GATE XE (Engineering Sciences) 2014 Question Paper & Solutions

Question 1

A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is

Accepted Answer

understanding

Answer

meaning

Answer

concentration

Answer

stability

Question 2

Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive.

Accepted Answer

virtues

Answer

vice

Answer

choices

Answer

strength

Question 3

Rajan was not happy that Sajan decided to do the project on his own. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of the statements below is logically valid and can be inferred from the above sentences?

Accepted Answer

Rajan had believed that Sajan and he would be working together.

Answer

Rajan has decided to work only in a group.

Answer

Rajan and Sajan were formed into a group against their wishes.

Answer

Sajan had decided to give in to Rajan’s request to work with him.

Question 4

If y = 5x2 + 3, then the tangent at x = 0, y = 3

Accepted Answer

is parallel to the x-axis

Answer

passes through x = 0, y = 0

Answer

has a slope of +1

Answer

has a slope of −1

Question 5

A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes?

Accepted Answer

1300

Question 6

Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK

Accepted Answer

OYEIK

Answer

ALRVX

Answer

EPVZB

Answer

ITZDF

Question 7

Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal’s floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct? Anuj Bhola Chandan Dilip Eswar Faisal

Accepted Answer

2 6 5 1 3 4

Answer

6 2 5 1 3 4

Answer

4 2 6 3 1 5

Answer

2 4 6 1 3 5 GA

Question 8

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

Accepted Answer

180

Question 9

One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft?

Accepted Answer

1.25

Answer

3.0

Answer

2.5

Answer

1.5

Question 10

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 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 estimated with better confidence than February rainfall (iv) In August, there is at least 500 mm of rainfall

Accepted Answer

(i) and (iii)

Answer

(i) and (ii)

Answer

(ii) and (iii)

Answer

(iii) and (iv)

Question 11

If 1, 0, and -1 are the eigenvalues of a 3 3× matrix A, then the trace of A A 5 2 + is equal to ______________.

Accepted Answer

2

Question 12

Which of the following is a solution of the differential equation ? 0 ), sin(ln 4 ' '' 2 > = + + x x y xy y x

Accepted Answer

) cos(ln ln 2 x x y − =

Answer

) sin(ln 2 x x y =

Answer

) sin(ln 2 x x y − =

Answer

) cos(ln ln 2 x x y =

Question 13

At , 0 = z the complex function 2| | ) ( z z z f =

Accepted Answer

satisfies the Cauchy-Riemann equations and is differentiable

Answer

satisfies the Cauchy-Riemann equations but is not differentiable.

Answer

does not satisfy the Cauchy-Riemann equations but is differentiable.

Answer

does not satisfy the Cauchy-Riemann equations and is not differentiable.

Question 14

Ten chocolates are distributed randomly among three children standing in a row. The probability that the first child receives exactly three chocolates is

Accepted Answer

9 10 3 2 5×

Answer

9 11 3 2 5×

Answer

9 3 1

Answer

3 1

Question 15

Let the function R f → ] 5 ,0 [: be defined by = ) (x f ≤ ≤ + < ≤ + < ≤ + .5 2 , 3 23 3 2 2 1 ,5 2 1 0 ,5 2 3 2 x x x x x x The number of points where f is not differentiable in (0, 5) , is ___________. XE (GATE 2014)

Accepted Answer

1

Question 16

An integrating factor of the differential equation 0 ) ( ) 3 ( 3 3 2 3 3 2 = − + + + dy xy e y x dx y y e y x y y is

Accepted Answer

3 1 y

Answer

y 1

Answer

2 1 y

Answer

y ln

Question 17

If a cubic polynomial passes through the points (0, 1), (1, 0), (2, 1) and (3, 10), then it also passes through the point

Accepted Answer

) 2 ,1 ( − −

Answer

) 11 ,2 ( − −

Answer

) 4 ,1 ( − −

Answer

) 23 ,2 ( − −

Question 18

Let the function R f → ∞) ,0 [: be such that 4 3 8 ) ( 2 + + = ′ x x x f for 0 > x and .1 ) 0 ( = f Then )1( f lies in the interval

Accepted Answer

[2, 3]

Answer

[0, 1]

Answer

[4, 5]

Answer

[6, 7]

Question 19

The perimeter of a rectangle having the largest area that can be inscribed in the ellipse 1 32 8 2 2 = +y x , is ________.

