Firstranker's choice
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GATE 2015
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Q. 1 – Q. 25 carry one mark each.
Q.1 At least one eigenvalue of a singular matrix is
(A) positive (B) zero (C) negative (D) imaginary
Q.2 At x = 0, the function f(x)= |x| has
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(A) a minimum (B) a maximum
(C) a point of inflexion (D) neither a maximum nor minimum
Q.3 Curl of vector V(x, y, z) = 2x² i +3z² j + y³k at x = y = z = 1 is
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(A) -3i (B) 3i (C) 3i-4j (D) 3i-6k
Q.4 The Laplace transform of ei5t where i = v–1, is
(A) s-5i (B) s+5i (C) s+5i (D) s-5i
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s2-25 s² + 25 s2-25 s² + 25Q.5 Three vendors were asked to supply a very high precision component. The respective probabilities
of their meeting the strict design specifications are 0.8, 0.7 and 0.5. Each vendor supplies one
component. The probability that out of total three components supplied by the vendors, at least one
will meet the design specification is
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Q.6 A small ball of mass 1 kg moving with a velocity of 12 m undergoes a direct central impact with a
stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball
after the impact will be
Q.7 A rod is subjected to a uni-axial load within linear elastic limit. When the change in the stress is
200 MPa, the change in the strain is 0.001. If the Poisson's ratio of the rod is 0.3, the modulus of
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rigidity (in GPa) isQ.8 A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gage
pressure of the gas is 2 MPa. The maximum shear stress (in MPa) in the wall is
(A) 35 (B) 70 (C) 140 (D) 280
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Firstranker's choice
GATE 2015
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Q.9 The number of degrees of freedom of the planetary gear train shown in the figure is
(A) 0 (B) 1 (C) 2 (D) 3Q.10 In a spring-mass system, the mass is m and the spring constant is k. The critical damping coefficient
of the system is 0.1 kg/s. In another spring-mass system, the mass is 2m and the spring constant is
8k. The critical damping coefficient (in kg/s) of this system is
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Q.11 The uniaxial yield stress of a material is 300 MPa. According to von Mises criterion, the shear yield
stress (in MPa) of the material is
Q.12 If the fluid velocity for a potential flow is given by V(x, y) = u(x, y)i+v(x, y)j with usual
notations, then the slope of the potential line at (x, y) is
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(A) ? (B) u (C)
u ?
u
2 ?
2 (D) u
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Q.13 Which of the following statements regarding a Rankine cycle with reheating are TRUE?
(i) increase in average temperature of heat addition
(ii) reduction in thermal efficiency
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(iii) drier steam at the turbine exit
(A) only (i) and (ii) are correct
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(B) only (ii) and (iii) are correct
(C) only (i) and (iii) are correct
(D) (i), (ii) and (iii) are correct
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Q.14 Within a boundary layer for a steady incompressible flow, the Bernoulli equation
(A) holds because the flow is steady
(B) holds because the flow is incompressible
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(C) holds because the flow is transitional
(D) does not hold because the flow is frictional
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Firstranker's choice
GATE 2015
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Q.15 If a foam insulation is added to a 4 cm outer diameter pipe as shown in the figure, the critical radius
of insulation (in cm) is
hydrodynamic and thermal boundary layer thicknesses, then
(?) d = dt (?) d > dt
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(C) d < dt (D) 8 = 0 but_d1 ? 0Q.17 The COP of a Carnot heat pump operating between 6 °C and 37 °C is
Q.18 The Van der Waals equation of state is P+ |(v–b) |= RT, where p is pressure, v is specific
volume, T is temperature and R is characteristic gas constant. The SI unit of a is
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(A) J/kg-K (B) m³/kg (C) m³/kg-s² (D) Pa/kg
Q.19 A rope-brake dynamometer attached to the crank shaft of an I.C. engine measures a brake power of
10 kW when the speed of rotation of the shaft is 400 rad/s. The shaft torque (in N-m) sensed by the
dynamometer is
Q.20 The atomic packing factor for a material with body centered cubic structure is
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Q.21 The primary mechanism of material removal in electrochemical machining (ECM) is
(A) chemical corrosion
(B) etching
(C) ionic dissolution
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(D) spark erosionFirstranker's choice
GATE 2015
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Q.22 Which one of the following statements is TRUE?
(A) The 'GO' gage controls the upper limit of a hole
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(B) The 'NO GO' gage controls the lower limit of a shaft
(C) The 'GO' gage controls the lower limit of a hole
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(D) The 'NO GO' gage controls the lower limit of a hole
Q.23 During the development of a product, an entirely new process plan is made based on design logic,
examination of geometry and tolerance information. This type of process planning is known as
(A) retrieval
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(B) generative(C) variant
(D) group technology based
Q.24 Annual demand of a product is 50000 units and the ordering cost is Rs. 7000 per order.
Considering the basic economic order quantity model, the economic order quantity is 10000 units.
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When the annual inventory cost is minimized, the annual inventory holding cost (in Rs.) isQ.25 Sales data of a product is given in the following table:
Month January February March April May
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Number of units sold 10 11 16 19 25
Regarding forecast for the month of June, which one of the following statements is TRUE?
(A) Moving average will forecast a higher value compared to regression.
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(B) Higher the value of order N, the greater will be the forecast value by moving average.
(C) Exponential smoothing will forecast a higher value compared to regression.
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(D) Regression will forecast a higher value compared to moving average.
Q. 26 – Q. 55 carry two marks each.
Q.26 The chance of a student passing an exam is 20%. The chance of a student passing the exam and
getting above 90% marks in it is 5%. GIVEN that a student passes the examination, the probability
that the student gets above 90% marks is
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(A) 1 (B) 1 (C) 2 (D) 5
18 4 9 18
Q.27 The surface integral [[ (9xi - 3yj) •nds over the sphere given by x² + y² + z² = 9 is
p
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SFirstranker's choice
GATE 2015
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Q.28 Consider the following differential equation:
dy
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-=-5y; initial condition: y=2 at t=0.dt
The value of y at t = 3 is
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(A) -5e-10 (B) 2e-10 (C) 2e-15 (D) -15e2
Q.29 The values of function f (x) at 5 discrete points are given below:
X 0 0.1 0.2 0.3 0.4
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f(x) 0 10 40 90 160
0.4
Using Trapezoidal rule with step size of 0.1, the value of [ f(x) dx is
0
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Q.30 The initial velocity of an object is 40 m/s. The acceleration a of the object is given by the following
expression:
a = -0.1v,
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where v is the instantaneous velocity of the object. The velocity of the object after 3 seconds will
be
Q.31 A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A
load of 10 kN is applied at the mid-point of PQ. The magnitude of bending moment (in kN-m) at
fixed end O is
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(A) 2.5 (B) 5 (C) 10 (D) 25Firstranker's choice
GATE 2015
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Q.32 For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is
(A) 10 (B) 14.14 (C) 20 (D) 28.28Q.33 A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2 kN normal to
the top surface as shown in the figure. The Young's modulus of elasticity of the material of the
beam is 210 GPa. The magnitude of slope (in radian) at Q (20 mm from the fixed end) is
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