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GATE ME 2022 Set 2

All 65 solved GATE ME 2022 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.

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Questions

65

Paper marks

100

Question formats

3

MCQ · NAT · MSQ

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 17Medium 33Hard 15

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Writing too many things on the ______ while teaching could make the students get _______.
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    Question

    Which one of the following is a representation (not to scale and in bold) of all values of xx satisfying the inequality 2−5x≤−6x−532 - 5x \leq -\frac{6x-5}{3} on the real number line?
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    Question

    If f(x)=2ln⁡(ex)f(x) = 2 \ln(\sqrt{e^x}), what is the area bounded by f(x)f(x) for the interval [0,2][0, 2] on the xx-axis?
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    Question

    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?
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    Question

    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).
    Target shape consisting of a square base with a triangular top
    1. A.
      Group of shapes including three triangles and one square
    2. B.
      Group of shapes including four triangles and one square
    3. C.
      Group of shapes including two triangles, one square, and one trapezoid
    4. D.
      Group of shapes including three triangles and one square

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    Question

    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.
    Which one of the following is the CORRECT logical inference based on the
    information in the above passage?
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    Question

    For the past mm 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 mm?
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    Question

    Consider the following functions for non-zero positive integers, pp and qq.f(p,q)=p×p×p×⋯×p (q terms)=pq;f(p,1)=pf(p, q) = p \times p \times p \times \dots \times p \text{ ($q$ terms)} = p^q; \quad f(p, 1) = pg(p,q)=pppp… (up to q terms);g(p,1)=pg(p, q) = p^{p^{p^{p^{\dots}}}} \text{ (up to $q$ terms)}; \quad g(p, 1) = pWhich one of the following options is correct based on the above?
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    Question

    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 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?
    Network diagram showing four cities P, Q, R, and S with one-way routes and their respective train schedules. P: 8 AM, 90 min; Q: 5 AM, 120 min; R: 7 AM, 60 min; S: 8 AM, 45 min.
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    Question

    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.
    Two squares, case M with 4 shaded circles and case N with 9 shaded circles
    What is the ratio of the areas of unshaded regions of case M to that of case N?
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Mechanical Engineering

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    Question

    F(t)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)F(t)?
    Plot of periodic square wave function F(t) against t
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    Question

    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 ∫AF⃗⋅dA⃗\int_A \vec{F} \cdot d\vec{A} of a vector field F⃗=3xi^+5yj^+6zk^\vec{F} = 3x\hat{i} + 5y\hat{j} + 6z\hat{k} over the entire surface AA of the cube is ______.
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    Question

    Consider the definite integral∫12(4x2+2x+6)dx.\int_{1}^{2} (4x^2 + 2x + 6)dx.Let IeI_e be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is IsI_s. The percentage error is defined as e=100×(Ie−Is)/Iee = 100 \times (I_e - I_s)/I_e. The value of ee is
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    Question

    Given ∫−∞∞e−x2dx=π\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}.
    If aa and bb are positive integers, the value of ∫−∞∞e−a(x+b)2dx\int_{-\infty}^{\infty} e^{-a(x+b)^2} dx is ________.
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    Question

    A polynomial ϕ(s)=ansn+an−1sn−1+⋯+a1s+a0\phi(s) = a_n s^n + a_{n-1} s^{n-1} + \dots + a_1 s + a_0 of degree n>3n > 3 with constant real coefficients an,an−1,…,a0a_n, a_{n-1}, \dots, a_0 has triple roots at s=−σs = -\sigma. Which one of the following conditions must be satisfied?
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    Question

    Which one of the following is the definition of ultimate tensile strength (UTS) obtained from a stress-strain test on a metal specimen?
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    Question

    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 gg is the acceleration due to gravity. The disc is then given a rapid spin ω\omega about its axis in the positive x-axis direction as shown, while the shaft remains at rest. The direction of rotation is defined by using the right-hand thumb rule. If the string AB is suddenly cut, assuming negligible energy dissipation, the shaft AE will
    Diagram of a shaft-disc assembly suspended by strings with coordinate axes
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    Question

