ME 2016 Paper-3-watermark PDF

Preview

Summary

Download ME 2016 Paper-3-watermark PDF

Description

www.gradeup.co

1. Based on the given statements, select the appropriate option with respect to grammar and usage. Statements i. The height of Mr. X is 6 feet. ii. The height of Mr. Y is 5 feet. a) Mr. X is longer than Mr. y. b) Mr. X is more elongated than Mr. Y. c) Mr. X is taller than Mr. Y. d) Mr. X is lengthier than Mr. Y. Ans. (C) In degrees of comparison Mr. X is taller than Mr. Y is apt. Positive degree – tall Comparative degree – taller Superlative degree – tallest 2. The students ____ the teacher on teacher’s day for twenty years of dedicated teaching. a) Facilitated b) Felicitated c) Fantasized d) Facilitated Ans. (B) The student felicitated the teacher on teach day for twenty years of dedicated teaching. 3. After India’s cricket world cup victory in 1 who was paying both tennis and cricket ti to concentrate only on cricket. And the What does the underlined phrase me a) History will rest in peace b) Rest is recorded in history bo c) Rest in well known d) Rest is archaic Ans. (C) ‘rest is history’ means ‘rest is well kn 4. Given (9 inch following stat a) 3 inches b) 9 inch c) 9 in d)

for ur shifts s. What is on of E in the pro a) 1:1 b) 1:2 c) 1:4 d) 2:1 Ans. (B) ‘M’ works with ency as E but worked for half as many days. So s respect they will do equal work if their shifts wo d have been for same timings. But M’s shift is for hrs, while E’s shift for 12 hrs. Hence E will do twice the work as M. Ratio of contribution of M : E in work, 1 : 2

1|Pag e

6. The Venn diagram shows the preference of the student population for leisure activities.

From the read b a) 4 b)

ho like to

d books or play

s were in existence in an he colonial period when they were arying degrees, they were intended nial interest. In the time of the economic rise of postcolonial India, conventional ways of knowledge have become obsolete. the following can be logically inferred from the statements? cial science disciplines have become obsolete. Social science disciplines had a pre-colonial origin. iii. Social science disciplines always promote colonialism. iv. Social science must maintain disciplinary boundaries. a) (ii) only b) (i) and (iii) only c) (ii) and (iv) only d) (iii) and (iv) only Ans. (A) Until the colonial period means pre-colonial origin. Other options can’t be inferred. 8. Two and a quarter hours back, when seen in a mirror, the reflection of a wall clock without number markings seemed to show 1:30. What is the actual current time shown by the clock? a) 8:15 b) 11:15 c) 12:15 d) 12:45 Ans. (D)

www.gradeup.co

Now, if A = −AT or AT = −A [A] =

1 1 (A  A) + (A ( A) 2 2

Symmetric part becomes zero while skew symmetric part is left therefore a square m x is called a skew symmetric AT = −A Mirror image of 1 : 20 is 10 : 30 10 : 30 was the time two and quarter hour back so time now will be 12 : 45

12.

Lt

x 0

log e (1  4 x e 3x 

a) 0 9. M and N start from the same location. M travels 10 km East and then 10 km North-East. N travels 5 km South and then 4 km South-East. What is the shortest distance (in km) between M and N at the end of their travel? a) 18.60 b) 22.50 c) 20.61 d) 25.00 Ans. (C)

b)

1 12

c

ontinuous d

See the adjoining figure for sol MM′ =5

2

+52

2

=5

age) under standard normal andom variable Z within limits from

2−2 (MM')  (N

NM′ = 10 + 5 MN = M′ =

2

to 99.8 mal curve (as shown in figure) has 68% s −1 to + 1, 95% area is o + 2 and 99.7% area is limits −3 to + 3

