ C. $the limit of the function at the point tends to infinity$ D. $the limit must exist at the point and the value of limit should be same as the value of the function at that point$
Restoring your progress…
The solution stays hidden until you check.
$f(x)$
Open question page
13
Q13MCQ1 markEasy
Divergence of the vector field $x^2 z \hat{i} + x y \hat{j} - y z^2 \hat{k}$ at $(1, -1, 1)$ is
Think it through. Then check your answer.
Question
$x^2 z \hat{i} + x y \hat{j} - y z^2 \hat{k}$
Your answer
Choose one option, then check your answer.
A. $0$ B. $3$ C. $5$ D. $6$
Restoring your progress…
The solution stays hidden until you check.
$\vec{F} = F_x \hat{i} + F_y \hat{j} + F_z \hat{k}$
Open question page
14
Q14NAT1 markEasy
A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the…
Think it through. Then check your answer.
Question
$A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is_______$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$2N$
Open question page
15
Q15NAT1 markEasy
The definite integral $\int_{1}^{3} \frac{1}{x} dx$ is evaluated using Trapezoidal rule with a step size of 1. The correct answer is _______
Think it through. Then check your answer.
Question
$\int_{1}^{3} \frac{1}{x} dx$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$I = \int_{1}^{3} \frac{1}{x} dx$
Open question page
16
Q16NAT1 markMedium
A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is 100 MPa. If the yield, ultimate and…
Think it through. Then check your answer.
Question
$A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is 100 MPa. If the yield, ultimate and corrected endurance strength of the shaft material are 300 MPa, 500 MPa and 200 MPa, respectively, then the factor of safety for the shaft is_______$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$+\sigma_b$
Open question page
17
Q17NAT1 markEasy
Two solid circular shafts of radii $R_1$ and $R_2$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $\tau_1$ and $\tau_2$ . If $R_1/ R_2=2$ ,…
Think it through. Then check your answer.
Question
$R_1$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$\tau_{max}$
Open question page
18
Q18MCQ1 markEasy
Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the…
Think it through. Then check your answer.
Question
$Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is$
Your answer
Choose one option, then check your answer.
A. $0$ B. $45$ C. $90$ D. $135$
Restoring your progress…
The solution stays hidden until you check.
$\phi$
Open question page
19
Q19MCQ1 markEasy
A mass $m_1$ of 100 kg travelling with a uniform velocity of 5 m/s along a line collides with a stationary mass $m_2$ of 1000 kg. After the collision, both the masses travel…
Think it through. Then check your answer.
Question
$m_1$
Your answer
Choose one option, then check your answer.
A. $0.6$ B. $0.1$ C. $0.01$ D. $0$
Restoring your progress…
The solution stays hidden until you check.
$e$
Open question page
20
Q20MCQ1 markEasy
Which one of following is NOT correct?
Think it through. Then check your answer.
Question
$Which one of following is NOT correct?$
Your answer
Choose one option, then check your answer.
A. $Intermediate principal stress is ignored when applying the maximum principal stress theory$ B. $The maximum shear stress theory gives the most accurate results amongst all the failure theories$ C. $As per the maximum strain energy theory, failure occurs when the strain energy per unit volume exceeds a critical value$ D. $As per the maximum distortion energy theory, failure occurs when the distortion energy per unit volume exceeds a critical value$
Restoring your progress…
The solution stays hidden until you check.
$\boxed{B}$
Open question page
21
Q21MCQ1 markMedium
Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with Gear 3. Gear 3 and Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of…
Think it through. Then check your answer.
Question
$Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with Gear 3. Gear 3 and Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of teeth on Gears 2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is$
Your answer
Choose one option, then check your answer.
A. $300 rpm counterclockwise$ B. $300 rpm clockwise$ C. $4800 rpm counterclockwise$ D. $4800 rpm clockwise$
Restoring your progress…
The solution stays hidden until you check.
$N_2 = 1200$
Open question page
22
Q22MCQ1 markEasy
Consider a long cylindrical tube of inner and outer radii, $r_i$ and $r_o$ , respectively, length, $L$ and thermal conductivity, $k$ . Its inner and outer surfaces are maintained at…
Think it through. Then check your answer.
Question
$r_i$
Your answer
Choose one option, then check your answer.
A. $\frac{1}{2\pi kL} \ln\left(\frac{r_i}{r_o}\right)$ B. $\frac{L}{2\pi r_i k}$ C. $\frac{1}{2\pi kL} \ln\left(\frac{r_o}{r_i}\right)$ D. $\frac{1}{4\pi kL} \ln\left(\frac{r_o}{r_i}\right)$
Restoring your progress…
The solution stays hidden until you check.
$Q = -kA \frac{dT}{dr}$
Open question page
23
Q23MCQ1 markMedium
Which one of the following pairs of equations describes an irreversible heat engine?
Think it through. Then check your answer.
Question
$Which one of the following pairs of equations describes an irreversible heat engine?$
Your answer
Choose one option, then check your answer.
A. $\oint \delta Q > 0$ B. $\oint \delta Q < 0$ C. $\oint \delta Q > 0$ D. $\oint \delta Q < 0$
Restoring your progress…
The solution stays hidden until you check.
$\oint \delta Q > 0$
