GATE AE 2018 Question Paper & Solutions

Verbal & Numerical Aptitude

Let a⃗, b⃗⃗ be two distinct vectors that are not parallel. The vector c⃗ = a⃗ × b⃗⃗ is (A) zero. (B) orthogonal to a⃗ alone. (C) orthogonal to a⃗ + b⃗⃗. (D) orthogonal to b⃗⃗ alone.

Verbal & Numerical Aptitude

Consider the function f(x, y) = x2 2 + y2 3 - 5. All the roots of this function

Verbal & Numerical Aptitude

Consider a vector field given by xî + yĵ + zk̂. This vector field is

Verbal & Numerical Aptitude

A jet aircraft is initially flying steady and level at its maximum endurance condition. For the aircraft to fly steady and level, but faster at the same altitude, the pilot should

Verbal & Numerical Aptitude

The pilot of a conventional airplane that is flying steady and level at some altitude, deflects the port side aileron up and the starboard aileron down. The aircraft will then

Verbal & Numerical Aptitude

A NACA 0012 airfoil has a trailing edge flap. The airfoil is operating at an angle of attack of 5 degrees with un-deflected flap. If the flap is now deflected by 5 degrees downwards, the CL versus 𝛼 curve

Verbal & Numerical Aptitude

A wire wo uld enclose an area of 1936 m2, 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? (A) 1096 (B) 1111 (C) 1243 (D) 2486

Verbal & Numerical Aptitude

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? (A) 50 (B) 89 (C) 146 (D) 175

Verbal & Numerical Aptitude

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? (A) 54 (B) 65 (C) 66 (D) 76 (GA) Set-2 GA 3/3

Verbal & Numerical Aptitude

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?

Structural Mechanics

Question 11 from official GATE AE 2018 Examination.

Incompressible & Compressible Aerodynamics

The pitching moment of a positively cambered NACA airfoil about its leading edge at zero- lift angle of attack is

Structural Mechanics

In a low -speed wind tunnel, t he angular location(s) from the front stagnation point on a circular cylinder where the static pressure equals the free-stream static pressure, is (A) ± 380 (B) ± 300 (C) ± 600 (D) 00

Structural Mechanics

A thermocouple, mounted flush in an insulated flat surface in a supersonic laminar flow of air measures the

Incompressible & Compressible Aerodynamics

A shock wave is moving into still air in a shock tube. Which one of the following happens to the air?

Airplane Performance & Stability

The highest limit load factor experienced by a civil transport aircraft is in the range (A) 0.0 - 2.0 (B) 2.0 - 5.0 (C) 5.0 - 8.0 (D) 8.0 - 10.0

Structural Mechanics

Determine the correctness or otherwise of the following statements, [a] and [r]: [a] A closed-section box beam configuration is used in aircraft wings. [r] Closed-section box beam configuration is capable of resisting torsional loads.

Structural Mechanics

The first law of thermodynamics is also known as conservation of

Structural Mechanics

In an ideal gas turbine cycle, the expansion in a turbine is represented by (A) an isenthalpic process. (B) an isentropic process. (C) an isobaric process. (D) an isochoric process.

Linear Algebra & Differential Equations

The determinant of the matrix [ 1 1 -1 2 1 0 3 1 1 ] is ______ (accurate to one decimal place).

Structural Mechanics

The theoretical maximum velocity (in m/s) of air expanding from a reservoir at 700 K is __________ (accurate to two decimal places). Specific heat of air at constant pressure is 1005 J/(kg-K).

Structural Mechanics

For a damped single degree of freedom system w ith damping ratio of 0.1, ratio of two successive peak amplitudes of free vibration is ___________ (accurate to two decimal places).

Structural Mechanics

The natural frequency (in rad/s) of the spring-mass system shown in the figure below is _____ (accurate to one decimal place).

Structural Mechanics

The stagnation pressures at the inlet and exit of a subsonic intake are 100 kPa and 98 kPa, respectively. The pressure recovery of this intake will be ______ (accurate to two decimal places).