(5  7

10. A wi One o oth W

b c) 1 d) 180 Ans. (B) 11. A real squ a) AT = A b) AT = A-1 c) AT = -A d) AT = A+ A-1 Ans. (C) We know that a

mmetric if

symmetric matix

2|Pag e

f ( x)  x3  x  1 obtained

after first iteration on application of Newton-Raphson scheme using an initial guess of e matric can be written as,

1 1 (A+ AT ) + (A AT ) 2 2 1 1 T T where (A+ A ) is a symmetric and (A  A ) is a skew 2 2 [A] =

15. The root of the function

x0  1

is

a) 0.682 b) 0.686 c) 0.750 d) 1.000 Ans. (C) According to Newton-Raphson schemexn+1 = xn −

f(x n ) f'(xn )

www.gradeup.co

x1 = x0 −

x1 =

f(x o ) (1 1 1) 1  1  1 2 f'(xo ) [3  (1)  1] 4

sections have the same cross-sectional are. The ratio is I1/I2is

3 = 0.75 4

16. A force F is acting on s bent bar which is clamped at one end as shown in the figure. a)

b)

The CORRECT free body diagram is

1  2  

c

a)

b)

  4 a l1 12 = l2   2 a 4 × a4    l1 =  /3 l2 2a/

d) Ans.. (A)While dra supports are remove supports are drawn. Fu clamped support resists f any tendency of rotation.

am all the plied due to those ed support or a any direction, as well as

17. The cross-sections of two solid bars made of the material are shown in the figure. The square crosssection has flexural (bending) rigidity I1, while the circular cross-section has flexural rigidity I2. Both

3|Pag e

18. The state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b).

The components

( xx , yy , xy ) are given by

www.gradeup.co

a) b)

Δ = 1 mm g = 10 m/s2

( p / 2,  p / 2, o) (0, 0, p )

wn =

( p,  p, p / 2) d) (0,0, p / 2) c)

g 10 100 rad/ s  3   10

22. Which of the bearin subjected to a thrust a) Deep groove ba b) Angular conta c) Cylindrical d) Single ro Ans. (C) straigh

Ans. (B) For stress system shown in figure (a) σx = p, σy = −p and τ = 0

  x  y    x  y     cos 2θ + τ sin 2θ 2   2  

τxx = 

 p- p   p- (  p)  cos 90o + 0 = 0   2   2 

=

elow SHOULD NOT be

bviously, load

τyy + τxx = σx + σy ⇒ τyy = (σx + σy) − τxy = 0

  x  y   sin 2θ − τ cos 2θ  2 

And |τxy| = −  =−

 p- ( p)   2 

sin(−90o) − 0 = p

bown in epth) of nnel is 0.9 width 200 nnel of width

∴ τxx = 0 τyy = 0 τxy = p 19. A rigid link PQ is undergoing plane in the figure (VP and VQ are non=zero velocity of point Q with respect to

at the same elevation.

Which one of a) VQP has c b) VQP ha c) VQP d) V An

20 mech a) 3(n – b) 3(n –1) c) 3n – 2j d) 2j – 3n + 4 Ans. (B) Number mechanism having given by Gruebler’s eq F = 3 (n – 1) − 2j

nge: 0.99 to 1.01

is

300 200 × 1 × V2 + 1000 1000 3 V2 ⇒ 0.9 − 0.6 = 10 0.3 10  V2 ⇒ 3 ⇒ 0.9 =

is planar le hinge joints is

21. The static deflection of a spring under gravity, when a mass of 1 kg is suspended from it, is 1 mm. Assume the acceleration due to gravity g =10 m/s2. The natural frequency of this spring-mass system (in rad/s) is_____ Ans. Range: 99 to 101 M = 1 kg

4|Pag e

Q1 = Q2 + Q3 ⇒ A1V1 = A2V2 + A3V3 ×1×3

V2 = 1m⁄s 24. For a certain two-dimensional incompressible flow, velocity field is given by

