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GATE ME 2015 Set 1

All 65 solved GATE ME 2015 Set 1 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

2

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 27Medium 38

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:
    Dhoni, as well as the other team members of Indian team, __________present on the occasion.
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    Question

    Choose the word most similar in meaning to the given word:
    Awkward
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    Question

    What is the adverb for the given word below?
    Misogynous
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    Question

    An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches M, N, O, and P, in that order. The cumulative distances travelled and the corresponding electricity consumption are shown in the Table below:
    StretchCumulative distance (km)Electricity used (kWh)
    M2012
    N4525
    O7545
    P10057
    The stretch where the electricity consumption per km is minimum is
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    Question

    Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is 1/61/6 and that of Ramesh is 1/81/8. What is the probability that only one of them will be selected?
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    Question

    In the following sentence certain parts are underlined and marked P, Q, and R. One of the parts may contain certain error or may not be acceptable in standard written communication. Select the part containing an error. Choose D as your answer if there is no error.
    The student corrected all the errors that the instructor marked on the answer book.
    PQR\quad\quad\quad\quad\quad\quad\text{P}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{Q}\quad\quad\quad\quad\quad\quad\quad\quad\text{R}
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    Question

    Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.
    Statements:
    I. All film stars are playback singers.
    II. All film directors are film stars.
    Conclusions:
    I. All film directors are playback singers.
    II. Some film stars are film directors.
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    Question

    A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer's 4. If the tiger and the deer cover 8 metre and 5 metre per leap respectively, what distance in metres will the tiger have to run before it catches the deer?
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    Question

    If a2+b2+c2=1a^2 + b^2 + c^2 = 1, then ab+bc+acab + bc + ac lies in the interval
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    Question

    Lamenting the gradual sidelining of the arts in school curricula, a group of prominent artists wrote to the Chief Minister last year, asking him to allocate more funds to support arts education in schools. However, no such increase has been announced in this year’s Budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funding in the future.
    Which of the statement(s) below is/are logically valid and can be inferred from the above statements?
    (i) The artists expected funding for the arts to increase this year.
    (ii) The Chief Minister was receptive to the idea of increasing funding for the arts.
    (iii) The Chief Minister is a prominent artist.
    (iv) Schools are giving less importance to arts education nowadays.
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Mechanical Engineering

55
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    Question

    If any two columns of a determinant P=∣478315962∣P = \begin{vmatrix} 4 & 7 & 8 \\ 3 & 1 & 5 \\ 9 & 6 & 2 \end{vmatrix} are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?
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    Question

    Among the four normal distributions with probability density functions as shown below, which one has the lowest variance?
    Four normal distribution curves labeled I, II, III, and IV
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    Question

    Simpson's 13\frac{1}{3} rule is used to integrate the function f(x)=35x2+95f(x) = \frac{3}{5} x^2 + \frac{9}{5} between x=0x = 0 and x=1x = 1 using the least number of equal sub-intervals. The value of the integral is ________.
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    Question

    The value of lim⁡x→01−cos⁡(x2)2x4\lim_{x \to 0} \frac{1 - \cos(x^2)}{2x^4} is
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    Question

    Given two complex numbers z1=5+(53)iz_1 = 5 + (5\sqrt{3})i and z2=23+2iz_2 = \frac{2}{\sqrt{3}} + 2i, the argument of z1z2\frac{z_1}{z_2} in degrees is
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    Question

    Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of
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    Question

    The Blasius equation related to boundary layer theory is a
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    Question

    For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is
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    Question

    For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,
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    Question

    A Carnot engine (CE-1) works between two temperature reservoirs A and B, where TA=900 KT_A = 900\text{ K} and TB=500 KT_B = 500\text{ K}. A second Carnot engine (CE-2) works between temperature reservoirs B and C, where TC=300 KT_C = 300\text{ K}. In each cycle of CE-1 and CE-2, all the heat rejected by CE-1 to reservoir B is used by CE-2. For one cycle of operation, if the net QQ absorbed by CE-1 from reservoir A is 150 MJ150\text{ MJ}, the net heat rejected to reservoir C by CE-2 (in MJ) is ___________
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    Question

    Air enters a diesel engine with a density of 1.0 kg/m31.0\text{ kg/m}^3. The compression ratio is 21. At steady state, the air intake is 30×10−3 kg/s30 \times 10^{-3}\text{ kg/s} and the net work output is 15 kW15\text{ kW}. The mean effective pressure (in kPa) is ___________
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    Question