    A structural member under loading has a uniform state of plane stress which in usual notations is given by σx=3P\sigma_x = 3P, σy=−2P\sigma_y = -2P and τxy=2P\tau_{xy} = \sqrt{2} P, where P>0P > 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 PP at which yielding starts (according to the maximum distortion energy theory) is
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    Question

    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 ºC800\text{ ºC}, then the solidification range is
    Phase diagram of a binary alloy with eutectic point at 30% B and 400 ºC
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    Question

    A shaft of diameter 25−0.07−0.04 mm25_{-0.07}^{-0.04}\text{ mm} is assembled in a hole of diameter 25−0.00+0.02 mm25_{-0.00}^{+0.02}\text{ mm}. Match the allowance and limit parameter in Column I with its corresponding quantitative value in Column II for this shaft-hole assembly.
    Allowance and limit parameter (Column I)Quantitative value (Column II)
    P Allowance1 0.09 mm
    Q Maximum clearance2 24.96 mm
    R Maximum material limit for hole3 0.04 mm
    4 25.0 mm
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    Question

    Match the additive manufacturing technique in Column I with its corresponding input material in Column II.
    Additive manufacturing technique (Column I)Input material (Column II)
    P Fused deposition modelling1 Photo sensitive liquid resin
    Q Laminated object manufacturing2 Heat fusible powder
    R Selective laser sintering3 Filament of polymer
    4 Sheet of thermoplastic or green compacted metal sheet
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    Question

    Which one of the following CANNOT impart linear motion in a CNC machine?
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    Question

    Which one of the following is an intensive property of a thermodynamic system?
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    Question

    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.
    A horizontal divergent channel with flow from left to right, showing points A and B inside the channel.
    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?
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    Question

    Which of the following non-dimensional terms is an estimate of Nusselt number?
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    Question

    A square plate is supported in four different ways (configurations (P) to (S) as shown in the figure). A couple moment CC 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?
    Four support configurations (P), (Q), (R), and (S) for a square plate with an applied couple moment C
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    Question

    Consider sand casting of a cube of edge length aa. A cylindrical riser is placed at the top of the casting. Assume solidification time, ts∝V/At_s \propto V/A, where VV is the volume and AA 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?
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    Question

    Which of these processes involve(s) melting in metallic workpieces?
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    Question

    The velocity field in a fluid is given to be V⃗=(4xy)i^+2(x2−y2)j^\vec{V} = (4xy)\hat{i} + 2(x^2 - y^2)\hat{j}. Which of the following statement(s) is/are correct?
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    Question

    A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of 20 N20\text{ N} each can be placed on the platforms. The number of discs placed on the left side platform is nn and that on the right side platform is mm.
    It is found that for n=5n = 5 and m=0m = 0, a force F=200 NF = 200\text{ N} (refer to part (i) of the figure) is just sufficient to initiate upward motion of the left side platform. If the force FF is removed then the minimum value of mm (refer to part (ii) of the figure) required to prevent downward motion of the left side platform is______ (in integer).
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    Question

    For a dynamical system governed by the equation,x¨(t)+2ζωnx˙(t)+ωn2x(t)=0,\ddot{x}(t) + 2\zeta\omega_n\dot{x}(t) + \omega_n^2x(t) = 0,the damping ratio ζ\zeta is equal to 12πlog⁡e2\frac{1}{2\pi}\log_e 2. The displacement xx of this system is measured during a hammer test. A displacement peak in the positive displacement direction is measured to be 44 mm. Neglecting higher powers (>1>1) of the damping ratio, the displacement at the next peak in the positive direction will be ___________ mm (in integer).
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    Question