2xyi  y2 j . The streamlines for

this flow are given by the family of curves

www.gradeup.co

a)

x 2 y 2  constant

b)

xy 2  constant

2 xy  y 2  constant d) xy  constant c)

Ans. (B) u = 2xy v = −y2

V  2 xyi y 2 j

dx dy = u v dx dy =  2 2 xy  y 1 dx  dy =  2 x y 1 dx dy   0 2 x y 1  ln x + ln y = ln c 2

d) inertia force to surface tension force Ans. (B) Grashoff number signifies the ratio of buoyance force to viscous force 27. The INCORRECT statement about the characteristic of critical point of a pure sub e is that a) there is no constant re vaporization process b) it has point of infle slope c) the ice directly c phase to vapour phase d) saturated li ates are identical Ans. (C) is heated le point pres or do

e . The the two

⇒ln x + 2 ln y = 2 ln c ⇒ xy2 = c − Tho ) = Cc(Tco − Tci) − Tho)

25. Steady one-dimensional heat co across the faces 1 and 3 of a com slabs A and B in perfect contact where kA, kB denote the resp conductivities. Using the da interface temperature T

⇒ Temperature of hot fluid will that of cold fluid and if the heat ong (for qmax), temperature Tho Thi − Tci) = CminΔ Tmax e and fluid velocities for an axial turbine are n the figure.

An

T1- T2 =  0.1   20   10     20 (130 − T) ×    0.1  

The magnitude of absolute velocity at entry is 300 m/s at an angle of 65o to the axial direction, while the magnitude of the absolute velocity at exit is 150 m/s. The exit velocity vector has a component in the downward direction. Given that the axial (horizontal) velocity is tha same at entry and exit, the specific work (in kJ/kg) is _____ Ans. Range: 50 to 54 e = Vt u1 − Vt u2 = [ Vt − Vt ]u … … … . . (1) 1

2

1

2

3 × 130 − 3T = 5T − 15 130 × 3 + 150 = 8T T = 67.5oC

As the flow velocity is same 150 cos β = 300 cos 65o ⇒ β = 32.30o Vt = 300 sin 65o and Vt = 150 sin 32.30o

26. Grashof number signifies the ratio of a) inertia face to viscous force b) buoyancy force to viscous force c) buoyancy force to inertia force

Substituting in equation (1) and solving we obtain E = 52.8 kJ/kg

1

5|Pag e

2

www.gradeup.co

30. Engineering strain of a mild steel sample is recorded as 0.100%. The true strain is a) 0.010% b) 0.055% c) 0.999% d) 0.101% Ans. (C) ϵ =

ϵ=

l2 - l1 l1

0.1 (Given) 100

T. S. ln(1 + ϵ) ∴ T. S = ln(1.001) = 0.099%

34. Match the following part programming codes with their respective functions Part Programming Codes Functions P. G01 I. Spindle stop Q. G03 II. Spindle rotation, clockwise R. M03 III. Circular interp n, anticlockwise S. M05 IV. Linear interp a) P-II, Q-I, R-IV, S-I b) P-IV, Q-II, R-III c) P-IV, Q-III, R d) P-III, Q-IV, Ans. (C) G0 G03 is us ise M03 is And

31. Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminium. The shape of the cavity is a cylinder with 15 mm diameter. The size of the moulds are such that the outside temperature of the moulds do not increase appreciably beyond the atmospheric temperature during solidification. The sequence of solidification in the mould from the fastest to slo (Thermal conductivities of steel, copper and a are 60.5, 401 and 237 W/m-K, respectively heats of steel, copper and aluminium are 903 J/kg-K, respectively. Densities of s aluminium are 7854, 8933 and 2700 .) a) Copper-Steel-Aluminium b) Aluminium-Steel-Copper c) Copper-Aluminium-Ste d) Steel-Copper-Alumin Ans. (C) α =

ed to

genvectors of

en matrix are identical, the eigen these identical be identical/linearly dependent. r of linearly independent eigen vectors