Structural Mechanics

A combustor is operating with a fuel -air ratio of 0.03. If the stoichiometric fuel -air ratio of the fuel used is 0.06, the equivalence ratio of the combustor will be _______ (accurate to two decimal places). /Artifact <</Attached [/Top ]/Subtype /Header /Type /Pagination >>BDC q 0 0 595.44 841.68 re W* n BT /GS0 gs /TT0 8.04 Tf 54 798.36 Td [(G)20.995 (A)21.007 (T)13.993 (E )-33.993 (2)-6.007 (0)-5.995 (1)-5.995 (8)-6.007 ( )-2.998 ( )-2.998 ( )-2.998 ( )-3.01 ( )-2.998 ( )]TJ ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 0.03 Tc 105.86 798.36 Td ( \ )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 0.03 Tc 307.87 798.36 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 438.46 798.36 Td [(A)20.995 (e)11.007 (r)5 (o)7.002 (sp)-6.007 (a)-2.998 (c)-2.998 (e)10.995 ( )-2.998 (En)-7.002 (g)7.002 (i)-5 (n)-5.995 (e)10.995 (e)10.995 (r)5 (i)-5 (n)-5.995 (g)]TJ ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 513.34 798.36 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n 52.56 795 490.44 0.48 re f* EMC Q /Artifact <</Attached [/Bottom ]/Subtype /Footer /Type /Pagination >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf -0.165 Tc 54 37.824Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT0 8.04 Tf 64.704 37.824 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n 52.56 46.104 317.95 0.48 re f* Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 530.86 37.704 Td (5)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 534.96 37.704 Td (/)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 537.12 37.704 Td (9)Tj ET Q q 369.07 35.784 172.01 9.12 re W* n BT /TT0 8.04 Tf 541.08 37.704 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 0 >>BDC q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf -0.0029 Tc 54 775.56 Td (Q. )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 70.584 775.56 Td (26)Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 83.544 775.56 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n BT /C2_0 12.96 Tf 86.784 775.56 Td <00B1>Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 93.264 775.56 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 96.504 775.56 Td [(Q.)-8.002 ( )]TJ ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 113.18 775.56 Td (55)Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 126.14 775.56 Td ( )Tj ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 129.38 775.56 Td [(carry)-10 ( tw)-8.997 (o )-8.002 (m)8.997 (arks e)-8.997 (ach.)]TJ ET Q q 0 0 595.44 841.68 re W* n BT /TT1 12.96 Tf 253.73 775.56 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 1 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 11.04 Tf 54 750.7 Td ( )Tj ET EMC Q q 59.424 667.42 33.96 80.64 re W* n /P <</Lang (en-US)/MCID 2 >>BDC q 59.424 667.42 33.96 80.64 re W* n BT /TT0 12 Tf 64.824 737.26 Td (Q.26)Tj ET Q q 59.424 667.42 33.96 80.64 re W* n BT /TT2 12 Tf 88.464 737.26 Td ( )Tj ET Q q 59.424 667.42 33.96 80.64 re W* n BT /TT0 12 Tf 100.82 737.26 Td ( )Tj ET EMC Q Q q 93.384 708.82 452.14 39.24 re W* n /P <</Lang (en-US)/MCID 3 >>BDC q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 99.144 730.9 Td [(The)5 ( sol)]TJ ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 134.78 730.9 Td [(uti)-3 (on of)3 ( the dif)3 (fe)7 (r)-6 (e)4 (nti)-3 (a)4 (l equa)6 (ti)-3 (on )]TJ ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 296.83 738.58 Td <0BD7>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 7.56 Tf 302.83 741.82 Td <0C2E>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 307.63 738.58 Td <0BEC>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 296.95 724.3 Td <0BD7>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 302.95 724.3 Td <0BEB>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 7.56 Tf 308.59 727.06 Td <0C2E>Tj ET Q 296.83 734.26 16.8 0.84 re f* q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 316.51 730.9 Td <0D45>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 329.11 730.9 Td <0375>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 0.009 Tc 338.47 738.58 Td <0BD70BEC>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 0.009 Tc 338.59 724.3 Td <0BD70BEB>Tj ET Q 338.47 734.26 11.64 0.84 re f* q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 353.71 730.9 Td <0D4C>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 367.03 730.9 Td <0372>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12.96 Tf 374.23 730.9 Td (,)Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12.96 Tf 377.47 730.9 Td ( )Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 380.71 730.9 Td [(g)10 (iven th)-9 (a)4 (t )]TJ ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 431.38 730.9 Td <0755>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 442.54 730.9 Td <0D4C>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 455.86 730.9 Td <0372>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 463.06 730.9 Td <0003>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 465.94 730.9 Td <008300900086>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 0.009 Tc 488.86 738.58 Td <0BD70BEC>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 9 Tf 0.009 Tc 488.98 724.3 Td <0BD70BEB>Tj ET Q 488.86 734.26 11.64 0.84 re f* q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 504.22 730.9 Td <0D4C>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 517.54 730.9 Td <0373>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 524.62 730.9 Td ( )Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 527.62 730.9 Td [(a)4 (t )]TJ ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 99.144 711.7 Td <0754>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 110.06 711.7 Td <0D4C>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 123.38 711.7 Td <0372>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /C2_1 12.96 Tf 130.58 711.7 Td <0003>Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 0.024 Tc 133.46 711.7 Td (is)Tj ET Q q 93.384 708.82 452.14 39.24 re W* n BT /TT0 12 Tf 141.5 711.7 Td ( )Tj ET EMC Q Q q 93.384 667.42 101.06 34.2 re W* n /P <</Lang (en-US)/MCID 4 >>BDC q 93.384 667.42 101.06 34.2 re W* n BT /TT0 12 Tf 98.784 689.26 Td [(\(A)5 (\) )]TJ ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 118.46 689.26 Td <0754>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 125.78 689.26 Td <123A>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 131.18 689.26 Td <0373>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 141.26 689.26 Td <0D46>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 153.86 689.26 Td <0741>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 9 Tf 160.94 694.06 Td <0B3F>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 9 Tf 167.54 694.06 Td <0B37>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 9 Tf 172.7 694.06 Td <0BEB>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /C2_1 12.96 Tf 178.85 689.26 Td <123B>Tj ET Q q 93.384 667.42 101.06 34.2 re W* n BT /TT0 12 Tf 184.25 689.26 Td ( )Tj ET EMC Q Q q 194.45 667.42 103.46 34.2 re W* n /P <</Lang (en-US)/MCID 5 >>BDC q 194.45 667.42 103.46 34.2 re W* n BT /TT0 12 Tf 199.85 686.62 