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Mechanical Engg. Set 3 (GATE) 2015

ME - Gate 2015 Paper - 3

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Questions

Question 1 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Fill in the blank with the correct idiom/phrase.

That boy from the town was a _______ in the sleepy village.

  1. dog out of herd
  2. sheep from the heap
  3. fish out of water
  4. bird from the flock
Question 2 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:

Apparent lifelessness ____________ dormant life.

  1. harbours
  2. leads to
  3. supports
  4. affects
Question 3 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Tanya is older than Eric.
Cliff is older than Tanya.
Eric is older than Cliff.
If the first two statements are true, then the third statement is

  1. true
  2. false
  3. uncertain
  4. Data insufficient
Question 4 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which of the conclusions logically follow(s).

Statements:
No manager is a leader.
All leaders are executives.
Conclusions:
I. No manager is an executive.
II. No executive is a manager.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Neither conclusion I nor II follows
  4. Both conclusions I and II follow
Question 5 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Select the appropriate option in place of underlined part of the sentence.

Increased productivity necessary reflects greater efforts made by the employees.

  1. Increase in productivity necessary
  2. Increase productivity is necessary
  3. Increase in productivity necessarily
  4. No improvement required
Question 6 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Choose the statement where underlined word is used correctly.

  1. When the teacher eludes to different authors, he is being elusive.
  2. When the thief keeps eluding the police, he is being elusive.
  3. Matters that are difficult to understand, identify of remember are allusive.
  4. Mirages can be allusive, but a better way to express them is illusory.
Question 7 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and line PR is parallel to the x-axis. The x and y coordinates of P, Q and R are integers that satisfy the inequalities – 4 $\leq$ x $\leq$ 5 and 6 $\leq$ y $\leq$ 16. How many different triangles could be constructed with these properties?

  1. 110
  2. 1,100
  3. 9,900
  4. 10,000
Question 8 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The ratio of momentum diffusivity (v) to thermal diffusivity ($\alpha$) is called

  1. Prandtl number
  2. Nusselt number
  3. Biot number
  4. Lewis number
Question 9 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

In a machining operation, if the generatrix and directrix both are straight lines, the surface obtained is

  1. cylindrical
  2. helical
  3. plane
  4. surface of revolution
Question 10 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two tails occur in the three tosses.
Based on the above information, which of the following statements is TRUE?

  1. X and Y are not independent.
  2. Y and Z are dependent.
  3. Y and Z are independent.
  4. X and Z are independent.
Question 11 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Which of the following statements are TRUE for damped vibrations?

P. For a system having critical damping, the value of damping ratio is unity and the system does not undergo a vibratory motion.
Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.
R. In case of damping due to dry friction between moving surfaces, resisting force of constant magnitude acts opposite to the relative motion.
S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity.

  1. P and Q only
  2. P and S only
  3. P, Q and R only
  4. Q and S only
Question 12 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

If P(X) = $\frac{1}{4}$, P(Y) = $\frac{1}{3}$ and P(X $\cap$Y) = $\frac{1}{12}$, then the value of P$\bigg(\frac{Y}{X}\bigg)$ is

  1. $\frac{1}{4}$
  2. $\frac{4}{25}$
  3. $\frac{1}{3}$
  4. $\frac{29}{50}$
Question 13 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

In full mould (cavity-less) casting process, the pattern is made of

  1. expanded polystyrene
  2. wax
  3. epoxy
  4. plaster of Paris
Question 14 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

In the notation (a/b/c) : (d/e/f) for summarizing the characteristics of queueing situation, the letters ‘b’ and ‘d’ respectively stand for

  1. service time distribution and queue discipline
  2. number of servers and size of calling source
  3. number of servers and queue discipline
  4. service time distribution and maximum number allowed in system
Question 15 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Let $\phi$ be an arbitrary smooth real valued scalar function and $\bar{V}$ be an arbitrary smooth vector valued function in a three-dimensional space. Which of the following is an identity?

  1. Curl ($\phi \bar{V}$) = $\nabla$ ($\phi Div\bar{V}$)
  2. Div $\bar{V}$ = 0
  3. Div Curl $\bar{V}$ = 0
  4. Div ($\phi \bar{V}$) = $\phi$ Div $\bar{V}$
Question 16 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Which of the following joining processes are autogenous?

  1. Diffusion welding
  2. Electroslag welding
  3. Tungsten inert gas welding
  4. Friction welding
  1. 1 and 4
  2. 2 and 3
  3. 2 and 4
  4. 1 and 3
Question 17 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

An air-standard diesel cycle consists of the following processes:

1–2: Air is compressed isentropically.
2–3: Heat is added at constant pressure.
3–4: Air expands isentropically to the original volume.
4–1: Heat is rejected at constant volume.
If $\gamma$ and T respectively denote the specific heat ratio and temperature, then the efficiency of the cycle is

  1. $1-\frac{T_4-T_1}{T_3-T_2}$
  2. $1-\frac{T_4-T_1}{\gamma(T_3-T_2)}$
  3. $1-\frac{\gamma(T_4-T_1)}{T_3-T_2}$
  4. $1-\frac{T_4-T_1}{(\gamma-1)(T_3-T_2)}$
Question 18 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

For the same material and mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation OO’ passing through the centre of gravity?

