Success TrackerSuccess Tracker
Log inSign up

The PYQ practice room

GATE ME 2018 Set 2

All 65 solved GATE ME 2018 Set 2 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

65

Paper marks

100

Question formats

2

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 27Medium 35Hard 3

Explore the questions

65 of 65 questions

General Aptitude (GA)

10
  1. Think it through. Then check your answer.

    Question

    “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
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  2. Think it through. Then check your answer.

    Question

    “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
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  3. Think it through. Then check your answer.

    Question

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

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  4. Think it through. Then check your answer.

    Question

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

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  5. Think it through. Then check your answer.

    Question

    The value of the expression 11+log⁡uvw+11+log⁡vwu+11+log⁡wuv\frac{1}{1+\log_u vw} + \frac{1}{1+\log_v wu} + \frac{1}{1+\log_w uv} is _________.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  6. Think it through. Then check your answer.

    Question

    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 nineteen students watched film C. How many students watched all three films?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  7. Think it through. Then check your answer.

    Question

    A wire would enclose an area of 1936 m21936\text{ 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 short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  8. Think it through. Then check your answer.

    Question

    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 additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?
    1. A.
      50
    2. B.
      89
    3. C.
      146
    4. D.
      175

    Answer checking is unavailable for this question. You can review the published solution without a score.

    Open question page
  9. Think it through. Then check your answer.

    Question

    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, then it is a number from 50 to 59.
    ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69.
    iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79.
    What is the house number?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  10. Think it through. Then check your answer.

    Question

    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, the following are the observations from the four trials:
    (1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT .
    Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page

Mechanical Engineering (Set 2)

55
  1. Think it through. Then check your answer.

    Question

    The Fourier cosine series for an even function f(x)f(x) is given by f(x)=a0+∑n=1∞ancos⁡(nx)f(x) = a_0 + \sum_{n=1}^{\infty} a_n \cos(nx). The value of the coefficient a2a_2 for the function f(x)=cos⁡2(x)f(x) = \cos^2(x) in [0,π][0, \pi] is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  2. Think it through. Then check your answer.

    Question

    The divergence of the vector field u⃗=ex(cos⁡yi^+sin⁡yj^)\vec{u} = e^x (\cos y \hat{i} + \sin y \hat{j}) is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  3. Think it through. Then check your answer.

    Question

    Consider a function uu which depends on position xx and time tt. The partial differential equation∂u∂t=∂2u∂x2\frac{\partial u}{\partial t} = \frac{\partial^2 u}{\partial x^2}is known as the
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  4. Think it through. Then check your answer.

    Question

    If yy is the solution of the differential equation y3dydx+x3=0y^3 \frac{dy}{dx} + x^3 = 0, y(0)=1y(0) = 1, the value of y(−1)y(-1) is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  5. Think it through. Then check your answer.

    Question

    The minimum axial compressive load, PP, required to initiate buckling for a pinned-pinned slender column with bending stiffness EIEI and length LL is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  6. Think it through. Then check your answer.

    Question

    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
    A frictionless gear train with four gears. The leftmost gear has 12 teeth and is given a torque T=100 N-m. It meshes with a 48-teeth gear. On the same shaft as the 48-teeth gear is another 12-teeth gear, which meshes with a 60-teeth gear on the right.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  7. Think it through. Then check your answer.

    Question

    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. Which one of the following statements is ALWAYS true?
    Single degree of freedom underdamped spring-mass-damper system
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  8. Think it through. Then check your answer.

    Question

    Pre-tensioning of a bolted joint is used to
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  9. Think it through. Then check your answer.

    Question

    The peak wavelength of radiation emitted by a black body at a temperature of 2000 K2000\text{ K} is 1.45 \mum1.45\text{ \mu m}. If the peak wavelength of emitted radiation changes to 2.90 \mum2.90\text{ \mu m}, then the temperature (in K) of the black body is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  10. Think it through. Then check your answer.

    Question

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

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  11. Think it through. Then check your answer.

    Question

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

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  12. Think it through. Then check your answer.

    Question

    Denoting LL as liquid and MM as solid in a phase-diagram with the subscripts representing different phases, a eutectoid reaction is described by
    1. A.
      M1→M2+M3M_1 \rightarrow M_2 + M_3
    2. B.
      L1→M1+M2L_1 \rightarrow M_1 + M_2
    3. C.
      L1+M1→M2L_1 + M_1 \rightarrow M_2
    4. D.
      M1+M2→M3M_1 + M_2 \rightarrow M_3

    Answer checking is unavailable for this question. You can review the published solution without a score.

