Aerospace Engineering Gate Yearwise 


Aerospace Engineering Gate 2014 Questions with Answer

Ques 27 GATE 2014

A 1.8m long steel beam of rectangular cross section (10mm× 6mm) is simply supported with a length of 1.2m between the supports and an overhang of 0.3m on either side. Young's modulus for the material of the beam is 200GPa. For a 50N load applied at the center of the beam, magnitude of the slopeof the beam at tip S is


(0.12 to 0.13) is the correct answer.

Ques 28 GATE 2014

There are 2 designs proposed for a shaft of length I, with a torque carrying capacity of T.Design I is a solid circular cross-section shaft of diameter30mm. Design II is a thin-walled circular shaft of average diameter 40mm. Thickness of the wall in Design II has to be determined such that maximum shear stress is the same in both the designs for the given torque T(so that same material can be used for manufacturing both the shafts). Ratio of mass of shaft using Design Ito the mass of shaft using Design II is

A

2.68

B

5.36

C

1.79

D

3.58


(a) is the correct answer.

Ques 29 GATE 2014

A structural member of rectangular cross-section 10mm 6mm and length Im is made of steel (Young's modulus is 200GPa and coefficient of thermal expansion is 12×10-6/°C). It is rigidly fixed at both the ends and then subjected to a gradual increase in temperature. Ignoring the three dimensional effects, the structural member will buckle if the temperature is increased by ΔT°C which is

A

19.74

B

9.87

C

78.96

D

39.48


(b) is the correct answer.

Ques 30 GATE 2014

A gas cylinder (closed thin-walled cylindrical pressure vessel) of diameter 30cm and wall thickness 1mm is subjected to a design maximum internal pressure of 5bar (0.5MPa). The material used for manufacturing this cylinder has a failure stress of 260MPa. Assuming von Mises failure criterion, the factor of safety (with respect to maximum allowable stress) for this cylinder is

A

2.8

B

2.0

C

6.9

D

4.0


(d) is the correct answer.

Ques 31 GATE 2014

A cantilevered beam is subjected to a parabolic distribution of shear traction at the right edge while the top and bottom surfaces are traction free. To solve this problem, following Airy's stress function is proposed: φ=C1xy+C2xy3+C3x2y2+C4x3y. This is an admissible Airy's function that would satisfy the bi-harmonic equation as well as the boundary conditions if and only if

A

C1=0, C2=λ, C3=0, C4=λ/(3d22)

B

C1=λ, C3=0 C4=0, C2=λ/(3d2)

C

C1=0, C2=0, C3=λ

D

C1=λ, C2=-λ/(3d2), C3=0 C4=0


(d) is the correct answer.

Ques 32 GATE 2014

1kg mass is hanging from a spring of stiffness 500N/m attached to a massless, symmetric beam of length 0.6m, moment of inertia about the bending axis/ =8.33×10-10m4 and Young's modulus E=210GPa as shown in the figure. The fundamental natural frequency (in rad/s) of the system is

A

3.24

B

20.36

C

22.36

D

3.56


(b) is the correct answer.

Ques 33 GATE 2014

The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent of the data fall below that value)

(i) On average, it rains mor more in July than in December
(ii) Every year, the amount of rainfall in August is more than that in January
(iii) July rainfall can be be estimated with better confidence than February rainfall
(iv) In August, there is at least 500 mm of rainfall

A

(i) and (ii)

B

(i) and (iii)

C

(ii) and (iii)

D

(iii) and (iv)


(b) is the correct answer.

Ques 34 GATE 2014

For a real symmetric matrix [A], which of the following statements is true:

A

The matrix is always diagonalizable and invertible.

B

The matrix is always invertible but not necessarily diagonalizable.

C

The matrix is always diagonalizable but not necessarily invertible.

D

The matrix is always neither diagonalizable nor invertible.


(c) is the correct answer.

Ques 35 GATE 2014

The series s=∑m=1∞(m2/3m)(x-2)m; converges for all x with |x-2|≤R given by

A

R=0

B

R=3

C

R=∞

D

R=1/3


(b) is the correct answer.

Ques 36 GATE 2014

The function given by f(x)={sin(1/x), x≠0; 0, x=0} is

A

Unbounded everywhere

B

Bounded

C

Bounded but not continuous at x=0

D

everywhere


(c) is the correct answer.

Ques 37 GATE 2014

Given the boundary-value d/dx(x dy/dx)+ky=0 , 01 and k=5 (given by y5) satisfy: )

A

∫01y1y5dx=0

B

∫01(dy1/dx)(dy5/dx)dx=0

C

∫01y1y5dx≠0

D

∫01(y1y5+dy1/dx dy5/dx)dx=0


(a) is the correct answer.

Ques 38 GATE 2014

The value of I=∫011000x4dx obtained by using Simpson's rule with 2 equally spaced intervals is,

A

200

B

208

C

180

D

208


(d) is the correct answer.

Ques 39 GATE 2014

If Then det(-[A]2+7[A]-3[I]) is

A

0

B

-324

C

324

D

6


(a) is the correct answer.

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