Td [(\(B)10 (\) )]TJ ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 218.81 694.3 Td <0B35>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 218.81 680.02 Td <0B37>Tj ET Q 218.81 689.98 5.16 0.84 re f* q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 226.25 687.34 Td <123A>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 231.65 686.62 Td <0373>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 241.73 686.62 Td <0D46>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 254.33 686.62 Td <0741>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 261.41 691.42 Td <0B3F>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 268.01 691.42 Td <0B37>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 9 Tf 273.17 691.42 Td <0BEB>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /C2_1 12.96 Tf 279.29 687.34 Td <123B>Tj ET Q q 194.45 667.42 103.46 34.2 re W* n BT /TT0 12 Tf 284.69 686.62 Td ( )Tj ET EMC Q Q q 297.91 667.42 126.02 34.2 re W* n /P <</Lang (en-US)/MCID 6 >>BDC q 297.91 667.42 126.02 34.2 re W* n BT /TT0 12 Tf 303.31 686.62 Td (\(C\) )Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 325.27 694.3 Td <0B35>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 325.27 680.02 Td <0B37>Tj ET Q 325.27 689.98 5.16 0.84 re f* q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 332.71 686.62 Td <123A>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 338.11 686.62 Td <0373>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 348.19 686.62 Td <0D45>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 360.79 686.62 Td <0741>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 367.87 691.42 Td <0B3F>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 374.47 691.42 Td <0B37>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 9 Tf 379.63 691.42 Td <0BEB>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /C2_1 12.96 Tf 385.75 686.62 Td <123B>Tj ET Q q 297.91 667.42 126.02 34.2 re W* n BT /TT0 12 Tf 391.15 686.62 Td ( )Tj ET EMC Q Q q 423.94 667.42 121.58 34.2 re W* n /P <</Lang (en-US)/MCID 7 >>BDC q 423.94 667.42 121.58 34.2 re W* n BT /TT0 12 Tf 429.34 683.98 Td [(\(D)5 (\) )]TJ ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 9 Tf 452.02 691.66 Td <0B35>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 9 Tf 452.02 677.38 Td <0B37>Tj ET Q 452.02 687.34 5.16 0.84 re f* q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 12.96 Tf -0.0547 Tc 459.34 683.98 Td <07540741>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 7.56 Tf 473.38 695.38 Td <0C37>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 7.56 Tf 479.02 695.38 Td <0C2F>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 7.56 Tf 483.46 695.38 Td <0CE3>Tj ET Q q 423.94 667.42 121.58 34.2 re W* n BT /C2_1 7.56 Tf 478.54 685.54 Td <0C2E>Tj ET Q 473.38 692.38 14.76 0.6 re f* q 423.94 667.42 121.58 34.2 re W* n BT /TT0 12 Tf 488.86 683.98 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 8 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 656.62 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 9 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 642.82 Td ( )Tj ET EMC Q q 59.424 488.83 33.96 150.98 re W* n /P <</Lang (en-US)/MCID 10 >>BDC q 59.424 488.83 33.96 150.98 re W* n BT /TT0 12 Tf 64.824 629.02 Td (Q.27)Tj ET Q q 59.424 488.83 33.96 150.98 re W* n BT /TT2 12 Tf 88.464 629.02 Td ( )Tj ET Q q 59.424 488.83 33.96 150.98 re W* n BT /TT0 12 Tf 100.82 629.02 Td ( )Tj ET EMC Q Q q 93.384 612.22 452.14 27.6 re W* n /P <</Lang (en-US)/MCID 11 >>BDC q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 99.144 629.02 Td [(The)5 ( )]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 120.5 629.02 Td [(re)7 (l)-11 (a)4 (ti)-3 (on )20 (be)4 (twe)4 (e)4 (n)-9 ( )20 (pre)-2 (ssure)]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 242.69 629.02 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 245.45 629.02 Td (\()Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT3 12 Tf 249.41 629.02 Td (p)Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 255.41 629.02 Td (\))Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 259.37 629.02 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 262.25 629.02 Td [(a)4 (nd )20 (ve)4 (lo)-11 (c)4 (it)-13 (y)]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 320.95 629.02 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 323.83 629.02 Td (\()Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT3 12 Tf 327.79 629.02 Td (V)Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT3 12 Tf 335.23 629.02 Td (\))Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 339.19 629.02 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 341.95 629.02 Td [(for)6 ( )20 (a)4 ( )20 (st)-12 (e)4 (a)4 (d)-19 (y)20 (, )20 (isentropi)-9 (c)4 ( )20 (fl)]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 460.78 629.02 Td (ow )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 478.18 629.02 Td [(a)4 (t )18 (two )20 (point)-3 (s )]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 99.144 615.22 Td [(a)4 (long)8 ( )-9 (a)4 ( stre)4 (a)4 (m)]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 168.98 615.22 Td [(li)-3 (ne)4 ( )]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 190.01 615.22 Td (is, \()Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT3 12 Tf 208.13 615.22 Td (c)Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 213.41 615.22 Td ( )Tj ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 216.41 615.22 Td [(is a c)5 (onst)-2 (a)4 (nt\))]TJ ET Q q 93.384 612.22 452.14 27.6 re W* n BT /TT0 12 Tf 279.77 615.22 Td ( )Tj ET EMC Q Q q 93.384 576.22 452.14 28.8 re W* n /P <</Lang (en-US)/MCID 12 >>BDC q 93.384 576.22 452.14 28.8 re W* n BT /TT0 12 Tf 98.784 588.7 Td [(\(A)5 (\))]TJ ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 115.46 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 118.1 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 120.74 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 123.38 588.7 Td <073F>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 129.26 588.7 Td <123A>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 134.3 588.7 Td <074C>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 140.54 585.22 Td <0B36>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 141.26 594.82 Td <0C0A>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 149.66 588.7 Td <0D46>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 161.3 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 163.94 588.7 Td <074C>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 169.94 585.22 Td <0B35>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 170.9 594.82 Td <0C0A>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /TT0 12 Tf 176.69 588.7 Td [(\) =)7 ( )]TJ ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 193.49 595.78 Td <0BCF>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 6.96 Tf 197.69 593.74 Td <0C2D>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 6.96 Tf 199.49 599.14 Td <0C2E>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 196.25 582.7 Td <0B36>Tj ET Q 193.49 591.7 10.56 0.84 