    Open question page
  13. Think it through. Then check your answer.

    Question

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

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  14. Think it through. Then check your answer.

    Question

    Match the following products with the suitable manufacturing process
    ProductManufacturing Process
    P Toothpaste tube1 Centrifugal casting
    Q Metallic pipes2 Blow moulding
    R Plastic bottles3 Rolling
    S Threaded bolts4 Impact extrusion
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  15. Think it through. Then check your answer.

    Question

    Feed rate in slab milling operation is equal to
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  16. Think it through. Then check your answer.

    Question

    Metal removal in electric discharge machining takes place through
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  17. Think it through. Then check your answer.

    Question

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

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  18. Think it through. Then check your answer.

    Question

    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 order quantity of the tyres is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  19. Think it through. Then check your answer.

    Question

    If A=[123045001]A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 5 \\ 0 & 0 & 1 \end{bmatrix} then det⁡(A−1)\det(A^{-1}) is __________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  20. Think it through. Then check your answer.

    Question

    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, the torsional stiffness of the shaft (in kN-m/rad) is ________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  21. Think it through. Then check your answer.

    Question

    Fatigue life of a material for a fully reversed loading condition is estimated from σa=1100N−0.15\sigma_a = 1100 N^{-0.15}, where σa\sigma_a is the stress amplitude in MPa and NN is the failure life in cycles. The maximum allowable stress amplitude (in MPa) for a life of 1×1051 \times 10^5 cycles under the same loading condition is ________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  22. Think it through. Then check your answer.

    Question

    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 LL is δL\delta_L. When the plate length is increased to twice its original length, the percentage change in laminar boundary layer thickness at the end of the plate (with respect to δL\delta_L) is ________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  23. Think it through. Then check your answer.

    Question

    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).
    P-V diagram of a reversible cycle showing a triangular path with vertices at (2, 400), (2, 650), and (2.5, 400) where P is in kPa and V is in m^3.
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  24. Think it through. Then check your answer.

    Question

    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 customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  25. Think it through. Then check your answer.

    Question

    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 portion), the total distance travelled (in m) by the ball is __________ (correct to two decimal places).

    Answer checking is unavailable for this question. You can review the published solution without a score.

    Open question page
  26. Think it through. Then check your answer.

    Question

    Let zz be a complex variable. For a counter-clockwise integration around a unit circle CC, centred at origin,∮C15z−4dz=Aπi,\oint_C \frac{1}{5z-4} dz = A\pi i ,the value of AA is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  27. Think it through. Then check your answer.

    Question

    Let X1X_1 and X2X_2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y=min⁡(X1,X2)Y = \min(X_1, X_2) is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  28. Think it through. Then check your answer.

    Question

    For a position vector r⃗=xi^+yj^+zk^\vec{r} = x\hat{i} + y\hat{j} + z\hat{k} the norm of the vector can be defined as ∣r⃗∣=x2+y2+z2|\vec{r}| = \sqrt{x^2 + y^2 + z^2}. Given a function ϕ=ln⁡∣r⃗∣\phi = \ln |\vec{r}|, its gradient ∇ϕ\nabla \phi is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  29. Think it through. Then check your answer.

    Question

    In a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180∘ m/s210 \angle 180^\circ \text{ m/s}^2. If the instantaneous acceleration of point Q is zero, the acceleration (in m/s2\text{m/s}^2) of point R is
    A diagram showing a rigid body with points P, Q, and R forming a right-angled triangle. PQ = 12, QR = 16, and PR = 20. Point Q is at the origin of a coordinate system with x and y axes.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  30. Think it through. Then check your answer.

    Question

    A rigid rod of length 1 m1 \text{ m} is resting at an angle θ=45∘\theta = 45^\circ as shown in the figure. The end P is dragged with a velocity of U=5 m/sU = 5 \text{ m/s} to the right. At the instant shown, the magnitude of the velocity VV (in m/s\text{m/s}) of point Q as it moves along the wall without losing contact is
    A rigid rod PQ of length 1m resting against a vertical wall (y-axis) and a horizontal floor (x-axis). Point Q is on the wall, point P is on the floor. The angle between the rod and the floor is $\theta = 45^\circ$. Velocity of P is $U = 5 \text{ m/s}$ to the right. Velocity of Q is $V$ downwards.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  31. Think it through. Then check your answer.