Open question page
24
Q24MCQ1 markEasy
Consider the turbulent flow of a fluid through a circular pipe of diameter, $D$ . Identify the correct pair of statements. I. The fluid is well-mixed II. The fluid is unmixed III.…
Think it through. Then check your answer.
Question
$D$
Your answer
Choose one option, then check your answer.
A. $I, III$ B. $II, IV$ C. $II, III$ D. $I, IV$
Restoring your progress…
The solution stays hidden until you check.
$Re_D \approx 2300$
Open question page
25
Q25MCQ1 markEasy
For a gas turbine power plant, identify the correct pair of statements. P. Smaller in size compared to steam power plant for same power output Q. Starts quickly compared to steam…
Think it through. Then check your answer.
Question
$For a gas turbine power plant, identify the correct pair of statements. P. Smaller in size compared to steam power plant for same power output Q. Starts quickly compared to steam power plant R. Works on the principle of Rankine cycle S. Good compatibility with solid fuel$
Your answer
Choose one option, then check your answer.
A. $P, Q$ B. $R, S$ C. $Q, R$ D. $P, S$
Restoring your progress…
The solution stays hidden until you check.
$Correct answer (A) P, Q Step-by-step solution Gas turbine power plants have several characteristics compared to steam power plants: P. Smaller in size: They have a much higher power-to-weight ratio, making them more compact for the same power output. Q. Starts quickly: They can be started and brought to full load in a matter of minutes, whereas steam plants take hours. R. Principle: Gas turbines work on the Brayton cycle, not the Rankine cycle (which is for steam plants). S. Fuel compatibility: Gas turbines typically require clean gaseous or liquid fuels; they are not directly compatible with solid fuels like coal without gasification. Therefore, the correct pair is P and Q. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
Open question page
26
Q26NAT1 markEasy
A source at a temperature of $500 K$ provides $1000 kJ$ of heat. The temperature of environment is $27^\circ C$ . The maximum useful work (in $kJ$ ) that can be obtained from the…
Think it through. Then check your answer.
Question
$500 K$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$T_H$
Open question page
27
Q27NAT1 markMedium
A sample of moist air at a total pressure of $85 kPa$ has a dry bulb temperature of $30^\circ C$ (saturation vapour pressure of water = $4.24 kPa$ ). If the air sample has a…
Think it through. Then check your answer.
Question
$85 kPa$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$P = 85 kPa$
Open question page
28
Q28MCQ1 markEasy
The process utilizing mainly thermal energy for removing material is
Think it through. Then check your answer.
Question
$The process utilizing mainly thermal energy for removing material is$
Your answer
Choose one option, then check your answer.
A. $Ultrasonic Machining$ B. $Electrochemical Machining$ C. $Abrasive Jet Machining$ D. $Laser Beam Machining$
Restoring your progress…
The solution stays hidden until you check.
$Correct answer (D) Laser Beam Machining Step-by-step solution Laser Beam Machining (LBM) is a thermal process where material is removed by melting and vaporization using a high-intensity laser beam. Ultrasonic Machining (USM) and Abrasive Jet Machining (AJM) are mechanical processes utilizing erosion. Electrochemical Machining (ECM) is a chemical process utilizing ion transfer. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
Open question page
29
Q29NAT1 markEasy
The actual sales of a product in different months of a particular year are given below: | September | October | November | December | January | February | | :--- | :--- | :--- |…
Think it through. Then check your answer.
Question
$The actual sales of a product in different months of a particular year are given below: September October November December January February 180280250190240 ? The forecast of the sales, using the 4-month moving average method, for the month of February is_______$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$\text{Forecast}_{\text{Feb}} = \frac{\text{Sales}_{\text{Jan}} + \text{Sales}_{\text{Dec}} + \text{Sales}_{\text{Nov}} + \text{Sales}_{\text{Oct}}}{4}$
Open question page
30
Q30NAT1 markMedium
A straight turning operation is carried out using a single point cutting tool on an AISI 1020 steel rod. The feed is $0.2$ mm/rev and the depth of cut is $0.5$ mm. The tool has a…
Think it through. Then check your answer.
Question
$0.2$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$t_1$
Open question page
31
Q31MCQ1 markEasy
A minimal spanning tree in network flow models involves
Think it through. Then check your answer.
Question
$A minimal spanning tree in network flow models involves$
Your answer
Choose one option, then check your answer.
A. $all the nodes with cycle/loop allowed$ B. $all the nodes with cycle/loop not allowed$ C. $shortest path between start and end nodes$ D. $all the nodes with directed arcs$
Restoring your progress…
The solution stays hidden until you check.
$Correct answer (B) all the nodes with cycle/loop not allowed Step-by-step solution A spanning tree of a connected graph is a subgraph that is a tree and includes all the vertices of the graph. By definition, a tree is a connected graph with no cycles (loops). Therefore, a minimal spanning tree involves all the nodes with no cycles allowed. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
Open question page