re f* q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 206.81 588.7 Td <0D46>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 12 Tf 217.01 588.7 Td <0003>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 221.09 595.78 Td <0BCF>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 6.96 Tf 225.29 593.74 Td <0C2E>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 6.96 Tf 227.09 599.14 Td <0C2E>Tj ET Q q 93.384 576.22 452.14 28.8 re W* n BT /C2_1 8.52 Tf 223.85 582.7 Td <0B36>Tj ET Q 221.09 591.7 10.56 0.84 re f* q 93.384 576.22 452.14 28.8 re W* n BT /TT0 12 Tf 231.53 588.7 Td ( )Tj ET EMC Q Q q 93.384 544.75 452.14 31.464 re W* n /P <</Lang (en-US)/MCID 13 >>BDC q 93.384 544.75 452.14 31.464 re W* n BT /TT0 12 Tf 98.784 555.91 Td [(\(B)10 (\))]TJ ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 114.74 555.91 Td <0003>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 117.38 555.91 Td <0003>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 120.02 555.91 Td <073F>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 126.02 555.91 Td <123A>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 131.06 555.91 Td <074C>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 137.3 551.83 Td <0B36>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 142.7 571.03 Td <0D02>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 138.02 561.67 Td <0D02>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 142.46 561.67 Td <0C37>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 147.62 561.67 Td <0C2D>Tj ET Q 138.02 568.15 13.92 0.6 re f* q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 154.94 555.91 Td <0D46>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 166.58 555.91 Td <0003>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 169.22 555.91 Td <074C>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 175.22 551.83 Td <0B35>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 180.89 571.03 Td <0D02>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 176.21 561.67 Td <0D02>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 180.77 561.67 Td <0C37>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 185.93 561.67 Td <0C2D>Tj ET Q 176.21 568.15 13.92 0.6 re f* q 93.384 544.75 452.14 31.464 re W* n BT /TT0 12 Tf 190.61 555.91 Td [(\) =)7 ( )]TJ ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 207.41 562.99 Td <0BCF>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 211.61 560.95 Td <0C2D>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 213.41 566.35 Td <0C2E>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 210.17 549.91 Td <0B36>Tj ET Q 207.41 558.91 10.56 0.84 re f* q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 220.61 555.91 Td <0D46>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 12 Tf 230.93 555.91 Td <0003>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 234.89 562.99 Td <0BCF>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 239.09 560.95 Td <0C2E>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 6.96 Tf 240.89 566.35 Td <0C2E>Tj ET Q q 93.384 544.75 452.14 31.464 re W* n BT /C2_1 8.52 Tf 237.65 549.91 Td <0B36>Tj ET Q 234.89 558.91 10.56 0.84 re f* q 93.384 544.75 452.14 31.464 re W* n BT /TT0 12 Tf 245.45 555.91 Td ( )Tj ET EMC Q Q q 93.384 517.63 452.14 27.12 re W* n /P <</Lang (en-US)/MCID 14 >>BDC q 93.384 517.63 452.14 27.12 re W* n BT /TT0 12 Tf 98.784 523.87 Td (\(C\))Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 114.74 523.87 Td <0003>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 117.38 523.87 Td <0003>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 120.02 523.87 Td <073F>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 126.02 523.87 Td <123A>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 131.06 523.87 Td <074C>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 137.3 519.79 Td <0B36>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 138.02 538.99 Td <0D02>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 142.46 538.99 Td <0C37>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 147.62 538.99 Td <0C2D>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 142.7 529.63 Td <0D02>Tj ET Q 138.02 536.11 13.92 0.6 re f* q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 154.94 523.87 Td <0D46>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 166.58 523.87 Td <0003>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 169.22 523.87 Td <074C>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 175.22 519.79 Td <0B35>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 176.21 538.99 Td <0D02>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 180.77 538.99 Td <0C37>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 185.93 538.99 Td <0C2D>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 180.89 529.63 Td <0D02>Tj ET Q 176.21 536.11 13.92 0.6 re f* q 93.384 517.63 452.14 27.12 re W* n BT /TT0 12 Tf 190.61 523.87 Td [(\) =)7 ( )]TJ ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 207.41 530.95 Td <0BCF>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 211.61 528.91 Td <0C2D>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 213.41 534.31 Td <0C2E>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 210.17 517.87 Td <0B36>Tj ET Q 207.41 526.87 10.56 0.84 re f* q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 220.61 523.87 Td <0D46>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 12 Tf 230.93 523.87 Td <0003>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 234.89 530.95 Td <0BCF>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 239.09 528.91 Td <0C2E>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 6.96 Tf 240.89 534.31 Td <0C2E>Tj ET Q q 93.384 517.63 452.14 27.12 re W* n BT /C2_1 8.52 Tf 237.65 517.87 Td <0B36>Tj ET Q 234.89 526.87 10.56 0.84 re f* q 93.384 517.63 452.14 27.12 re W* n BT /TT0 12 Tf 245.45 523.87 Td ( )Tj ET EMC Q Q q 93.384 488.83 452.14 28.8 re W* n /P <</Lang (en-US)/MCID 15 >>BDC q 93.384 488.83 452.14 28.8 re W* n BT /TT0 12 Tf 98.784 501.31 Td [(\(D)5 (\))]TJ ET Q q 93.384 488.83 452.14 28.8 re W* n BT /TT0 12 Tf 115.34 501.31 Td ( )Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 121.46 501.31 Td <073F>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 127.34 501.31 Td <123A>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 132.38 501.31 Td <074C>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 138.62 497.83 Td <0B36>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 139.34 507.43 Td <0C0A>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 144.5 507.43 Td <0B3F>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 150.74 507.43 Td <0B35>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 158.78 501.31 Td <0D46>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 170.42 501.31 Td <0003>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 173.06 501.31 Td <074C>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 179.09 497.83 Td <0B35>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 180.05 507.43 Td <0C0A>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 185.33 507.43 Td <0B3F>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 191.57 507.43 Td <0B35>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /TT0 12 Tf 196.97 501.31 Td [(\) =)7 ( )]TJ ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 213.77 508.39 Td <0BCF>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 6.96 Tf 217.97 506.35 Td <0C2D>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 6.96 Tf 219.77 511.75 Td <0C2E>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 216.53 495.31 Td <0B36>Tj ET Q 213.77 504.31 10.56 0.84 re f* q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 227.09 501.31 Td <0D46>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 12 Tf 237.29 501.31 Td <0003>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 241.37 508.39 Td <0BCF>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 6.96 Tf 245.57 506.35 Td <0C2E>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 6.96 Tf 247.37 511.75 Td <0C2E>Tj ET Q q 93.384 488.83 452.14 28.8 re W* n BT /C2_1 8.52 Tf 244.13 495.31 Td <0B36>Tj ET Q 241.37 504.31 10.56 0.84 re f* q 93.384 488.83 452.14 28.8 re W* n BT /TT0 12 Tf 251.81 501.31 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 16 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 11.04 Tf 54 478.87 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 17 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 11.04 Tf 54 466.27 Td ( )Tj ET EMC Q q 59.424 385.49 33.96 78.024 re W* n /P <</Lang (en-US)/MCID 18 >>BDC q 59.424 385.49 33.96 78.024 re W* n BT /TT0 12 Tf 64.824 452.71 Td (Q.28)Tj ET Q q 59.424 385.49 33.96 78.024 re W* n BT /TT2 12 Tf 88.464 452.71 Td ( )Tj ET Q q 59.424 385.49 33.96 78.024 re W* n BT /TT0 12 Tf 100.82 452.71 Td ( )Tj ET EMC Q Q q 93.384 407.47 452.14 56.04 re W* n /P <</Lang (en-US)/MCID 19 >>BDC q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 99.144 452.71 Td [(A )-27 (thi)-3 (n )-29 (a)4 (irf)4 (oil)-3 ( )-29 (is )-32 (mount)-3 (e)4 (d )-29 (in )-31 (a)4 ( )-29 (low)]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 262.01 452.71 Td (-)Tj ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 265.97 452.71 Td [(spe)-6 (e)4 (d, )-29 (subsoni)-3 (c)-5 ( )-29 (wind )-29 (tunnel, )-29 (in )-31 (whic)4 (h )-29 (th)-11 (e)4 ( )-29 (Ma)3 (c)4 (h )-29 (numb)-11 (e)4 (r )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 99.144 437.95 Td [(is )-52 (0.1. )-49 (At)10 ( )-49 (a)4 ( )-49 (point)6 ( )-49 (on )-49 (the)12 ( )-39 (a)4 (irf)4 (oil)-3 (, )-49 (the )-47 (pre)7 (ssure)5 ( )-49 (c)4 (oe)4 (f)-6 (f)-6 (icie)4 (nt )-51 (is )-52 (mea)6 (sure)6 (d )-49 (to )-51 (be)4 ( )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /C0_0 12 Tf 459.94 437.95 Td <0010>Tj ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 466.54 437.95 Td [(1.2. )-59 (I)23 (f )-46 (the )-47 (flow)3 ( )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 99.144 424.27 Td [(ve)4 (locit)-11 (y)20 ( )-29 (is )-32 (incr)5 (e)-5 (a)4 (se)3 (d )-29 (suc)-6 (h )-29 (that )-29 (the )-27 (fr)6 (e)4 (e)]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 284.33 424.27 Td (-)Tj ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 288.29 424.27 Td [(str)-9 (e)4 (a)4 (m )-31 (Ma)-6 (c)4 (h )-29 (number)5 ( )-29 (is )-32 (0.6, )-29 (the)]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 441.82 424.27 Td ( )Tj ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 445.18 424.27 Td [(pre)-2 (ssure)5 ( )-29 (c)4 (oe)4 (f)-6 (fic)5 (ient )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 99.144 410.47 Td [(a)4 (t t)-3 (he)4 ( sa)3 (me point on t)-3 (he)4 ( a)-5 (irf)4 (oil)-3 ( will)-3 ( a)4 (pprox)-6 (im)-3 (a)4 (tel)-9 (y)30 ( )-9 (be)4 (: )]TJ ET Q q 93.384 407.47 452.14 56.04 re W* n BT /TT0 12 Tf 360.43 410.47 Td ( )Tj ET EMC Q Q q 93.384 385.49 106.22 14.784 re W* n /P <</Lang (en-US)/MCID 20 >>BDC q 93.384 385.49 106.22 14.784 re W* n BT /TT0 12 Tf 98.784 388.49 Td [(\(A)5 (\) )]TJ ET Q q 93.384 385.49 106.22 14.784 re W* n BT /C0_0 12 Tf 118.34 388.49 Td <0010>Tj ET Q q 93.384 385.49 106.22 14.784 re W* n BT /TT0 12 Tf 124.94 388.49 Td (3.5)Tj ET Q q 93.384 385.49 106.22 14.784 re W* n BT /TT0 12 Tf 140.06 388.49 Td ( )Tj ET EMC Q Q q 199.61 385.49 106.34 14.784 re W* n /P <</Lang (en-US)/MCID 21 >>BDC q 199.61 385.49 106.34 14.784 re W* n BT /TT0 12 Tf 205.01 388.49 Td [(\(B)10 (\) )]TJ ET Q q 199.61 385.49 106.34 14.784 re W* n BT /C0_0 12 Tf 223.85 388.49 Td <0010>Tj ET Q q 199.61 385.49 106.34 14.784 re W* n BT /TT0 12 Tf 230.45 388.49 Td (2.9)Tj ET Q q 199.61 385.49 106.34 14.784 re W* n BT /TT0 12 Tf 245.57 388.49 Td ( )Tj ET EMC Q Q q 305.95 385.49 106.2 14.784 re W* n /P <</Lang (en-US)/MCID 22 >>BDC q 305.95 385.49 106.2 14.784 re W* n BT /TT0 12 Tf 311.35 388.49 Td (\(C\) )Tj ET Q q 305.95 385.49 106.2 14.784 re W* n BT /C0_0 12 Tf 330.31 388.49 Td <0010>Tj ET Q q 305.95 385.49 106.2 14.784 re W* n BT /TT0 12 Tf 336.91 388.49 Td (1.5)Tj ET Q q 305.95 385.49 106.2 14.784 re W* n BT /TT0 12 Tf 351.91 388.49 Td ( )Tj ET EMC Q Q q 412.15 385.49 133.37 14.784 re W* n /P <</Lang (en-US)/MCID 23 >>BDC q 412.15 385.49 133.37 14.784 re W* n BT /TT0 12 Tf 417.58 388.49 Td [(\(D)5 (\) )]TJ ET Q q 412.15 385.49 133.37 14.784 re W* n BT /C0_0 12 Tf 440.14 388.49 Td <0010>Tj ET Q q 412.15 385.49 133.37 14.784 re W* n BT /TT0 12 Tf 446.74 388.49 Td (0.75)Tj ET Q q 412.15 385.49 133.37 14.784 re W* n BT /TT0 12 Tf 467.86 388.49 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 24 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 374.69 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 25 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 360.89 Td ( )Tj ET EMC Q q 59.424 293.93 33.96 63.96 re W* n /P <</Lang (en-US)/MCID 26 >>BDC q 59.424 293.93 33.96 63.96 re W* n BT /TT0 12 Tf 64.824 347.09 Td (Q.29)Tj ET Q q 59.424 293.93 33.96 63.96 re W* n BT /TT2 12 Tf 88.464 347.09 Td ( )Tj ET Q q 59.424 293.93 33.96 63.96 re W* n BT /TT0 12 Tf 100.82 347.09 Td ( )Tj ET EMC Q Q q 93.384 330.29 452.14 27.6 re W* n /P <</Lang (en-US)/MCID 27 >>BDC q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 99.144 347.09 Td [(A )-97 (soli)-4 (d )-99 (c)4 (irc)5 (ular)5 ( )-99 (sha)-6 (ft )-98 (of)-6 ( )-99 (diame)4 (ter)5 ( )]TJ ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT3 12 Tf 268.25 347.09 Td (d)Tj ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 274.25 347.09 Td ( )Tj ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 278.45 347.09 Td [(is )-102 (unde)4 (r )-96 (pu)-9 (r)-6 (e)4 ( )-99 (torsion )-101 (of )-96 (ma)-7 (g)10 (nit)-3 (ude)4 ( )]TJ ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT3 12 Tf 454.42 347.09 Td (T)Tj ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 461.14 347.09 Td [(. )-99 (The)5 ( )-99 (max)-7 (im)-3 (u)10 (m)8 ( )]TJ ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 99.144 333.29 Td [(tensil)-2 (e)4 ( stre)4 (ss ex)-7 (pe)4 (rie)5 (nc)4 (e)4 (d)-9 ( a)4 (t an)-17 (y)20 ( point)-3 ( on the sha)5 (ft )-8 (is )]TJ ET Q q 93.384 330.29 452.14 27.6 re W* n BT /TT0 12 Tf 353.83 333.29 Td ( )Tj ET EMC Q Q q 93.384 293.93 106.22 29.16 re W* n /P <</Lang (en-US)/MCID 28 >>BDC q 93.384 293.93 106.22 29.16 re W* n