    Question

    A bar of circular cross section is clamped at ends P and Q as shown in the figure. A torsional moment T=150T = 150 Nm is applied at a distance of 100 mm from end P. The torsional reactions (TP,TQ)(T_P, T_Q) in Nm at the ends P and Q respectively are
    Torsional bar clamped at P and Q with torque T applied at 100 mm from P and 200 mm from Q
    (All dimensions are in mm)
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  32. Think it through. Then check your answer.

    Question

    In a cam-follower, the follower rises by hh as the cam rotates by δ\delta (radians) at constant angular velocity ω\omega (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period. Assuming that the magnitudes of the acceleration and deceleration are same, the maximum velocity of the follower is
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  33. Think it through. Then check your answer.

    Question

    A bimetallic cylindrical bar of cross sectional area 1 m2^2 is made by bonding Steel (Young’s modulus = 210 GPa) and Aluminium (Young’s modulus = 70 GPa) as shown in the figure. To maintain tensile axial strain of magnitude 10−610^{-6} in Steel bar and compressive axial strain of magnitude 10−610^{-6} in Aluminum bar, the magnitude of the required force PP (in kN) along the indicated direction is
    Bimetallic bar with Steel and Aluminium sections, clamped at both ends, with force P at the interface
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  34. Think it through. Then check your answer.

    Question

    Air flows at the rate of 1.5 m3/s1.5\text{ m}^3/\text{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 mm400\text{ mm} and 200 mm200\text{ mm}. Take the air density as 1.2 kg/m31.2\text{ kg}/\text{m}^3 and assume inviscid incompressible flow. The change in pressure (p2−p1)(p_2 - p_1) (in kPa) between sections 1 and 2 is
    A horizontal pipe with air flow, showing section 1 with diameter 400 mm and section 2 with diameter 200 mm.
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  35. Think it through. Then check your answer.

    Question

    The problem of maximizing z=x1−x2z = x_1 - x_2 subject to constraints x1+x2≤10x_1 + x_2 \leq 10, x1≥0x_1 \geq 0, x2≥0x_2 \geq 0 and x2≤5x_2 \leq 5 has
    Your answer

    Choose one option, then check your answer.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  36. Think it through. Then check your answer.

    Question

    Given the ordinary differential equationd2ydx2+dydx−6y=0\frac{d^2y}{dx^2} + \frac{dy}{dx} - 6y = 0with y(0)=0y(0) = 0 and dydx(0)=1\frac{dy}{dx}(0) = 1, the value of y(1)y(1) is _________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  37. Think it through. Then check your answer.

    Question

    A steel wire is drawn from an initial diameter (did_i) of 10 mm to a final diameter (dfd_f) of 7.5 mm. The half cone angle (α\alpha) of the die is 5° and the coefficient of friction (μ\mu) between the die and the wire is 0.1. The average of the initial and final yield stress [(σY)avg(\sigma_Y)_{avg}] is 350 MPa. The equation for drawing stress σf\sigma_f, (in MPa) is given as:σf=(σY)avg{1+1μcot⁡α}[1−(dfdi)2μcot⁡α]\sigma_f = (\sigma_Y)_{avg}\{1 + \frac{1}{\mu \cot\alpha}\}\left[1 - \left(\frac{d_f}{d_i}\right)^{2\mu \cot\alpha}\right]The drawing stress (in MPa) required to carry out this operation is ______ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  38. Think it through. Then check your answer.

    Question

    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 mm. The shear angle (in degrees) for this process is ______ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  39. Think it through. Then check your answer.

    Question

    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 floor, the linear acceleration (in m/s2^2) of the centre of the disc is ________ (correct to two decimal places).
    A circular disc on a floor with a horizontal force of 100 N applied at its center.
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  40. Think it through. Then check your answer.