September	October	November	December	January	February
180	280	250	190	240	?

Q32MCQ1 markEasy

Think it through. Then check your answer.

Question

Match the casting defects (Group A) with the probable causes (Group B): Group A Group B P: Hot tears 1: Improper fusion of two streams of liquid metal Q: Shrinkage 2: Low permeability of the sand mould R: Blow holes 3: Volumetric contraction both in liquid and solid stage S: Cold Shut 4: Differential cooling rate

Group A	Group B
P: Hot tears	1: Improper fusion of two streams of liquid metal
Q: Shrinkage	2: Low permeability of the sand mould
R: Blow holes	3: Volumetric contraction both in liquid and solid stage
S: Cold Shut	4: Differential cooling rate

Correct answer (B) P-4, Q-3, R-2, S-1 Step-by-step solution The matching of casting defects with their causes is as follows: Hot tears (P) : These are cracks caused by tensile stresses during cooling, often due to differential cooling rates (4) . Shrinkage (Q) : Caused by volumetric contraction (3) during solidification and cooling. Blow holes (R) : Caused by trapped gases when the permeability of the sand mould is low (2) . Cold Shut (S) : Occurs due to improper fusion of two streams of liquid metal (1) . Thus, the correct match is P-4, Q-3, R-2, S-1. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

Review answer and solution without JavaScript

Interactive answer checking needs JavaScript. The published solution is available below.

Correct answer (B) P-4, Q-3, R-2, S-1 Step-by-step solution The matching of casting defects with their causes is as follows: Hot tears (P) : These are cracks caused by tensile stresses during cooling, often due to differential cooling rates (4) . Shrinkage (Q) : Caused by volumetric contraction (3) during solidification and cooling. Blow holes (R) : Caused by trapped gases when the permeability of the sand mould is low (2) . Cold Shut (S) : Occurs due to improper fusion of two streams of liquid metal (1) . Thus, the correct match is P-4, Q-3, R-2, S-1.