BT /TT0 12 Tf 98.784 308.93 Td [(\(A)5 (\))]TJ ET Q q 93.384 293.93 106.22 29.16 re W* n BT /TT0 12 Tf 115.34 308.93 Td ( )Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /TT0 12 Tf 118.34 308.93 Td ( )Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 121.7 316.01 Td <0B370B36>Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 8.52 Tf 131.54 316.01 Td <0BCD>Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 8.52 Tf 121.46 302.93 Td <0C17>Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 8.52 Tf 127.22 302.93 Td <0BD7>Tj ET Q q 93.384 293.93 106.22 29.16 re W* n BT /C2_1 6.96 Tf 132.86 305.45 Td <0C2F>Tj ET Q 121.46 311.93 15.96 0.84 re f* q 93.384 293.93 106.22 29.16 re W* n BT /TT0 12 Tf 137.42 308.93 Td ( )Tj ET EMC Q Q q 199.61 293.93 106.34 29.16 re W* n /P <</Lang (en-US)/MCID 29 >>BDC q 199.61 293.93 106.34 29.16 re W* n BT /TT0 12 Tf 205.01 308.93 Td [(\(B)10 (\))]TJ ET Q q 199.61 293.93 106.34 29.16 re W* n BT /TT0 12 Tf 220.85 308.93 Td ( )Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /TT0 12 Tf 223.85 308.93 Td ( )Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 227.21 316.01 Td <0B350B3A>Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 8.52 Tf 237.05 316.01 Td <0BCD>Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 8.52 Tf 226.97 302.93 Td <0C17>Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 8.52 Tf 232.85 302.93 Td <0BD7>Tj ET Q q 199.61 293.93 106.34 29.16 re W* n BT /C2_1 6.96 Tf 238.49 305.45 Td <0C30>Tj ET Q 226.97 311.93 15.96 0.84 re f* q 199.61 293.93 106.34 29.16 re W* n BT /TT0 12 Tf 242.93 308.93 Td ( )Tj ET EMC Q Q q 305.95 293.93 106.2 29.16 re W* n /P <</Lang (en-US)/MCID 30 >>BDC q 305.95 293.93 106.2 29.16 re W* n BT /TT0 12 Tf 311.35 308.93 Td (\(C\) )Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 333.55 316.01 Td <0B370B36>Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 8.52 Tf 343.39 316.01 Td <0BCD>Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 8.52 Tf 333.31 302.93 Td <0C17>Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 8.52 Tf 339.19 302.93 Td <0BD7>Tj ET Q q 305.95 293.93 106.2 29.16 re W* n BT /C2_1 6.96 Tf 344.83 305.45 Td <0C30>Tj ET Q 333.31 311.93 15.96 0.84 re f* q 305.95 293.93 106.2 29.16 re W* n BT /TT0 12 Tf 349.27 308.93 Td ( )Tj ET EMC Q Q q 412.15 293.93 133.37 29.16 re W* n /P <</Lang (en-US)/MCID 31 >>BDC q 412.15 293.93 133.37 29.16 re W* n BT /TT0 12 Tf 417.58 308.93 Td [(\(D)5 (\) )]TJ ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 8.52 Tf -0.0131 Tc 440.5 316.01 Td <0B350B3A>Tj ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 8.52 Tf 450.34 316.01 Td <0BCD>Tj ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 8.52 Tf 440.26 302.93 Td <0C17>Tj ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 8.52 Tf 446.02 302.93 Td <0BD7>Tj ET Q q 412.15 293.93 133.37 29.16 re W* n BT /C2_1 6.96 Tf 451.66 305.45 Td <0C2F>Tj ET Q 440.26 311.93 15.96 0.84 re f* q 412.15 293.93 133.37 29.16 re W* n BT /TT0 12 Tf 456.22 308.93 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 32 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 11.04 Tf 54 283.97 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 33 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 270.41 Td ( )Tj ET EMC Q q 59.424 97.224 33.96 170.18 re W* n /P <</Lang (en-US)/MCID 34 >>BDC q 59.424 97.224 33.96 170.18 re W* n BT /TT0 12 Tf 64.824 256.61 Td (Q.30)Tj ET Q q 59.424 97.224 33.96 170.18 re W* n BT /TT2 12 Tf 88.464 256.61 Td ( )Tj ET Q q 59.424 97.224 33.96 170.18 re W* n BT /TT0 12 Tf 100.82 256.61 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 35 >>BDC q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 99.144 256.61 Td [(A )12 (c)4 (lampe)4 (d)]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 151.34 256.61 Td (-)Tj ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 155.3 256.61 Td [(c)4 (lampe)4 (d)-9 ( )10 (be)4 (a)-5 (m, )8 (subj)-2 (e)4 (c)4 (ted )12 (to a )12 (point)-3 ( )10 (lo)-11 (a)4 (d )10 (P)-3 ( )10 (a)4 (t )8 (the)-7 ( )10 (mi)-3 (dspa)3 (n, )10 (is )7 (sh)-10 (own )12 (in )8 (the )12 (fi)-8 (g)10 (u)-9 (re)7 ( )]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 99.144 242.81 Td [(be)4 (low. The)5 ( )]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 156.02 242.81 Td [(ma)-7 (g)10 (nit)-3 (ude)4 ( )]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 209.69 242.81 Td [(of)-6 ( the )]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 240.41 242.81 Td [(mom)-3 (e)4 (nt re)5 (a)4 (c)4 (ti)-3 (on a)4 (t t)-13 (he)4 ( two f)3 (ix)-11 (e)4 (d e)4 (nds of the)4 ( )-9 (be)4 (a)4 (m i)-3 (s)]TJ ET Q q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 495.1 242.81 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 36 >>BDC q 93.384 118.22 452.14 149.18 re W* n BT /TT0 12 Tf 475.42 118.34 Td ( )Tj ET EMC Q q 93.384 97.224 106.22 13.8 re W* n /P <</Lang (en-US)/MCID 37 >>BDC q 93.384 97.224 106.22 13.8 re W* n BT /TT0 12 Tf 98.784 100.22 Td [(\(A)5 (\) )]TJ ET Q q 93.384 97.224 106.22 13.8 re W* n BT /TT0 12 Tf 118.34 100.22 Td [(P)-13 (L)21 (/2)]TJ ET Q q 93.384 97.224 106.22 13.8 re W* n BT /TT0 12 Tf 141.74 100.22 Td ( )Tj ET EMC Q Q q 199.61 97.224 106.34 13.8 re W* n /P <</Lang (en-US)/MCID 38 >>BDC q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 205.01 100.22 Td [(\(B)10 (\))]TJ ET Q q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 220.85 100.22 Td ( )Tj ET Q q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 223.85 100.22 Td [(P)-13 (L)11 (/4)]TJ ET Q q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 247.25 100.22 Td ( )Tj ET Q q 199.61 97.224 106.34 13.8 re W* n BT /TT0 12 Tf 250.37 100.22 Td ( )Tj ET EMC Q Q q 305.95 97.224 106.2 13.8 re W* n /P <</Lang (en-US)/MCID 39 >>BDC q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 311.35 100.22 Td (\(C\))Tj ET Q q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 327.31 100.22 Td ( )Tj ET Q q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 330.31 100.22 Td [(P)-13 (L)21 (/8)]TJ ET Q q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 353.59 100.22 Td ( )Tj ET Q q 305.95 97.224 106.2 13.8 re W* n BT /TT0 12 Tf 359.71 100.22 Td ( )Tj ET EMC Q Q q 412.15 97.224 133.37 13.8 re W* n /P <</Lang (en-US)/MCID 40 >>BDC q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 417.58 100.22 Td [(\(D)5 (\))]TJ ET Q q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 434.14 100.22 Td ( )Tj ET Q q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 437.14 100.22 Td [(P)-13 (L)21 (/16)]TJ ET Q q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 466.42 100.22 Td ( )Tj ET Q q 412.15 97.224 133.37 13.8 re W* n BT /TT0 12 Tf 472.54 100.22 Td ( )Tj ET EMC Q Q /P <</Lang (en-US)/MCID 41 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 86.424 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 42 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 72.624 Td ( )Tj ET EMC Q /P <</Lang (en-US)/MCID 43 >>BDC q 0 0 595.44 841.68 re W* n BT /TT0 12 Tf 54 58.824 Td ( )Tj ET EMC Q /P <</MCID 44 >>BDC q 93.36 118.32 452.04 149.16 re W* n q 311.4 0 0 121.56 163.32 118.32 cm /Im0 Do Q EMC Q 6/9