    Question

    A frictionless circular piston of area 10−2 m210^{-2}\text{ m}^2 and mass 100 kg100\text{ kg} sinks into a cylindrical container of the same area filled with water of density 1000 kg/m31000\text{ kg/m}^3 as shown in the figure. The container has a hole of area 10−3 m210^{-3}\text{ m}^2 at the bottom that is open to the atmosphere. Assuming there is no leakage from the edges of the piston and considering water to be incompressible, the magnitude of the piston velocity (in m/s) at the instant shown is _____ (correct to three decimal places).
    A cylindrical container filled with water to a height of 0.5 m. A 100 kg piston is on top of the water. A small hole is at the bottom right. Gravity $g = 10\text{ m/s}^2$ is acting downwards. Atmospheric pressure $p_{atm}$ is above the piston and at the hole exit.
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  41. Think it through. Then check your answer.

    Question

    A 0.2 m0.2\text{ m} thick infinite black plate having a thermal conductivity of 3.96 W/m-K3.96\text{ W/m-K} is exposed to two infinite black surfaces at 300 K300\text{ K} and 400 K400\text{ K} as shown in the figure. At steady state, the surface temperature of the plate facing the cold side is 350 K350\text{ K}. The value of Stefan-Boltzmann constant, σ\sigma, is 5.67×10−8 W/m2 K45.67 \times 10^{-8}\text{ W/m}^2\text{ K}^4. Assuming 1-D heat conduction, the magnitude of heat flux through the plate (in W/m2\text{W/m}^2) is ________ (correct to two decimal places).
    A 0.2 m thick plate between two infinite surfaces. Left surface is at 300 K, right surface is at 400 K. There is vacuum between the surfaces and the plate.
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  42. Think it through. Then check your answer.

    Question

    Air is held inside a non-insulated cylinder using a piston (mass M=25 kgM=25\text{ kg} and area A=100 cm2A=100\text{ cm}^2) and stoppers (of negligible area), as shown in the figure. The initial pressure PiP_i and temperature TiT_i of air inside the cylinder are 200 kPa200\text{ kPa} and 400∘C400^\circ\text{C}, respectively. The ambient pressure P∞P_\infty and temperature T∞T_\infty are 100 kPa100\text{ kPa} and 27∘C27^\circ\text{C}, respectively. The temperature of the air inside the cylinder (∘C^\circ\text{C}) at which the piston will begin to move is ________ (correct to two decimal places).
    A vertical cylinder with air inside. A piston of mass $M=25\text{ kg}$ and area $A=100\text{ cm}^2$ is resting on stoppers. Above the piston is ambient pressure $P_\infty = 100\text{ kPa}$ and $T_\infty = 27^\circ\text{C}$. Inside is $P_i = 200\text{ kPa}$ and $T_i = 400^\circ\text{C}$. Gravity $g = 10\text{ m/s}^2$.
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  43. Think it through. Then check your answer.

    Question

    A standard vapor compression refrigeration cycle operating with a condensing temperature of 35∘C35^\circ C and an evaporating temperature of −10∘C-10^\circ C develops 15 kW15\text{ kW} of cooling. The p−hp-h diagram shows the enthalpies at various states. If the isentropic efficiency of the compressor is 0.750.75, the magnitude of compressor power (in kW\text{kW}) is _________ (correct to two decimal places).
    $p-h$ diagram for a vapor compression refrigeration cycle showing enthalpies at various states: $h_1 = 400\text{ kJ/kg}$, $h_{2s} = 475\text{ kJ/kg}$, $h_3 = h_4 = 250\text{ kJ/kg}$
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  44. Think it through. Then check your answer.

    Question

    Ambient air is at a pressure of 100 kPa100\text{ kPa}, dry bulb temperature of 30∘C30^\circ C and 60%60\% relative humidity. The saturation pressure of water at 30∘C30^\circ C is 4.24 kPa4.24\text{ kPa}. The specific humidity of air (in g/kg\text{g/kg} of dry air) is ________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  45. Think it through. Then check your answer.

    Question

    A test is conducted on a one-fifth scale model of a Francis turbine under a head of 2 m2\text{ m} and volumetric flow rate of 1 m3/s1\text{ m}^3\text{/s} at 450 rpm450\text{ rpm}. Take the water density and the acceleration due to gravity as 103 kg/m310^3\text{ kg/m}^3 and 10 m/s210\text{ m/s}^2, respectively. Assume no losses both in model and prototype turbines. The power (in MW\text{MW}) of a full sized turbine while working under a head of 30 m30\text{ m} is _______ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  46. Think it through. Then check your answer.