Open question page

33
Q33MCQ1 markMedium
Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work interaction, because
Think it through. Then check your answer.
Question
$Cutting tool is much harder than the workpiece. Yet the tool wears out during the tool-work interaction, because$
Your answer
Choose one option, then check your answer.
A. $extra hardness is imparted to the workpiece due to coolant used$ B. $oxide layers on the workpiece surface impart extra hardness to it$ C. $extra hardness is imparted to the workpiece due to severe rate of strain$ D. $vibration is induced in the machine tool$
Restoring your progress…
The solution stays hidden until you check.
$Correct answer (C) extra hardness is imparted to the workpiece due to severe rate of strain Step-by-step solution During machining, the workpiece material undergoes severe plastic deformation at very high strain rates. This leads to significant strain hardening, which increases the hardness of the workpiece material at the tool-chip interface. This increased hardness contributes to the wear of the cutting tool despite its initial higher hardness. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
Open question page
34
Q34MCQ1 markEasy
The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table. [figure] | Point on the graph |…
Think it through. Then check your answer.
Question
$Stress-strain curve for mild steel showing stress $\sigma$ vs strain $\epsilon$ with points P, Q, R, S, T, and U marked.$
Your answer
Choose one option, then check your answer.
A. $P-1, Q-2, R-3, S-4, T-5, U-6$ B. $P-3, Q-1, R-4, S-2, T-6, U-5$ C. $P-3, Q-4, R-1, S-5, T-2, U-6$ D. $P-4, Q-1, R-5, S-2, T-3, U-6$
Restoring your progress…
The solution stays hidden until you check.
$Correct answer(C) P-3, Q-4, R-1, S-5, T-2, U-6Step-by-step solutionBased on the standard stress-strain curve for mild steel:P is the Proportionality Limit (3), where stress is linear with strain.Q is the Elastic Limit (4), the maximum stress without permanent set.R is the Upper Yield Point (1), where yielding begins.S is the Lower Yield Point (5), where stress stabilizes during yielding.T is the Ultimate Tensile Strength (2), the maximum stress on the curve.U is the Failure (6) point where fracture occurs.Matching these gives: P-3, Q-4, R-1, S-5, T-2, U-6, which is option (C).Turn this into a strength.Explore AI-powered practice and doubt support with Success Tracker.$
Open question page
35
Q35MCQ1 markMedium
The hot tearing in a metal casting is due to
Think it through. Then check your answer.
Question
$The hot tearing in a metal casting is due to$
Your answer
Choose one option, then check your answer.
A. $high fluidity$ B. $high melt temperature$ C. $wide range of solidification temperature$ D. $low coefficient of thermal expansion$
Restoring your progress…
The solution stays hidden until you check.
$Correct answer (C) wide range of solidification temperature Step-by-step solution Hot tearing is a defect that occurs in the mushy zone (semi-solid state) during solidification. It is caused by tensile stresses that the solidifying metal cannot withstand. Alloys with a wide solidification temperature range are more prone to this because they spend more time in the mushy zone, where the liquid film between grains can be easily pulled apart by contraction stresses. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.$
Open question page
36
Q36MCQ2 marksEasy
An analytic function of a complex variable $z = x + i y$ is expressed as $f(z) = u(x, y) + i v(x, y)$ , where $i = \sqrt{-1}$ . If $u(x, y) = x^2 - y^2$ , then expression for…
Think it through. Then check your answer.
Question
$z = x + i y$
Your answer
Choose one option, then check your answer.
A. $xy + c$ B. $\frac{x^2 + y^2}{2} + c$ C. $2xy + c$ D. $\frac{(x - y)^2}{2} + c$
Restoring your progress…
The solution stays hidden until you check.
$u(x, y) = x^2 - y^2$
Open question page
37
Q37MCQ2 marksMedium
Consider two solutions $x(t) = x_1(t)$ and $x(t) = x_2(t)$ of the differential equation $\frac{d^2x(t)}{dt^2} + x(t) = 0, t > 0$ , such that…
Think it through. Then check your answer.
Question
$x(t) = x_1(t)$
Your answer
Choose one option, then check your answer.
A. $1$ B. $-1$ C. $0$ D. $\pi/2$
Restoring your progress…
The solution stays hidden until you check.
$\frac{d^2x}{dt^2} + x = 0$
Open question page
38
Q38MCQ2 marksEasy
A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective…
Think it through. Then check your answer.
Question