Structural Mechanics

Question 26 from official GATE AE 2018 Examination.

Structural Mechanics

Question 27 from official GATE AE 2018 Examination.

Structural Mechanics

Question 28 from official GATE AE 2018 Examination.

Structural Mechanics

Question 29 from official GATE AE 2018 Examination.

Structural Mechanics

Question 30 from official GATE AE 2018 Examination.

Structural Mechanics

Which of the following statement(s) is/are true about the state of a body in plane strain condition? P: All the points in the body undergo displacements in one plane only, for example the x -y plane, leading to 𝜀zz = 𝛾xz = 𝛾yz = 0. Q: All the components of stress perpendicular to the plane of deformation, for example the x-y plane, of the body are equal to zero, i.e. 𝜎zz = 𝜏xz = 𝜏yz = 0. R: Except the normal component, all the other components of stress perpendicular to the plane of deformation of the body, for example the x -y plane, are equal to zero, i.e. 𝜎zz ≠ 0, 𝜏xz = 𝜏yz = 0. (A) P only (B) Q only (C) P and Q (D) P and R

Air-Breathing & Rocket Propulsion

An aircraft with a turbojet engine flies at a velocity of 100 m/s. If the jet exhaust velocity is 300 m/s, the propulsive efficiency of the engine, assuming a negligible fuel-air ratio, is (A) 0.33 (B) 0.50 (C) 0.67 (D) 0.80

Air-Breathing & Rocket Propulsion

An aircraft with a turboprop engine produces a thrust of 500 N and flies at 100 m/s. If the propeller efficiency is 0.5, the shaft power produced by the engine is (A) 50 kW (B) 100 kW (C) 125 kW (D) 500 kW

Structural Mechanics

An axial compressor that generates a stagnation pressure ratio of 4.0, operates with inlet and exit stagnation temperatures of 300 K and 480 K, respectively. If the ratio of specific heats (𝛾) is 1.4, the isentropic efficiency of the compressor is (A) 0.94 (B) 0.81 (C) 0.72 (D) 0.63

Air-Breathing & Rocket Propulsion

A rocket has an initial mass of 150 kg. After operating for a duration of 10 s, its final mass is 50 kg. If the acceleration due to gravity is 9.81 m/s2 and the thrust produced by the rocket is 19.62 kN, the specific impulse of the rocket is (A) 400 s (B) 300 s (C) 200 s (D) 100 s

Structural Mechanics

Consider the vector field v⃗ = - y r2 î + x r2 ĵ ; where r = √x2 + y2. The contour integral ∮ v⃗ ⋅ ds⃗⃗⃗⃗⃗, where ds⃗⃗⃗⃗⃗ is tangent to the contour that encloses the origin, is __________ (accurate to two decimal places).

Structural Mechanics

The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to equi- potential lines of the potential function 𝜙(r) = 1 r2+4 , where r = √x2 + y2, is _______ (accurate to two decimal places). 7/9

Structural Mechanics

Assuming ISA standard sea level conditions (288.16 K, density of 1.225 kg/m 3, g = 9.81 m/s2, R = 287 J/(kg-K)), the density (in kg/m3) of air at Leh, which is at an altitude of 3500 m above mean sea level is ________ (accurate to two decimal places).

Structural Mechanics

Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).

Incompressible & Compressible Aerodynamics

An aircraft with mass of 400,000 kg cruises at 240 m/s at an altitude of 10 km. Its lift to drag ratio at cruise is 15. Assuming g as 9.81 m/s2, the power (in MW) needed for it to cruise is _______ (accurate to two decimal places).

Airplane Performance & Stability

A statically-stable aircraft has a CL𝛼= 5 (where the angle of attack, α, is measured in radians). The coefficient of moment of the aircraft about the center of gravity is given as CM,c.g = 0.05 - 4𝛼. The mean aerodynamic chord of the aircraft wing is 1 m. The location (positive towards the nose ) of the neutral point of the aircraft from the center of gravity is ______ (in m, accurate to two decimal places).

Structural Mechanics

An aircraft with a gross weight of 2000 kg , has a speed of 130 m/s at sea level, where the conditions are: 1 atmosphere (pressure), 288 K (temperature), and 1.23 kg/m3 (density). The speed (in m/s) required by the aircraft at an altitude of 9000 m, where the conditions are: 0.31 atmosphere, 230 K, and 0. 47 kg/m3, to maintain a steady, level flight is ________ (accurate to two decimal places).

Incompressible & Compressible Aerodynamics

A pitot probe on an aircraft in a steady, level flight records a pressure of 55,000 N/m 2. The static pressure and density are 45,280 N/m2 and 0.6 kg/m3, respectively. The wing area and the lift coefficient are 16 m2 and 2, respectively. The wing loading (in N/m2) on this aircraft is _________ (accurate to one decimal place).

Space Dynamics

A spacecraft forms a circular orbit at an altitude of 150 km above the surface of a spherical Earth. Assuming the gravitational parameter, µ = 3.986 × 10 14 m3/s2 and radius of earth, RE = 6,400 km, the velocity required for the injection of the spacecraft, parallel to the local horizon, is _______________ (accurate to two decimal places).

Incompressible & Compressible Aerodynamics

Air at 50 kPa pressure and 400 K temperature flows in a duct at Mach 3.0. A part of the flow leaks through an opening on the duct wall into the ambient, where the pressure is 30 kPa. The maximum Mach number achieved in the discharge is _______ (accurate to two decimal places). (Ratio of specific heats of air is 𝛾 = 1.4). 8/9

Incompressible & Compressible Aerodynamics

Consider a 20 0 half-angle wedge in a supersonic flow at Mach 3 .0 at standard sea -level conditions. If the shock-wave angle on the wedge is 360, the Mach number of the tangential component of the flow post-shock is _______ (accurate to two decimal places).