  1. (A)
  2. (B)
  3. (C)
  4. (D)
Question 19 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

In the figure, link 2 rotates with constant angular velocity $\omega_2$. A slider link 3 moves outwards with a constant relative velocity VQ/p, where Q is a point on slider 3 and P is a point on link 2. The magnitude and direction of Coriolis component of acceleration are

  1. 2 $\omega_2$VQ/P; direction of VQ/P rotated by 90o in the direction of $\omega_2$
  2. $\omega_2$VQ/P; direction of VQ/P rotated by 90o in the direction of $\omega_2$
  3. 2 $\omega_2$ VQ/P; direction of VQ/P rotated by 90o opposite to the direction of $\omega_2$
  4. $\omega_2$VQ/P; direction of VQ/P rotated by 90o opposite to the direction of $\omega_2$
Question 20 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

A weight of 500 N is supported by two metallic ropes, as shown in the figure. The respective values of tensions T1 and T2 are

  1. 433 N and 250 N
  2. 250 N and 433 N
  3. 353.5 N and 250 N
  4. 250 N and 353.5 N
Question 21 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Saturated vapour is condensed to saturated liquid in a condenser. The heat capacity ratio is Cr = $\frac{^Cmin}{^Cmax}$. The effectiveness (e) of the condenser is

  1. $\frac{1-exp[-NTU(1+C_r)]}{1+C_r}$
  2. $\frac{1-exp[-NTU(1-C_r)]}{1-C_rexp[-NTU(1-C_r)]}$
  3. $\frac{NTU}{1+NTU}$
  4. $1-exp(-NTU)$
Question 22 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Couette flow is characterized by

  1. steady, incompressible, laminar flow through a straight circular pipe
  2. fully developed turbulent flow through a straight circular pipe
  3. steady, incompressible, laminar flow between two fixed parallel plates
  4. steady, incompressible, laminar flow between one fixed plate and the other moving with a constant velocity
Question 23 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

A drill is positioned at point P and it has to proceed to point Q. The coordinates of point Q in the incremental system of defining position of a point in CNC part program will be

  1. (3, 12)
  2. (5, 7)
  3. (7, 12)
  4. (4, 7)
Question 24 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The thermodynamic cycle shown in the figure (T – s diagram) indicates

  1. reversed Carnot cycle
  2. reversed Brayton cycle
  3. vapour compression cycle
  4. vapour absorption cycle
Question 25 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

A rigid container of volume 0.5 m3 contains 1.0 kg of water at 120oC $(v_f=0.00106m^3/kg,v_g=0.8908m^3/kg)$. The state of water is

  1. compressed liquid
  2. saturated liquid
  3. a mixture of saturated liquid and saturated vapour
  4. superheated vapour
Question 26 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

For the given fluctuating fatigue load, the values of stress amplitude and stress ratio respectively are

  1. 100 MPa and 5
  2. 250 MPa and 5
  3. 100 MPa and 0.20
  4. 250 MPa and 0.20
Question 27 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

The strain hardening exponent n of stainless steel SS 304 with distinct yield and UTS values undergoing plastic deformation is

  1. n < 0
  2. n = 0
  3. 0 < n < 1
  4. n = 1
Question 28 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

The number of degrees of freedom of the linkage, as shown in the figure, is

  1. – 3
  2. 0
  3. 1
  4. 2
Question 29 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

A gear train is made up of five spur gears, as shown in the figure. Gear 2 is driver and gear 6 is driven member. N2, N3, N4, N5 and N6 represent number of teeth on gears 2, 3, 4, 5 and 6, respectively. Which of the following gears act(s) as idler(s)?

  1. Only 3
  2. Only 4
  3. Only 5
  4. Both 3 and 5
Question 30 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Three parallel pipes connected at the two ends have flow-rates Q1, Q2 and Q3, and the corresponding frictional head losses are hL1, hL2 and hL3, respectively. The correct expressions for total flow rate (Q) and frictional head loss across the two ends (hL) are

  1. Q = Q1 + Q2 + Q3; hL = hL1 + hL2 + hL3
  2. Q = Q1 + Q2 + Q3; hL = hL1 = hL2 = hL3
  3. Q = Q1 = Q2 = Q3; hL = hL1 + hL2 + hL3
  4. Q = Q1 = Q2 = Q3; hL = hL1 = hL2 = hL3
Question 31 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Orthogonal turning of a mild steel tube with a tool of rake angle 10o is carried out at a feed of 0.14 mm/rev. If the thickness of the chip produced is 0.28 mm, the respective values of shear angle and shear strain will be

  1. $28^020'and2.19$
  2. $22^020'and3.53$
  3. $24^030'and4.19$
  4. $37^020'and5.19$
Question 32 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Which of the following statements are TRUE when the cavitation parameter $\sigma$= 0?