$A machine produces 0, 1 or 2 defective pieces in a day with associated probability of 1/6, 2/3 and 1/6, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are$
Your answer
Choose one option, then check your answer.
A. $1 and 1/3$ B. $1 and 2/3$ C. $1 and 4/3$ D. $1/3 and 4/3$
Restoring your progress…
The solution stays hidden until you check.
$X$
Open question page
39
Q39NAT2 marksMedium
The real root of the equation $5x - 2\cos x - 1 = 0$ (up to two decimal accuracy) is _______
Think it through. Then check your answer.
Question
$5x - 2\cos x - 1 = 0$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$f(x) = 5x - 2\cos x - 1 = 0$
Open question page
40
Q40NAT2 marksHard
A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is 0.2. The dimensions shown in the figure…
Think it through. Then check your answer.
Question
$A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is 0.2. The dimensions shown in the figure are in mm. The braking torque (in N.m) for the brake shoe is_______$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$P = 1000$
Open question page
41
Q41NAT2 marksMedium
A body of mass ( $M$ ) 10 kg is initially stationary on a $45^\circ$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is 0.5.…
Think it through. Then check your answer.
Question
$M$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$W_x = Mg \sin \theta$
Open question page
42
Q42MCQ2 marksMedium
Consider a simply supported beam of length, $50h$ , with a rectangular cross-section of depth, $h$ , and width, $2h$ . The beam carries a vertical point load, $P$ , at its mid-point.…
Think it through. Then check your answer.
Question
$50h$
Your answer
Choose one option, then check your answer.
A. $0.02$ B. $0.10$ C. $0.05$ D. $0.01$
Restoring your progress…
The solution stays hidden until you check.
$P$
Open question page
43
Q43NAT2 marksEasy
The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1 kg, stiffness 100 N/m and viscous damping coefficient of 25 N.s/m is _______
Think it through. Then check your answer.
Question
$The damping ratio of a single degree of freedom spring-mass-damper system with mass of 1 kg, stiffness 100 N/m and viscous damping coefficient of 25 N.s/m is_______$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$\zeta$
Open question page
44
Q44MCQ2 marksMedium
An annular disc has a mass $m$ , inner radius $R$ and outer radius $2R$ . The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $v$ , the…
Think it through. Then check your answer.
Question
$m$
Your answer
Choose one option, then check your answer.
A. $\frac{9}{16} mv^2$ B. $\frac{11}{16} mv^2$ C. $\frac{13}{16} mv^2$ D. $\frac{15}{16} mv^2$
Restoring your progress…
The solution stays hidden until you check.
$K = K_{trans} + K_{rot} = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$
Open question page
45
Q45MCQ2 marksHard
A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘A’ is equal to zero? [figure]
Think it through. Then check your answer.
Question
$P$
Your answer
Choose one option, then check your answer.
A. $0.5L$ B. $0.25L$ C. $0.33L$ D. $0.66L$
Restoring your progress…
The solution stays hidden until you check.
$P$
Open question page
46
Q46MCQ2 marksMedium
Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by $t$ , lying in the interval $0$ to…
Think it through. Then check your answer.
Question
$t$
Your answer
Choose one option, then check your answer.
A. $x(t) = \cos t, y(t) = \sin t$ B. $x(t) = \cos t, y(t) = 2\sin t$ C. $x(t) = \frac{1}{2} + \cos t, y(t) = 2\sin t$ D. $x(t) = \frac{1}{2} + \cos t, y(t) = \sin t$
Restoring your progress…
The solution stays hidden until you check.
$H = r_{max} - r_{min}$
Open question page
47
Q47NAT2 marksMedium
A four-wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a…
Think it through. Then check your answer.
Question
$A four-wheel vehicle of mass 1000 kg moves uniformly in a straight line with the wheels revolving at 10 rad/s. The wheels are identical, each with a radius of 0.2 m. Then a constant braking torque is applied to all the wheels and the vehicle experiences a uniform deceleration. For the vehicle to stop in 10 s, the braking torque (in N.m) on each wheel is_______$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$m = 1000$
Open question page
48
Q48NAT2 marksMedium
A slider-crank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter…
Think it through. Then check your answer.
Question
$A slider-crank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter clockwise. For the given configuration, the speed (in m/s) of the slider is_______$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$r = 60$