Incompressible & Compressible Aerodynamics

The boundary layer thickness at the location of a sensor on a flat plate in an incompressible, laminar flow of air is required to be restricted to 1 mm for an effective measurement. If the flow velocity is 20 m/s with 1 bar pressure, 300 K temperature, and 1.789×10 ˗5 kg/(m-s) viscosity, the maximum distance (in mm) of the sensor location from the leading edge is ________ (accurate to one decimal place).

Incompressible & Compressible Aerodynamics

Gross weight of an airplane is 7000 N, wing area is 16 m2, and the maximum lift coefficient is 2.0. Assuming density at the altitude as 1.23 kg/m3, the stall speed (in m/s) of the aircraft is _________ (accurate to two decimal places).

Structural Mechanics

A thin-walled tube with external radius of 100 mm and wall thickness of 2 mm, is fixed at one end. It is subjected to a compressive force of 1 N acting at a point on the circumference parallel to its length. The maximum normal stress (in kPa) experienced by the structure is _____________ (accurate to two decimal places).

Structural Mechanics

A 1 m long massless cantilever beam oscillates at 2Hz, while a 60 kg mass is attached at the tip of it. The flexural rigidity of the beam (in kN-m2) is _________________ (accurate to two decimal places).

Structural Mechanics

A cantilever beam having a rectangular cross-section of width 60 mm and depth 100 mm, is made of aluminum alloy. The material mechanical properties are: Young's modulus, E = 73 GPa and ultimate stress, 𝜎u = 480 MPa. Assuming a factor of safety of 4, the maximum bending moment (in kN-m) that can be applied on the beam is _____ (accurate to one decimal place).

Structural Mechanics

The components of stress in a bo dy under plane stress condition, in the absence of body forces, is given by: 𝜎xx = Ax2; 𝜎yy = 12x2 - 6y2 and 𝜎xy = 12xy. The coefficient, A, such that the body is under equilibrium is _____ (accurate to one decimal place).

Structural Mechanics

An axial compressor rotor with 50 % degree of reaction, operates with an axial velocity of 200 m/s. The absolute flow angle at the inlet of the rotor is 22 o with reference to the axial direction. If the axial velocity is assumed to remain constant through the rotor, the magnitude of the relativ e velocity (in m/s) at the rotor exit is __________ ( accurate to one decimal place). 9/9

Structural Mechanics

The relative velocity of air leaving a straight radial impeller of a centrifugal compressor is 100 m/s. If the impeller tip speed is 200 m/s, for a slip free operation, the absolute velocity (in m/s) at the impeller exit is _________ (accurate to one decimal place).

Airplane Performance & Stability

An aircraft wind tunnel model, having a pitch axis mass moment of inertia (Iyy) of 0.014 kg-m2, is mounted in such a manner that it has pure pitching motion about its centre of gravity, where it is supported through a frictionless hinge. If the pitching moment (M) derivative with respect to angle of attack (α), denoted by 'M α', is -0.504 N-m/rad and the pitching moment (M) derivative with respect to pitch rate (q), denoted by 'Mq', is -0.0336 N-m/(rad/s), the damping ratio of the resulting motion due to an initial disturbance in pitch angle is approximately _________ (accurate to three decimal places). END OF THE QUESTION PAPER Q.No. Type Section Key/Range Marks 1 MCQ GA D 1 2 MCQ GA A 1 3 MCQ GA B 1 4 MCQ GA A 1 5 MCQ GA C 1 6 MCQ GA C 2 7 MCQ GA C 2 8 MCQ GA Marks to All 2 9 MCQ GA D 2 10 MCQ GA B 2 1 MCQ AE C 1 2 MCQ AE B 1 3 MCQ AE B 1 4 MCQ AE C 1 5 MCQ AE B 1 6 MCQ AE C 1 7 MCQ AE A 1 8 MCQ AE C 1 9 MCQ AE B 1 10 MCQ AE C 1 11 MCQ AE B 1 12 MCQ AE A 1 13 MCQ AE B 1 Q.No. Type Section Key/Range Marks 14 MCQ AE B 1 15 MCQ AE B 1 16 MCQ AE B 1 17 MCQ AE A 1 18 MCQ AE C 1 19 MCQ AE B 1 20 NAT AE 0.0 to 0.0 1 21 NAT AE 1185.00 to 1186.50 1 22 NAT AE 1.75 to 1.95 1 23 NAT AE 2.0 to 2.0 1 24 NAT AE 0.98 to 0.98 1 25 NAT AE 0.50 to 0.50 1 26 MCQ AE B 2 27 MCQ AE C 2 28 MCQ AE C 2 29 MCQ AE D 2 30 MCQ AE C 2 31 MCQ AE D 2 32 MCQ AE B 2 33 MCQ AE B 2 34 MCQ AE B 2 35 MCQ AE C 2 36 NAT AE 6.25 to 6.35 2 Q.No. Type Section Key/Range Marks 37 NAT AE 0.68 to 0.73 2 38 NAT AE 0.85 to 0.88 2 39 NAT AE 9.80 to 9.81 2 40 NAT AE 62.00 to 63.50 2 41 NAT AE ‐0.81 to ‐0.79 2 42 NAT AE 209.00 to 211.00 2 43 NAT AE 18000 to 19440 2 44 NAT AE 7.80 to 7.80 (or) 7800 to 7802 2 45 NAT AE 3.30 to 3.40 2 46 NAT AE 1.90 to 2.20 2 47 NAT AE 47.0 to 55.0 2 48 NAT AE 18.80 to 18.90 2 49 NAT AE ‐2.50 to ‐2.20 2 50 NAT AE 3.10 to 3.20 2 51 NAT AE 12.0 to 12.0 2 52 NAT AE ‐6.0 to ‐6.0 2 53 NAT AE 215.0 to 216.5 2 54 NAT AE 222.0 to 225.0 2 55 NAT AE 0.195 to 0.205 2

Structural Mechanics

Question 56 from official GATE AE 2018 Examination.

Structural Mechanics

Question 57 from official GATE AE 2018 Examination.

Structural Mechanics

Question 58 from official GATE AE 2018 Examination.

Structural Mechanics

Question 59 from official GATE AE 2018 Examination.

Structural Mechanics

Question 60 from official GATE AE 2018 Examination.

Structural Mechanics

Question 61 from official GATE AE 2018 Examination.

Structural Mechanics

Question 62 from official GATE AE 2018 Examination.

Structural Mechanics

Question 63 from official GATE AE 2018 Examination.

Structural Mechanics

Question 64 from official GATE AE 2018 Examination.

Structural Mechanics

Question 65 from official GATE AE 2018 Examination.