    A stream of moist air (mass flow rate =10.1 kg/s= 10.1\text{ kg/s}) with humidity ratio of 0.01 kgkg dry air0.01\text{ }\frac{\text{kg}}{\text{kg dry air}} mixes with a second stream of superheated water vapour flowing at 0.1 kg/s0.1\text{ kg/s}. Assuming proper and uniform mixing with no condensation, the humidity ratio of the final stream (in kgkg dry air\frac{\text{kg}}{\text{kg dry air}}) is ________
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    Question

    A wheel of radius rr rolls without slipping on a horizontal surface shown below. If the velocity of point PP is 10 m/s10\text{ m/s} in the horizontal direction, the magnitude of velocity of point QQ (in m/s\text{m/s}) is ________
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    Question

    Consider a slider crank mechanism with nonzero masses and inertia. A constant torque τ\tau is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle, θ\theta versus time
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    Question

    Consider a stepped shaft subjected to a twisting moment applied at B as shown in the figure. Assume shear modulus, G=77 GPaG = 77\text{ GPa}. The angle of twist at C (in degrees) is ________.
    Stepped shaft with torque applied at B
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    Question

    Two identical trusses support a load of 100 N100\text{ N} as shown in the figure. The length of each truss is 1.0 m1.0\text{ m}; cross-sectional area is 200 mm2200\text{ mm}^2; Young's modulus E=200 GPaE = 200\text{ GPa}. The force in the truss AB (in N) is ________.
    Two trusses supporting a 100N load
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    Question

    Consider a steel (Young's modulus E=200 GPaE = 200\text{ GPa}) column hinged on both sides. Its height is 1.0 m1.0\text{ m} and cross-section is 10 mm×20 mm10\text{ mm} \times 20\text{ mm}. The lowest Euler critical buckling load (in N) is ________.
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    Question

    A swimmer can swim 10 km in 2 hours when swimming along the flow of a river. While swimming against the flow, she takes 5 hours for the same distance. Her speed in still water (in km/h) is _______
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    Question

    Which one of the following is the most conservative fatigue failure criterion?
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    Question

    Which one of the following types of stress-strain relationship best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics, (σ=stress and ϵ=strain\sigma = \text{stress and } \epsilon = \text{strain})?
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    Question

    Match the following products with preferred manufacturing processes:
    ProductProcess
    P Rails1 Blow molding
    Q Engine crankshaft2 Extrusion
    R Aluminium channels3 Forging
    S PET water bottles4 Rolling
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    Question

    Holes of diameter 25.0+0.020+0.04025.0^{+0.040}_{+0.020} mm are assembled interchangeably with the pins of diameter 25.0−0.008+0.00525.0^{+0.005}_{-0.008} mm. The minimum clearance in the assembly will be
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    Question

    Under certain cutting conditions, doubling the cutting speed reduces the tool life to (116)th(\frac{1}{16})^{th} of the original. Taylor's tool life index (nn) for this tool-workpiece combination will be ________
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    Question

    In a linear arc welding process, the heat input per unit length is inversely proportional to
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    Question

    The function of interpolator in a CNC machine controller is to
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    Question

    Consider a spatial curve in three-dimensional space given in parametric form by
    x(t)=cos⁡t,y(t)=sin⁡t,z(t)=2πt,0≤t≤π2x(t) = \cos t, y(t) = \sin t, z(t) = \frac{2}{\pi}t, 0 \leq t \leq \frac{\pi}{2}.
    The length of the curve is _________
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    Question

    Consider an ant crawling along the curve (x−2)2+y2=4(x - 2)^2 + y^2 = 4, where xx and yy are in meters. The ant starts at the point (4,0)(4, 0) and moves counter-clockwise with a speed of 1.57 meters per second1.57\text{ meters per second}. The time taken by the ant to reach the point (2,2)(2, 2) is (in seconds) ________
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    Question

    Find the solution of d2ydx2=y\frac{d^2y}{dx^2} = y which passes through the origin and the point (ln⁡2,34)(\ln 2, \frac{3}{4}).
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    Question

    The probability of obtaining at least two "SIX" in throwing a fair dice 4 times is
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    Question

    In the assembly shown below, the part dimensions are:
    L1=22.0±0.01L_1 = 22.0^{\pm 0.01} mm,
    L2=L3=10.0±0.005L_2=L_3 = 10.0^{\pm 0.005} mm.
    Assuming the normal distribution of part dimensions, the dimension L4L_4 in mm for assembly condition would be:
    Diagram of an assembly with parts L1, L2, L3, and L4
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    Question