Open question page
49
Q49NAT2 marksEasy
Consider an objective function $Z(x_1, x_2) = 3x_1 + 9x_2$ and the constraints $x_1 + x_2 \leq 8$ , $x_1 + 2x_2 \leq 4$ , $x_1 \geq 0, x_2 \geq 0$ . The maximum value of the…
Think it through. Then check your answer.
Question
$Z(x_1, x_2) = 3x_1 + 9x_2$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$x_1 + x_2 \leq 8$
Open question page
50
Q50NAT2 marksMedium
A mass-spring-dashpot system with mass $m = 10$ kg, spring constant $k = 6250$ N/m is excited by a harmonic excitation of $10 \cos(25t)$ N. At the steady state, the vibration…
Think it through. Then check your answer.
Question
$m = 10$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$m = 10$
Open question page
51
Q51MCQ2 marksEasy
A certain amount of an ideal gas is initially at a pressure $p_1$ and temperature $T_1$ . First, it undergoes a constant pressure process 1-2 such that $T_2 = 3T_1/4$ . Then, it…
Think it through. Then check your answer.
Question
$p_1$
Your answer
Choose one option, then check your answer.
A. $0.25$ B. $0.75$ C. $1.0$ D. $1.5$
Restoring your progress…
The solution stays hidden until you check.
$\frac{V_1}{T_1} = \frac{V_2}{T_2}$
Open question page
52
Q52NAT2 marksMedium
An amount of $100$ kW of heat is transferred through a wall in steady state. One side of the wall is maintained at $127^\circ\text{C}$ and the other side at $27^\circ\text{C}$ .…
Think it through. Then check your answer.
Question
$100$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$\dot{Q} = 100$
Open question page
53
Q53MCQ2 marksEasy
A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is maintained constant. Ignore frictional effect due to viscosity…
Think it through. Then check your answer.
Question
$A siphon is used to drain water from a large tank as shown in the figure below. Assume that the level of water is maintained constant. Ignore frictional effect due to viscosity and losses at entry and exit. At the exit of the siphon, the velocity of water is$
Your answer
Choose one option, then check your answer.
A. $\sqrt{2g(Z_Q - Z_R)}$ B. $\sqrt{2g(Z_P - Z_R)}$ C. $\sqrt{2g(Z_O - Z_R)}$ D. $\sqrt{2gZ_Q}$
Restoring your progress…
The solution stays hidden until you check.
$\frac{P_P}{\rho g} + \frac{V_P^2}{2g} + Z_P = \frac{P_R}{\rho g} + \frac{V_R^2}{2g} + Z_R$
Open question page
54
Q54NAT2 marksEasy
Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness ( $l$ ). The conductivity of one section is $k$ and that of the other…
Think it through. Then check your answer.
Question
$l$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$q$
Open question page
55
Q55NAT2 marksHard
A fluid of dynamic viscosity $2 \times 10^{-5}$ kg/m.s and density $1$ kg/m $^3$ flows with an average velocity of $1$ m/s through a long duct of rectangular ( $25$ mm $\times$ $15$ …
Think it through. Then check your answer.
Question
$2 \times 10^{-5}$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$D_h$
Open question page
56
Q56NAT2 marksHard
At the inlet of an axial impulse turbine rotor, the blade linear speed is $25$ m/s, the magnitude of absolute velocity is $100$ m/s and the angle between them is $25^\circ$ . The…
Think it through. Then check your answer.
Question
$25$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$u = 25$
Open question page
57
Q57MCQ2 marksEasy
A solid sphere of radius $r_1 = 20\text{ mm}$ is placed concentrically inside a hollow sphere of radius $r_2 = 30\text{ mm}$ as shown in the figure. [figure] The view factor…
Think it through. Then check your answer.
Question
$r_1 = 20\text{ mm}$
Your answer
Choose one option, then check your answer.
A. $\frac{2}{3}$ B. $\frac{4}{9}$ C. $\frac{8}{27}$ D. $\frac{9}{4}$
Restoring your progress…
The solution stays hidden until you check.
$F_{11} = 0$
Open question page
58
Q58NAT2 marksMedium
A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at $19$ liter/s is heated from $10^\circ$ C to $38^\circ$ C. Shell side water at…
Think it through. Then check your answer.
Question
$19$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$Q = \dot{m}_c C_p (T_{c,out} - T_{c,in})$
Open question page
59
Q59NAT2 marksMedium
A diesel engine has a compression ratio of 17 and cut-off takes place at 10% of the stroke. Assuming ratio of specific heats ( $\gamma$ ) as 1.4, the air-standard efficiency (in…
Think it through. Then check your answer.
Question
$\gamma$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$r = 17$
Open question page
60
Q60MCQ2 marksMedium
