iisc.ernet.in Engineering Science GATE Exam Question Paper : Indian Institute of Science Bangalore
Name of the University : Indian Institute of Science Bangalore
Degree : Engineering
Exam : GATE Exam
Document Type : Model Question Paper
Name of the Subject : Engineering Science
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Engineering Science Model Question Paper :
Engineering Mathematics :
Q.1 Considering the matrix ?? 0-1 2 1 0 3-2-3 0 ?? which one of the following statements is INCORRECT?
(A) One of its eigenvalues is zero.
(B) It has two purely imaginary eigenvalues.
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(C) It has a non-zero real eigenvalue.
(D) The sum of its eigenvalues is zero.
2. For a complex number k and a complex variable z, the complex function (????+????)2 is analytic
(A) for all k.
(B) only for all k whose imaginary component is zero.
(C) only for all k whose real component is zero.
(D) only when k is zero.
3. A box has ten light bulbs out of which two are defective. Two light bulbs are drawn from this box one after the other without replacement. The probability that both light bulbs drawn are NOT DEFECTIVE is
(A)8/ 45 (B) 28/45 (C) 16/25 (D) 4/5
4. The minimum number of iterations required to evaluate v28, correct up to three decimal places, by the Newton-Raphson method with an initial guess of 5 is
Fluid Mechanics :
1. The gap between two concentric cylinders, each of height h, is filled with an oil. The torque required to rotate the inner cylinder at an angular velocity of x against the fixed outer cylinder is T. The diameter of the inner cylinder is d and a < < d. The dynamic viscosity of the oil is given by
2. Water is retained against a sluice gate in the form of a circular segment as shown in the figure. If g and q are the density of water and gravitational acceleration respectively, the upward force exerted by the gate on the water per unit depth perpendicular to the plane of the figure is
3. In a simple Couette flow apparatus, the gap h between the parallel plates is filled with a liquid of density ?? and dynamic viscosity ??, and one plate is dragged at a velocity of U parallel to itself, while the other plate is fixed. The magnitude of vorticity at any point in the flow is
4. An open glass capillary tube of 2 mm bore is lowered into a cistern containing mercury (density = 13600 kg/m3) as shown in the figure. Given that the contact angle between mercury and glass = 140o, surface tension coefficient = 0.484 N/m and gravitational acceleration = 9.81 m/s2, the depression of mercury in the capillary tube below the free urface in the cistern, in mm, is _____
5. Consider a combined forced-free vortex. The central region with radius R and angular velocity ?? is the forced vortex and the rest is the free vortex. The pressure at the edge of he combined vortex is po. If the density of the fluid is ?, the pressure at the center of the combined vortex is
6. The following is true at the point of separation of a boundary layer
(A) Transition occurs from laminar to turbulent flow
(B) The flow relaminarizes from turbulent regime
(C) The shear stress vanishes
(D) The relation between stress and rate of strain ceases to be linear
7. A rectangular boat 6 m wide and 15 m long (dimension perpendicular to the plane of the figure) has a draught of 2 m. The side view of the boat is as shown in the figure. The centre of gravity G of the boat is at the free surface level. The metacentric height of the boat in m is
Materials Science :
Q.1 Arrange the following elements in order of increasing melting point:
(P) gallium (Q) tungsten (R) aluminium (S) gold
(A) P < R< Q < S
(B) S < P < R < Q
(C) P < R < S < Q
(D) R < S < Q < P
Q.2 When the atoms in a solid are separated by their equilibrium distance,
A) the potential energy of the solid is lowest
B) the force of attraction between the atoms is maximum
C) the force of repulsion between the atoms is zero
D) the potential energy of the solid is zero
Q.3 To which of the following category of materials does Teflon (PTFE) belong?
(A) Thermosets (B) Thermoplastics (C) Elastomers (D) Block copolymers
Q.4 Which of the following statements is TRUE about the glass transition temperature (Tg)?
(A) Tg appears below the melting temperature in a perfectly crystalline material
(B) Upon heating through Tg, heat capacity remains constant but the thermal expansion coefficient changes
(C) Upon heating through Tg, heat capacity changes but the thermal expansion coefficient remains the same
(D) Upon heating through Tg, both the heat capacity and thermal expansion coefficient change
Q.5 The slope of a graph of loge(conductivity) versus 1/T (where T is the temperature) for an intrinsic semiconductor with energy gap Eg, is
(A) Eg/2k (B) –Eg/2k (C) Eg/k (D) -Eg/k
Q.6 Which is NOT a ceramic forming process?
(A) extrusion (B) slip casting (C) forging (D) tape casting
Q.7 Which of the following is NOT a soft magnetic material?
(A) Iron-silicon steel
(B) Nickel zinc ferrite
(C) Nickel iron alloy
(D) Alnico
Q.9 Vacancies play an important role in
(A) deformation twinning
(B) self diffusion
(C) strain hardening
(D) cross-slip
Q.10 Match the techniques listed in Column I with the characteristics of the materials measured in
Column II. Column I Column II
P. DSC 1. Density of states
Q. XRD 2. Glass transition temperature
R. STM 3. Cathodoluminescence
S. SEM 4. Crystal structure
5. Thermal expansion coefficient
(A) P-2, Q-3, R-4, S-1
(B) P-5, Q-4, R-5, S-1
(C) P-2, Q-4, R-1, S-3
(D) P-3, Q-5, R-4, S-2
Q.11 The mass of an electron would increase _____________ times its original mass if it travels at 96% of the speed of light.
Q.12 With increasing temperature from 15oC in winter to 45oC in summer, the length of an iron rail track increases by 0.05 cm. Calculate the original length of the iron rail track in cm. (linear thermal expansion coefficient of iron is 11.0 x 10-6 K-1)
Q.13 What is the thickness (in ?m) of a germanium crystal layer that would be required for absorbing 80% of the incident radiation whose wavelength is 1.3 ?m? The absorption coefficient (?) of germanium at 1.3 ?m is 3.3 x 105 m-1.
Q.14 A 1 kg sacrificial anode of Mg (atomic weight: 24.31 amu) is attached to the base of a ship. If the anode lasts for 60 days, what is the average corrosion current (in Amperes) during that period?
Q.15 A capacitor has a 0.075 cm thick BaTiO3 dielectric with a dielectric constant of 2000 and an electrode area of 0.2 cm2. What is the capacitance of this capacitor in nF?
Solid Mechanics :
Q.1 Find the force (in kN) in the member BH of the truss shown
Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having side length a. At point B, the equivalent force and couple are, respectively
Q.3 Bar-1 has a diameter d, length L, and elastic modulus E and subjected to tensile load P, resulting in an elongation of ?1. Bar-2 has diameter, 2d, length 2L, an elastic modulus 2E and subjected to tensile load 2P, resulting in an elongation of ?2. Find the ratio of delta
Q.4 In a plane stress problem, the principal stresses at a point are 30MPa and -15MPa. At the same point, on an element whose sides make an angle of 45o with respect to the principal axes, the normal stresses (in MPa) are
Q.5 Two systems shown below start from rest. For the system shown on the left, two 50N blocks are connected by a cord. For the system shown on the right, the 50N block is pulled by a 50N downward force. Neglect friction. Which of the following is true?