    An electric car manufacturer underestimated the January sales of car by 2020 units, while the actual sales was 120120 units. If the manufacturer uses exponential smoothing method with a smoothing constant of α=0.2\alpha = 0.2, then the sales forecast for the month of February of the same year is ___________units (in integer).
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    Question

    The demand of a certain part is 10001000 parts/year and its cost is ₹1000₹1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering is ₹100₹100/order and the lead time for receiving the orders is 55 days. If the holding cost is ₹20₹20/part/year, the inventory level for placing the orders is _________ parts (round off to the nearest integer).
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    Question

    Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume cvc_v is equal to 750 J·kg−1^{-1}·K−1^{-1}. A stirrer performs 225 kJ of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be ___________ bar (in integer).
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    Question

    Wien’s law is stated as follows: λmT=C\lambda_m T = C, where CC is 2898μm⋅K2898 \mu m \cdot K and λm\lambda_m is the wavelength at which the emissive power of a black body is maximum for a given temperature TT. The spectral hemispherical emissivity (ϵλ\epsilon_\lambda) of a surface is shown in the figure below (1A˚=10−10m1\text{\AA} = 10^{-10}m). The temperature at which the total hemispherical emissivity will be highest is __________ K (round off to the nearest integer).
    Graph of spectral hemispherical emissivity \epsilon_\lambda versus wavelength \lambda in Angstroms, showing a bell-shaped curve peaking at 6000 \text{\AA}
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    For the exact differential equation,dudx=−xu22+x2u,\frac{du}{dx} = \frac{-xu^2}{2+x^2u},which one of the following is the solution?
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    Question

    A rigid homogeneous uniform block of mass 1 kg, height h=0.4h = 0.4 m and width b=0.3b = 0.3 m is pinned at one corner and placed upright in a uniform gravitational field (g=9.81g = 9.81 m/s2^2), supported by a roller in the configuration shown in the figure. A short duration (impulsive) force FF, producing an impulse IFI_F, is applied at a height of d=0.3d = 0.3 m from the bottom as shown. Assume all joints to be frictionless. The minimum value of IFI_F required to topple the block is
    A rectangular block of height h and width b, pinned at the bottom right corner and supported by a roller at the bottom left. An impulsive force F is applied horizontally to the left face at a height d from the bottom. Gravity g acts downwards.
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    Question

    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 as shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress σxx\sigma_{xx} is ________.
    Two loading diagrams, Loading - I and Loading - II, showing stress states on square elements.
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    A rigid body in the XX-YY plane consists of two point masses (11 kg each) attached to the ends of two massless rods, each of 11 cm length, as shown in the figure. It rotates at 3030 RPM counter-clockwise about the ZZ-axis passing through point OO. A point mass of 2\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 OO. The length of the third rod is ________ cm.
    Diagram showing two 1 kg masses on 1 cm rods at 90 degrees to each other, rotating about O in the X-Y plane.
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    Question

    A spring mass damper system (mass mm, stiffness kk, and damping coefficient cc) excited by a force F(t)=Bsin⁡ωtF(t) = B \sin \omega t, where BB, ω\omega and tt are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of the system (marked as (i) to (iv)) are shown just to the right of the system figure. In the figures of the responses, AA is the amplitude of response shown in red color and the dashed lines indicate its envelope. The responses represent only the qualitative trend and those are not drawn to any specific scale.
    spring-mass-damper system and four qualitative response plots
    Four different parameter and forcing conditions are mentioned below.
    (P) c>0c > 0 and ω=k/m\omega = \sqrt{k/m}
    (Q) c<0c < 0 and ω≠0\omega \neq 0
    (R) c=0c = 0 and ω=k/m\omega = \sqrt{k/m}
    (S) c=0c = 0 and ω≅k/m\omega \cong \sqrt{k/m}Which one of the following options gives correct match (indicated by arrow →\rightarrow) of the parameter and forcing conditions to the responses?
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    Question