    A DC welding power source has a linear voltage-current (VV-II) characteristic with open circuit voltage of 80 V80\text{ V} and a short circuit current of 300 A300\text{ A}. For maximum arc power, the current (in Amperes) should be set as ________
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    Question

    A triangular facet in a CAD model has vertices: P1(0,0,0)P_1(0,0,0); P2(1,1,0)P_2(1,1,0) and P3(1,1,1)P_3(1,1,1). The area of the facet is
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    Question

    Following data refers to the activities of a project, where, node 1 refers to the start and node 5 refers to the end of the project.
    ActivityDuration (days)
    1-22
    2-31
    4-33
    1-43
    2-53
    3-52
    4-54
    The critical path (CP) in the network is
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    Question

    For a canteen, the actual demand for disposable cups was 500 units in January and 600 units in February. The forecast for the month of January was 400 units. The forecast for the month of March considering smoothing coefficient as 0.75 is ________
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    Question

    An orthogonal turning operation is carried out under the following conditions: rake angle = 5∘5^\circ; spindle rotational speed = 400 rpm; axial feed = 0.4 m/min and radial depth of cut = 5 mm. The chip thickness, tct_c, is found to be 3 mm. The shear angle (in degrees) in this turning process is ________
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    Question

    The solidification time of a casting is proportional to (VA)2\left(\frac{V}{A}\right)^2, where VV is the volume of the casting and AA is the total casting surface area losing heat. Two cubes of same material and size are cast using sand casting process. The top face of one of the cubes is completely insulated. The ratio of the solidification time for the cube with top face insulated to that of the other cube is
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    Question

    In a slab rolling operation, the maximum thickness reduction (Δhmax\Delta h_{max}) is given by Δhmax=μ2R\Delta h_{max} = \mu^2 R, where RR is the radius of the roll and μ\mu is the coefficient of friction between the roll and the sheet. If μ=0.1\mu = 0.1, the maximum angle subtended by the deformation zone at the centre of the roll (bite angle in degrees) is ________
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    Question

    Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is
    Schematic of a rigid rod pivoted at its center with a spring of stiffness $k=400$ N/m at distance $r$ and a mass $m=1$ kg at distance $2r$
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    Question

    For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively
    A truss with a 100 kN load applied at joint P at an angle of 60° to the horizontal. Joint Q is a pin support and joint R is a roller support. The distance QR is 4 m and the angle at R is 45°.
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    Question

    A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20%. The height (in m) to which the ball will rise is ________
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    Question

    A pinion with radius r1r_1, and inertia I1I_1 is driving a gear with radius r2r_2 and inertia I2I_2. Torque τ1\tau_1 is applied on pinion. The following are free body diagrams of pinion and gear showing important forces (F1F_1 and F2F_2) of interaction. Which of the following relations hold true?
    Free body diagrams of a pinion and a gear. The pinion has radius $r_1$, inertia $I_1$, applied torque $\tau_1$, and interaction force $F_1$. The gear has radius $r_2$, inertia $I_2$, and interaction force $F_2$. Angular displacements are $\theta_1$ and $\theta_2$.
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    Question

    A triangular facet in a CAD model has vertices: P1(0,0,0)P1(0,0,0); P2(1,1,0)P2(1,1,0) and P3(1,1,1)P3(1,1,1). The area of the facet is
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    Question

    Following data refers to the activities of a project, where, node 1 refers to the start and node 5 refers to the end of the project.
    ActivityDuration (days)
    1-22
    2-31
    4-33
    1-43
    2-53
    3-52
    4-54
    The critical path (CP) in the network is
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    Question

    For a canteen, the actual demand for disposable cups was 500 units in January and 600 units in February. The forecast for the month of January was 400 units. The forecast for the month of March considering smoothing coefficient as 0.75 is __________
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    Question

    A precision instrument package (m=1m = 1 kg) needs to be mounted on a surface vibrating at 6060 Hz. It is desired that only 5%5\% of the base surface vibration amplitude be transmitted to the instrument. Assume that the isolation is designed with its natural frequency significantly lesser than 6060 Hz, so that the effect of damping may be ignored. The stiffness (in N/m) of the required mounting pad is _______
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    Question

    A horizontal plate has been joined to a vertical post using four rivets arranged as shown in the figure. The magnitude of the load on the worst loaded rivet (in N) is _______
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    Question