k C

Steel ∶ α = 1. Copper ∶ α Aluminu Copp

e value of the line integral rcle of radius Here,

b c) w non-c d) samp non-condu Ans. (B) In a sample both sh make a successful

cally ectrically



, where is a

units is____

F ( x, y)  yi  2 xj

and

r ' is the UNIT tangent

vector on the curve C at an arc length s from a reference point on the curve. i and j are the basis vectors in the x-y Cartesian reference. In evaluating the line integral, the curve has to traversed in the counter-clockwise direction. Ans. Range: 15.9 to 16.1

e and the ting in order to

33. Internal gas are ma d by a) hobbing b) shaping with pinion cutter c) shaping with rack cutter d) milling Ans. (B) Internal gears are manufactured by shaping process with pinion cutter

6|Pag e

4

Applying Green’s theorem

www.gradeup.co

40. An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, ad start moving due to gravity. The tension in the string (in N) is ____

38.

lim x2  x  1  x x 

is Ans. Ra

a) 0 b)  c) ½ d) - 

1 t

Ans. (C) Let x = ; then

lim =

1 1  1 1 2     t t t

 lim

1  t- t  1 t

x 

lim x 2  x  1  x x 

2

t 0

Since the function has 0/0 from now, we Hopital rule,

 lim t 0

2  1  t- t  1 1  (1   lim  t 0 t  2 

Applying limit now,

lim x 2 + x-1 - x  x 

1 2

0……….①

39. Three cards probability th a)

16 552

T = m2a = −20.38 a + 200 … … … . ② quation ① and ② 10.19a + 100 = 200 − 20.38 a ∴ 30.57 a = 100 ∴ a = 3.27m⁄s2 ∴ T = 10.19 × 3.27 + 100 = 133.32 N

b)

d)

165

Ans. (A) c3 Number of wa be drawn = 4c1 × 4c1 × 4c1 The required probability



drawn 52 and a jack can

41. A circular disc of radius 100 mm and mass 1 kg initially at rest at position A, rolls without slipping down a curved path as show in figure. The speed v of the disc when it reaches position B is ___m/s. Acceleration due to gravity g = 10 m/s2.

4 4 51  50 6

384 16  132600 5525 Ans. Range: 19.9 to 20.1

7|Pag e

www.gradeup.co

Applying energy conservation, Total energy at B  Total energy at A    Mgh =     when the disc is at rest When disc is rolling without slipping     1 1 1 1 MR2 2 MV 2   2  MV 2   2 2 2 2 2

R  = 2gh 2 V2 4  2gh  V2  gh But Rω = V ⇒ 2 3 2

(ii) V2 BI   (i) 5 AI BI AI  sin(71.58) sin(45) BI  1.34 AI V2  1.34 5 V2 = 2.99

2

⇒ V2 +

43. A un

oa

Substituting, g = 10 m⁄s2 and h = 30 meters, we get V =

4gh/ 3 = 20m⁄s 42. A rigid rod (AB) of length L = 2 m is under translational as well as rotational motion in th (see the figure). The point A has the velocit m/s. The end B is constrained to move on direction.

The magnitude o is____ Ans. Range:

dimension L = 2δ. If L on’s ratio of the plate

 

y E

P (1   ) E

 2  0.001  250   )    0.2   3 (1 2   200  10 44. Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. α = 90 α = 26.56 V1 = i + 2j a. b = |a| |b| c cos θ =

a .b ;cos | a || b |

θ = 63.43 V1 = (AI)w V1 = i + 2j V1 =

5

5 = (AI)w … … … (i) V2 = (BI)w … … … . (ii)

8|Pag e

Here, θs is the twist and  S is the maximum shear stress in the solid shaft, whereas is the twist and 

H

is the

maximum shear stress in the hollow shaft. Which one of the following is TRUE? θH a) θs = θH and  S = H

 S > H c) θs < θH and  S...