    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.
    PartMilling (hours)Polishing (hours)
    P186
    P232
    P334
    P446
    P557
    P664
    P721
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    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 ₹__________.
    M1M2M3Profit per piece (₹)
    P1220150
    P2312100
    Maximum quantity available per day705040
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    A tube of uniform diameter DD is immersed in a steady flowing inviscid liquid stream of velocity VV, as shown in the figure. Gravitational acceleration is represented by gg. The volume flow rate through the tube is ______.
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    The steady velocity field in an inviscid fluid of density 1.51.5 is given to be V⃗=(y2−x2)i^+(2xy)j^\vec{V} = (y^2 - x^2)\hat{i} + (2xy)\hat{j}. Neglecting body forces, the pressure gradient at (x=1,y=1)(x = 1, y = 1) is __________ .
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    In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to 250 kJ/kg250\text{ kJ/kg}. The exit of the compressor is superheated at condenser pressure with specific enthalpy equal to 300 kJ/kg300\text{ kJ/kg}. At the condenser exit, the refrigerant is throttled to the evaporator pressure. The coefficient of performance (COP) of the cycle is 33. If the specific enthalpy of the saturated liquid at evaporator pressure is 50 kJ/kg50\text{ kJ/kg}, then the dryness fraction of the refrigerant at entry to evaporator is _________.
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    AA is a 3×53 \times 5 real matrix of rank 2. For the set of homogeneous equations Ax=0Ax = 0, where 00 is a zero vector and xx is a vector of unknown variables, which of the following is/are true?
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    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>0Q > 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)?
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    If the sum and product of eigenvalues of a 2×22 \times 2 real matrix [3ppq]\begin{bmatrix} 3 & p \\ p & q \end{bmatrix} are 4 and −1-1 respectively, then ∣p∣|p| is ______ (in integer).
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    Question