  1. The local pressure is reduced to vapour pressure.
  2. Cavitation starts.
  3. Boiling of liquid starts.
  4. Cavitation stops.
  1. 1, 2 and 4
  2. Only 2 and 3
  3. Only 1 and 3
  4. 1, 2 and 3
Question 33 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

A solid sphere 1 of radius r is placed inside a hollow, closed hemispherical surface 2 of radius ‘4r ’. The shape factor F2-1 is

  1. $\frac{1}{12}$
  2. $\frac{1}{2}$
  3. 2
  4. 12
Question 34 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

The given figure shows a single degree of freedom system. The system consists of a massless rigid bar OP hinged at O and a mass m at end P. The natural frequency of vibration of the system is

  1. $f_n=\frac{1}{2\pi}\sqrt{\frac{k}{4m}}$
  2. $f_n=\frac{1}{2\pi}\sqrt{\frac{k}{4\pi}}$
  3. $f_n=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$
  4. $f_n=\frac{1}{2\pi}\sqrt{\frac{2k}{m}}$
Question 35 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Maximize Z = 3X1+ 2X2
Subject to
–2X1 + 3X2 $\leq$ 9
X1 – 5X2 $\geq$ – 20
X1, X2 $\geq$ 0
The above problem has

  1. unbounded solution
  2. infeasible solution
  3. alternative optimum solution
  4. degenerate solution
Question 36 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

In a CNC milling operation, the tool has to machine the circular arc from point (20, 20) to (10, 10) at sequence number 5 of the CNC part program. If the center of the arc is at (20, 10) and the machine has incremental mode of defining position coordinates, the correct tool path command is

  1. N05 G90 G01 X – 10 Y – 10 R10
  2. N05 G91 G03 X – 10 Y – 10 R10
  3. N05 G90 G03 X20 Y20 R10
  4. N05 G91 G02 X20 Y20 R10
Question 37 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

Laplace transform of the function f (t) is given by
F(s) = L{f (t)} = $\int\limits_0^\infty f(t)e^{-st}dt.$
Laplace transform of the function shown below is given by

  1. $\frac{1-e^{-2_s}}{s}$
  2. $\frac{1-e^{-s}}{2s}$
  3. $\frac{2-2e^{-s}}{s}$
  4. $\frac{1-2e^{-s}}{s}$
Question 38 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

For the matrix P = $\begin{bmatrix}
\ 4+3i & -i \
\ i & 4-3i \
\end{bmatrix}$, where i = $\sqrt{-1}$, the inverse of matrix P is

  1. $\frac{1}{24}\begin{bmatrix} \ 4-3i & i \\ \ -i & 4+3i \\ \end{bmatrix}$
  2. $\frac{1}{25}\begin{bmatrix} \ i & 4-3i \\ \ 4+ 3i & -i \\ \end{bmatrix}$
  3. $\frac{1}{24}\begin{bmatrix} \ 4+3i & -i \\ \ i & 4-3i \\ \end{bmatrix}$
  4. $\frac{1}{25}\begin{bmatrix} \ 4+3i & -i \\ \ i & 4-3i \\ \end{bmatrix}$
Question 39 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

A brick wall $\bigg(k=0.9\frac{w}{m.k}\bigg)$ of thickness 0.18 m separates the warm air in a room from the cold ambient air. On a particular winter day, the outside air temperature is -5oC and the room needs to be maintained at 27oC. The heat transfer coefficient associated with outside air is 20$\frac{W}{m^2k}$. Neglecting the convective resistance of the air inside the room, the heat loss (in $\frac{W}{m^2}$) is

  1. 88
  2. 110
  3. 128
  4. 160
Question 40 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

A shaft of length 90 mm has a tapered portion of length 55 mm. The diameter of the taper is 80 mm at one end and 65 mm at the other. If the taper is made by tailstock set over method, the taper angle and the set over respectively are

  1. $15^032'and12.16mm$
  2. $18^032'and15.66mm$
  3. $11^022'and10.26mm$
  4. $10^032and14.46mm$
Question 41 Multiple Choice (Single Answer)

Directions: Carry Two Marks Each.

The value of moment of inertia of the section, as shown in the figure, about the axis XX is

  1. 8.5050 x 106 mm4
  2. 6.8850 x 106 mm4
  3. 7.7625 x 106 mm4
  4. 8.5725 x 106 mm4
Question 42 Multiple Choice (Single Answer)

Directions: Carry One Mark Each.

Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be held to complete the league round of matches?

  1. 20
  2. 10
  3. 8
  4. 5
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