    For flow through a pipe of radius RR, the velocity and temperature distribution are as follows:
    u(r,x)=C1u(r,x) = C_1, and T(r,x)=C2[1−(rR)3]T(r,x) = C_2 \left[ 1 - \left( \frac{r}{R} \right)^3 \right], where C1C_1 and C2C_2 are constants.
    The bulk mean temperature is given by Tm=2UmR2∫0Ru(r,x)T(r,x)rdrT_m = \frac{2}{U_m R^2} \int_{0}^{R} u(r,x) T(r,x) r dr, with UmU_m being the mean velocity of flow. The value of TmT_m is
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    Question

    Considering massless rigid rod and small oscillations, the natural frequency (in rad/s) of vibration of the system shown in the figure is
    A rigid rod pivoted at its center. A spring with stiffness $k = 400$ N/m is attached at a distance $r$ to the left of the pivot. A mass $m = 1$ kg is attached at a distance $2r$ to the right of the pivot.
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    For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively
    A truss PQR. Node Q is a pin support, node R is a roller support. Distance QR is 4 m. A force of 100 kN is applied at P at an angle of $60^\circ$ to the horizontal. The angle at R is $45^\circ$.
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    A ball of mass 0.1 kg, initially at rest, is dropped from height of 1 m. Ball hits the ground and bounces off the ground. Upon impact with the ground, the velocity reduces by 20%. The height (in m) to which the ball will rise is ________
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    Temperature of nitrogen in a vessel of volume 2 m32\text{ m}^3 is 288 K288\text{ K}. A U-tube manometer connected to the vessel shows a reading of 70 cm70\text{ cm} of mercury (level higher in the end open to atmosphere). The universal gas constant is 8314 J/kmol-K8314\text{ J/kmol-K}, atmospheric pressure is 1.01325 bar1.01325\text{ bar}, acceleration due to gravity is 9.81 m/s29.81\text{ m/s}^2 and density of mercury is 13600 kg/m313600\text{ kg/m}^3. The mass of nitrogen (in kg) in the vessel is ________
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    Air (ρ=1.2 kg/m3\rho = 1.2\text{ kg/m}^3 and kinematic viscosity, ν=2×10−5 m2/s\nu = 2 \times 10^{-5}\text{ m}^2\text{/s}) with a velocity of 2 m/s2\text{ m/s} flows over the top surface of a flat plate of length 2.5 m2.5\text{ m}. If the average value of friction coefficient is Cf=1.328RexC_f = \frac{1.328}{\sqrt{Re_x}}, the total drag force (in N) per unit width of the plate is ________
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    Water (ρ=1000 kg/m3\rho = 1000\text{ kg/m}^3) flows through a venturimeter with inlet diameter 80 mm80\text{ mm} and throat diameter 40 mm40\text{ mm}. The inlet and throat gauge pressures are measured to be 400 kPa400\text{ kPa} and 130 kPa130\text{ kPa} respectively. Assuming the venturimeter to be horizontal and neglecting friction, the inlet velocity (in m/s) is ________
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    A well insulated rigid container of volume 1 m31\text{ m}^3 contains 1.0 kg1.0\text{ kg} of an ideal gas [Cp=1000 J/(kg.K)C_p = 1000\text{ J/(kg.K)} and Cv=800 J/(kg.K)C_v = 800\text{ J/(kg.K)}] at a pressure of 105 Pa10^5\text{ Pa}. A stirrer is rotated at constant rpm in the container for 1000 rotations and the applied torque is 100 N-m100\text{ N-m}. The final temperature of the gas (in K) is ________.
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    Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, 20 percent of the mass is extracted for process heating and the remaining steam expands isentropically to 9 kPa9\text{ kPa}.
    Inlet to turbine: P=14 MPaP = 14\text{ MPa}, T=560∘CT = 560^\circ\text{C}, h=3486 kJ/kgh = 3486\text{ kJ/kg}, s=6.6 kJ/(kg.K)s = 6.6\text{ kJ/(kg.K)}
    Intermediate stage: h=2776 kJ/kgh = 2776\text{ kJ/kg}
    Exit of turbine: P=9 kPaP = 9\text{ kPa}, hf=174 kJ/kgh_f = 174\text{ kJ/kg}, hg=2574 kJ/kgh_g = 2574\text{ kJ/kg}, sf=0.6 kJ/(kg.K)s_f = 0.6\text{ kJ/(kg.K)}, sg=8.1 kJ/(kg.K)s_g = 8.1\text{ kJ/(kg.K)}If the flow rate of steam entering the turbine is 100 kg/s100\text{ kg/s}, then the work output (in MW) is ________.
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