    Question

    The true stress (in MPa) versus true strain relationship for a metal is given by σ=1020ϵ0.4\sigma = 1020 \epsilon^{0.4}. The cross-sectional area at the start of a test (when the stress and strain values are equal to zero) is 100 mm2100\text{ mm}^2. The cross-sectional area at the time of necking (in mm2\text{mm}^2) is ________ (correct to two decimal places)
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  47. Think it through. Then check your answer.

    Question

    A steel wire is drawn from an initial diameter (did_i) of 10 mm10\text{ mm} to a final diameter (dfd_f) of 7.5 mm7.5\text{ mm}. The half cone angle (α\alpha) of the die is 5∘5^\circ and the coefficient of friction (μ\mu) between the die and the wire is 0.10.1. The average of the initial and final yield stress [(σY)avg][(\sigma_Y)_{avg}] is 350 MPa350\text{ MPa}. The equation for drawing stress σf\sigma_f, (in MPa) is given as:σf=(σY)avg{1+1μcot⁡α}[1−(dfdi)2μcot⁡α]\sigma_f = (\sigma_Y)_{avg} \left\{1 + \frac{1}{\mu \cot \alpha}\right\} \left[1 - \left(\frac{d_f}{d_i}\right)^{2\mu \cot \alpha}\right]The drawing stress (in MPa) required to carry out this operation is _________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  48. Think it through. Then check your answer.

    Question

    Following data correspond to an orthogonal turning of a 100 mm100\text{ mm} diameter rod on a lathe.
    Rake angle: +15∘+15^\circ; Uncut chip thickness: 0.5 mm0.5\text{ mm}; nominal chip thickness after the cut: 1.25 mm1.25\text{ mm}. The shear angle (in degrees) for this process is _______ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  49. Think it through. Then check your answer.

    Question

    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 test 1, a drill lasted 300 holes at 150 rpm while in test 2, another drill lasted 200 holes at 300 rpm. The maximum number of holes that can be made by another drill from the above batch at 200 rpm is ______ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  50. Think it through. Then check your answer.

    Question

    For sand-casting a steel rectangular plate with dimensions 80 mm × 120 mm × 20 mm, a cylindrical riser has to be designed. The height of the riser is equal to its diameter. The total solidification time for the casting is 2 minutes. In Chvorinov’s law for the estimation of the total solidification time, exponent is to be taken as 2. For a solidification time of 3 minutes in the riser, the diameter (in mm) of the riser is __________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  51. Think it through. Then check your answer.

    Question

    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 _______.
    directed graph with nodes 1 to 6 and arc lengths
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  52. Think it through. Then check your answer.

    Question

    A circular hole of 2525 mm diameter and depth of 2020 mm is machined by EDM process. The material removal rate (in mm3/min\text{mm}^3/\text{min}) is expressed as4×104IT−1.23,4 \times 10^4 IT^{-1.23},where I=300I = 300 A and the melting point of the material, T=1600∘CT = 1600^\circ\text{C}. The time (in minutes) for machining this hole is ________ (correct to two decimal places)
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  53. Think it through. Then check your answer.

    Question

    A welding operation is being performed with voltage = 3030 V and current = 100100 A. The cross-sectional area of the weld bead is 2020 mm2mm^2. The work-piece and filler are of titanium for which the specific energy of melting is 1414 J/mm3J/mm^3. Assuming a thermal efficiency of the welding process 70%70\%, the welding speed (in mm/s) is __________ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  54. Think it through. Then check your answer.

    Question

    Steam in the condenser of a thermal power plant is to be condensed at a temperature of 30∘C30^\circ\text{C} with cooling water which enters the tubes of the condenser at 14∘C14^\circ\text{C} and exits at 22∘C22^\circ\text{C}. The total surface area of the tubes is 50 m250 \text{ m}^2, and the overall heat transfer coefficient is 2000 W/m2K2000 \text{ W/m}^2\text{K}. The heat transfer (in MW) to the condenser is ______ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page
  55. Think it through. Then check your answer.

    Question

    A vehicle powered by a spark ignition engine follows air standard Otto cycle (γ=1.4\gamma=1.4). The engine generates 70 kW while consuming 10.3 kg/hr of fuel. The calorific value of fuel is 44,000 kJ/kg. The compression ratio is _______ (correct to two decimal places).
    Your answer

    Enter a number. Decimals, negative values and scientific notation are accepted.

    Restoring your progress…

    The solution stays hidden until you check.
    Open question page