Accepted Answer

24

Question 20

If the work done in moving a particle once around a circle 4 2 2 = +y x under the force field j ax y i ay x y x F ) ) ρ ) 2 ( ) 2 ( ) , ( + + − = is π 16 , then a is equal to _________. XE (GATE 2014)

Accepted Answer

2

Question 21

Let r and s be real numbers. If = 0 3 0 2 0 2 1 s r A and − = 1 1 1 s b , then the system of linear equations b AX = has

Accepted Answer

infinitely many solutions for . 2 2 = =r s XE (GATE 2014)

Answer

no solutions for . 2r s ≠

Answer

infinitely many solutions for . 2 2 ≠ =r s

Answer

a unique solution for . 2 2 = =r s

Question 22

A dam with a curved shape is shown in the figure. The cross sectional area of the dam (shaded portion) is 100 m2 and its centroid is at 10 x = m. The vertical component of the hydrostatic force, zF , is acting at a distance p x . The value of p x is ____ m.

Accepted Answer

7

Question 23

For an unsteady incompressible fluid flow, the velocity field is ( ) 2 ˆ ˆ 3 3 6 V x t i xyt j = + − ρ , where x , y are in meters and t is in seconds. Acceleration in m/s2 at the point 10 x = m and 0 y = , as measured by a stationary observer is

Accepted Answer

303

Answer

162

Answer

43

Answer

13

Question 24

For an incompressible flow, the existence of components of acceleration for different types of flow is described in the table below. Type of Flow Components of Acceleration P: Steady and uniform 1: Local exists, convective does not exist Q: Steady and non-uniform 2: Both exist R: Unsteady and uniform 3: Both do not exist S: Unsteady and non-uniform 4: Local does not exist, convective exists Which one of the following options connecting the left column with the right column is correct?

Accepted Answer

P – 3; Q – 4; R – 1; S – 2 15 m 40 m O G px x x z zF XE (GATE 2014)

Answer

P – 1; Q – 4; R – 3; S – 2

Answer

P – 4; Q – 1; R – 2; S – 3

Answer

P – 3; Q – 2; R – 1; S – 4

Question 25

Velocity in a two-dimensional flow field is specified as: 2 2 ; u x y v y x = = − . The magnitude of the rate of angular deformation at a location ( 2 x = m and 1 y = m) is ____ s-1.

Accepted Answer

3

Question 26

For a plane irrotational flow, equi-potential lines and streamlines are

Accepted Answer

at an angle of 90o to each other.

Answer

parallel to each other.

Answer

at an angle of 45o to each other.

Answer

at an angle of 60o to each other.

Question 27

Flow around a Rankine half-body is represented by the superposition of

Accepted Answer

source and uniform flows.

Answer

source and vortex flows.

Answer

vortex and uniform flows.

Answer

source, vortex and uniform flows.

Question 28

It is required to carry out model studies on a boat having a characteristic length of 3.6 m and travelling at a speed of 3 m/s. Assume the acceleration due to gravity as 10 m/s2 and neglect the effects due to viscous and surface tension forces. The value of appropriate non-dimensional number is ____.

Accepted Answer

0.48 to 0.52

Question 29

Which one of the following velocity profiles typically represents a fully developed incompressible, turbulent flow in a pipe?

Accepted Answer

Answer

XE (GATE 2014)

Question 30

Consider an incompressible, laminar flow past a circular cylinder of diameter d . The flow is uniform at the far upstream. Which one of the following figures typically represents the wake velocity profile just downstream of the cylinder?