    Given z=x+iy,i=−1z = x + iy, i = \sqrt{-1}. CC is a circle of radius 2 with the centre at the origin. If the contour CC is traversed anticlockwise, then the value of the integral 12π∫C1(z−i)(z+4i)dz\frac{1}{2\pi} \int_C \frac{1}{(z-i)(z+4i)} dz is _______ (round off to one decimal place).
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    A shaft of length LL is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is did_i and the external diameter of the rim is dod_o, as shown in the figure. The modulus of rigidity of the core and rim materials are GiG_i and GoG_o, respectively. It is given that do=2did_o = 2d_i and Gi=3GoG_i = 3G_o. When the shaft is twisted by application of a torque along the shaft axis, the maximum shear stress developed in the outer rim and the inner core turn out to be τo\tau_o and τi\tau_i, respectively. All the deformations are in the elastic range and stress-strain relations are linear. Then the ratio τi/τo\tau_i/\tau_o is ______ (round off to 2 decimal places).
    Cross-section of a composite shaft showing inner core of diameter $d_i$ and outer rim of diameter $d_o$
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    A rigid beam AD of length 3a=63a = 6 m is hinged at frictionless pin joint A and supported by two strings as shown in the figure. String BC passes over two small frictionless pulleys of negligible radius. All the strings are made of the same material and have equal cross-sectional area. A force F=9F = 9 kN is applied at C and the resulting stresses in the strings are within linear elastic limit. The self-weight of the beam is negligible with respect to the applied load. Assuming small deflections, the tension developed in the string at C is _________ kN (round off to 2 decimal places).
    Rigid beam AD supported by strings at B, C, and D with a force F applied at C
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    In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the 2 cm long link is ω2=5\omega_2 = 5 rad/s. Given the dimensions as shown, the magnitude of the angular velocity ω4\omega_4 of the 4 cm long link is given by _____ rad/s (round off to 2 decimal places).
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    A shaft AC rotating at a constant speed carries a thin pulley of radius r=0.4r = 0.4 m at the end C which drives a belt. A motor is coupled at the end A of the shaft such that it applies a torque MzM_z about the shaft axis without causing any bending moment. The shaft is mounted on narrow frictionless bearings at A and B where AB = BC = L=0.5L = 0.5 m. The taut and slack side tensions of the belt are T1=300T_1 = 300 N and T2=100T_2 = 100 N, respectively. The allowable shear stress for the shaft material is 80 MPa. The self-weights of the pulley and the shaft are negligible. Use the value of π\pi available in the on-screen virtual calculator. Neglecting shock and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is _______ mm (round off to 2 decimal places).
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    A straight-teeth horizontal slab milling cutter is shown in the figure. It has 4 teeth and diameter (DD) of 200 mm. The rotational speed of the cutter is 100 rpm and the linear feed given to the workpiece is 1000 mm/minute. The width of the workpiece (ww) is 100 mm, and the entire width is milled in a single pass of the cutter. The cutting force/tooth is given by F=KtcwF = K t_c w, where specific cutting force K=10K = 10 N/mm2^2, ww is the width of cut, and tct_c is the uncut chip thickness.
    The depth of cut (dd) is D/2D/2, and hence the assumption of dD≪1\frac{d}{D} \ll 1 is invalid. The maximum cutting force required is ________ kN (round off to one decimal place).
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    In an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is 0.5 mm0.5\text{ mm} and the shear angle is 15∘15^\circ. The orthogonal rake angle of the tool is 0∘0^\circ and the width of cut is 2 mm2\text{ mm}. The workpiece material is perfectly plastic and its yield shear strength is 500 MPa500\text{ MPa}. The cutting force is _________ N (round off to the nearest integer).
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    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 as shown in the figure. The pitch (pp) and included angle of the thread are 4 mm4\text{ mm} and 60∘60^\circ, respectively. The diameter of the best size wire is ___________ mm (round off to 2 decimal places).
    A diagram showing a wire of diameter $d$ placed in a V-thread groove of a metric screw. The wire touches the flanks at the pitch line. Labels include 'Flank', 'Wire', 'Pitch line', an included angle of $60^\circ$, and dimensions $0.25p$ and $0.5p$.
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    In a direct current arc welding process, the power source has an open circuit voltage of 100100 V and short circuit current of 10001000 A. Assume a linear relationship between voltage and current. The arc voltage (VV) varies with the arc length (ll) as V=10+5lV = 10 + 5l, where VV is in volts and ll is in mm. The maximum available arc power during the process is _________ kVA (in integer).