Consider the given project network, where numbers along various activities represent the normal time. The free float on activity 4-6 and the project duration, respectively, are…
Think it through. Then check your answer.
Question
$Consider the given project network, where numbers along various activities represent the normal time. The free float on activity 4-6 and the project duration, respectively, are$
Your answer
Choose one option, then check your answer.
A. $2, 13$ B. $0, 13$ C. $-2, 13$ D. $2, 12$
Restoring your progress…
The solution stays hidden until you check.
$3 + 2 + 5 + 5 = 15$
Open question page
61
Q61MCQ2 marksMedium
A manufacturer can produce 12000 bearings per day. The manufacturer received an order of 8000 bearings per day from a customer. The cost of holding a bearing in stock is Rs. 0.20…
Think it through. Then check your answer.
Question
$A manufacturer can produce 12000 bearings per day. The manufacturer received an order of 8000 bearings per day from a customer. The cost of holding a bearing in stock is Rs. 0.20 per month. Setup cost per production run is Rs. 500. Assuming 300 working days in a year, the frequency of production run should be$
Your answer
Choose one option, then check your answer.
A. $4.5 days$ B. $4.5 months$ C. $6.8 days$ D. $6.8 months$
Restoring your progress…
The solution stays hidden until you check.
$P = 12000$
Open question page
62
Q62MCQ2 marksMedium
A cylindrical blind riser with diameter $d$ and height $h$ , is placed on the top of the mold cavity of a closed type sand mold as shown in the figure. If the riser is of constant…
Think it through. Then check your answer.
Question
$d$
Your answer
Choose one option, then check your answer.
A. $1:2$ B. $2:1$ C. $1:4$ D. $4:1$
Restoring your progress…
The solution stays hidden until you check.
$t$
Open question page
63
Q63NAT2 marksHard
The diameter of a recessed ring was measured by using two spherical balls of diameter $d_2=60$ mm and $d_1=40$ mm as shown in the figure. The distance $H_2=35.55$ mm and…
Think it through. Then check your answer.
Question
$d_2=60$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$d_1 = 40$
Open question page
64
Q64MCQ2 marksEasy
Which pair of following statements is correct for orthogonal cutting using a single-point cutting tool? P. Reduction in friction angle increases cutting force Q. Reduction in…
Think it through. Then check your answer.
Question
$Which pair of following statements is correct for orthogonal cutting using a single-point cutting tool? P. Reduction in friction angle increases cutting force Q. Reduction in friction angle decreases cutting force R. Reduction in friction angle increases chip thickness S. Reduction in friction angle decreases chip thickness$
Your answer
Choose one option, then check your answer.
A. $P and R$ B. $P and S$ C. $Q and R$ D. $Q and S$
Restoring your progress…
The solution stays hidden until you check.
$\phi$
Open question page
65
Q65NAT2 marksMedium
For spot welding of two steel sheets (base metal) each of 3 mm thickness, welding current of 10000 A is applied for 0.2 s. The heat dissipated to the base metal is 1000 J.…
Think it through. Then check your answer.
Question
$^3$
Your answer
Enter a number. Decimals, negative values and scientific notation are accepted.
Numerical answer
Restoring your progress…
The solution stays hidden until you check.
$H_g$
Open question page

Point on the graph	Description of the point
P	1. Upper Yield Point
Q	2. Ultimate Tensile Strength
R	3. Proportionality Limit
S	4. Elastic Limit
T	5. Lower Yield Point
U	6. Failure

Your revision session

0 / 65

attempted

Correct

Incorrect

—

Accuracy

Saved in this browser only. Revision practice, not a timed score or account activity.

Success Tracker

AI-powered practice, built around you

Unlimited practice on eligible plans

Personalised practiceChoose topics and build confidence in your weaker areas.
AI doubt supportAsk follow-up questions when a solution does not click.
Progress that guides youTrack practice in your account and revisit mistakes.

Try GATE ME 2014 Set 3 as a timed test. Test access depends on your practice allowance.

Start with a free account View plans and allowances

Free practice and AI usage have limits. This page stays readable without an account. AI responses can be wrong; check the solution and source material.

Question navigator

CorrectIncorrectReview

Explore the questions

General Aptitude (GA)

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

MECHANICAL – ME

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer

Step-by-step solution

Question

Correct answer