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    A cylindrical billet of 100 mm100\text{ mm} diameter and 100 mm100\text{ mm} length is extruded by a direct extrusion process to produce a bar of L-section. The cross sectional dimensions of this L-section bar are shown in the figure. The total extrusion pressure (pp) in MPa for the above process is related to extrusion ratio (rr) asp=Ksσm[0.8+1.5ln⁡(r)+2ld0],p = K_s \sigma_m \left[ 0.8 + 1.5 \ln(r) + \frac{2l}{d_0} \right],where σm\sigma_m is the mean flow strength of the billet material in MPa, ll is the portion of the billet length remaining to be extruded in mm, d0d_0 is the initial diameter of the billet in mm, and KsK_s is the die shape factor.
    If the mean flow strength of the billet material is 50 MPa50\text{ MPa} and the die shape factor is 1.051.05, then the maximum force required at the start of extrusion is ________ kN (round off to one decimal place).
    Cross-sectional dimensions of the L-section bar
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    A project consists of five activities (A, B, C, D and E). The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor(s) are listed in the table. The expected time of the project completion is __________ weeks (in integer).
    ActivityOptimistic timeMost likely timePessimistic timeImmediate predecessor(s)
    A456None
    B135A
    C123A
    D246C
    E345B, D
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    A rigid tank of volume of 8 m38\text{ m}^3 is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature inside the pipeline are maintained at 600 kPa600\text{ kPa} and 306 K306\text{ K}, respectively. The filling of the tank begins by opening the valve and the process ends when the tank pressure is equal to the pipeline pressure. During the filling process, heat loss to the surrounding is 1000 kJ1000\text{ kJ}. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kg⋅K1.005\text{ kJ/kg}\cdot\text{K} and 0.718 kJ/kg⋅K0.718\text{ kJ/kg}\cdot\text{K}, respectively. Neglect changes in kinetic energy and potential energy. The final temperature of the tank after the completion of the filling process is _________ K (round off to the nearest integer).
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    At steady state, 500 kg/s of steam enters a turbine with specific enthalpy equal to 3500 kJ/kg and specific entropy equal to 6.5 kJ∙kg⁻¹∙K⁻¹. It expands reversibly in the turbine to the condenser pressure. Heat loss occurs reversibly in the turbine at a temperature of 500 K. If the exit specific enthalpy and specific entropy are 2500 kJ/kg and 6.3 kJ∙kg⁻¹∙K⁻¹, respectively, the work output from the turbine is ________ MW (in integer).
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    A uniform wooden rod (specific gravity = 0.60.6, diameter = 44 cm and length = 88 m) is immersed in the water and is hinged without friction at point A on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = 11.411.4) is attached to the free end of the rod to keep the assembly in static equilibrium inside the water. For simplicity, assume that the radius of the ball is much smaller than the length of the rod. Assume density of water = 10310^3 kg/m3^3 and π=3.14\pi = 3.14. Radius of the ball is _______ cm (round off to 2 decimal places).
    A uniform wooden rod hinged at point A on the waterline, with a lead ball attached to its free end, submerged in water.
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    Consider steady state, one-dimensional heat conduction in an infinite slab of thickness 2L2L (L=1L = 1 m) as shown in the figure. The conductivity (kk) of the material varies with temperature as k=CTk = CT, where TT is the temperature in K, and CC is a constant equal to 2 W∙m⁻¹∙K⁻². There is a uniform heat generation of 1280 kW/m3^3 in the slab. If both faces of the slab are maintained at 600 K, then the temperature at x=0x = 0 is ________ K (in integer).
    Slab with boundaries at x = -L and x = L, both at 600K, center at x = 0
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    Saturated vapor at 200∘C200 ^\circ\text{C} condenses to saturated liquid at the rate of 150 kg/s150 \text{ kg/s} on the shell side of a heat exchanger (enthalpy of condensation hfg=2400 kJ/kgh_{fg} = 2400 \text{ kJ/kg}). A fluid with cp=4 kJ⋅kg−1⋅K−1c_p = 4 \text{ kJ}\cdot\text{kg}^{-1}\cdot\text{K}^{-1} enters at 100∘C100 ^\circ\text{C} on the tube side. If the effectiveness of the heat exchanger is 0.90.9, then the mass flow rate of the fluid in the tube side is ________ kg/s\text{kg/s} (in integer).
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    Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s1 \text{ kg/s} in a uniformly heated pipe with diameter of 0.1 m0.1 \text{ m} and length of 40 m40 \text{ m}. A constant heat flux of magnitude 15000 W/m215000 \text{ W/m}^2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200 ∘C200 \text{ }^\circ\text{C}. The Reynolds number (ReRe) of the flow is 8500085000, and the Prandtl number (PrPr) of the fluid is 55. The thermal conductivity and the specific heat of the fluid are 0.08 W⋅m−1⋅K−10.08 \text{ W}\cdot\text{m}^{-1}\cdot\text{K}^{-1} and 2600 J⋅kg−1⋅K−12600 \text{ J}\cdot\text{kg}^{-1}\cdot\text{K}^{-1}, respectively. The correlation Nu=0.023Re0.8Pr0.4Nu = 0.023 Re^{0.8} Pr^{0.4} is applicable, where the Nusselt Number (NuNu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ ∘C^\circ\text{C} (round off to the nearest integer).
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