Accepted Answer

Answer

d d d d XE (GATE 2014)

Question 31

A container of square cross-section is partially filled with a liquid of density 1 ρ . The cylinder is intended to float in another liquid of density 2 ρ as shown in the figure. The distance between metacentre and centre of buoyancy is sub I V , where I and sub V are area moment of inertia of the cross-section and submerged volume, respectively. Neglect the weight of the container. Which one of the following is the correct condition for stability?

Accepted Answer

2 1 1 2 1 0 6 b h h b ρ ρ ρ ρ − − >

Answer

2 1 1 2 1 0 6 b h h b ρ ρ ρ ρ − + >

Answer

2 1 1 2 1 0 6 b h h b ρ ρ ρ ρ + − >

Answer

2 1 1 2 1 0 6 b h h b ρ ρ ρ ρ + + >

Question 32

In a steady state two-dimensional potential flow field due to a point source, the acceleration of a particle at a distance r from the point source is

Accepted Answer

proportional to 3 r −.

Answer

proportional to 1 r−.

Answer

proportional to r .

Answer

a constant.

Question 33

Velocity in a two-dimensional flow at time t and location ( ) ,x y is described as: ( ) 2 ˆ ˆ 3 1 V t i x j = + − ρ . The equation for the path line of a particle passing through the point (1,0) at 0 t = is

Accepted Answer

( ) 4 3 1 64 0 x y − − =

Answer

4 3 4 0 x y − =

Answer

( ) 3 4 1 2 0 x y − − =

Answer

( ) 4 3 1 16 0 x y + − = h b XE (GATE 2014)

Question 34

The gravity driven flow over a hump of height h in a canal is shown in the figure. The height of the free surface from the canal bed at upstream of the hump is H . The free surface height reduces to 1 H above the hump. Assuming the canal bed to be horizontal, the discharge per unit width is given by

Accepted Answer

ඩ 2𝑔𝑔(𝐻𝐻−𝐻𝐻1 −ℎ) 1 𝐻𝐻1 2 −1 𝐻𝐻2

Answer

ඩ 2𝑔𝑔ℎ 1 (𝐻𝐻1 + ℎ)2 −1 𝐻𝐻2

Answer

ඩ 2𝑔𝑔(𝐻𝐻−𝐻𝐻1) 1 (𝐻𝐻1 + ℎ)2 −1 𝐻𝐻2

Answer

ඩ 2𝑔𝑔(𝐻𝐻−𝐻𝐻1) 1 𝐻𝐻1 2 −1 𝐻𝐻2

Question 35

Steady state incompressible flow through a pipe network is shown in the figure. Inlets marked as (1), (2) and (3) and exit marked as (4), are shown with their respective diameters. The exit flow rate at (4) is 0.1 m3/s. A 20% increase in flow rate through (3) results in a 10% increase in flow rate through (4). The original velocity through inlet (3) is _____ m/s. H h 1 H 5 cm 10 cm (3) (2) (1) (4) XE (GATE 2014)

Accepted Answer

17.55 to 17.75

Question 36

A reducing elbow is used to deflect water upward by 30o as shown in the figure. The mass flow rate at the inlet is 14 kg/s. Water is entering at a gauge pressure of 200 kPa and exits to the atmosphere. The cross-sectional area is 113 cm2 at the inlet and 7 cm2 at the exit. Density of water and acceleration due to gravity are 1000 kg/m3 and 10 m/s2, respectively. Magnitude of x - component of the water force on the elbow is ____ N.

Accepted Answer

2033 to 2036

Question 37

A source with a strength of 1k and a vortex with a strength of 2k are located at the origin. The resultant velocity at a radial distance r from the origin due to the superposition of the source and vortex is expressed as

Accepted Answer

2 2 1 2 k k r +

Answer

1 2 k k r +

Answer

2 2 1 2 k k r −

Answer

1 2 k k r −

Question 38

Velocity potential for an incompressible fluid flow is given as: ( ) 2 2 2 2 x y y φ = + − . Assume the value of stream function at the origin to be zero. The value of stream function at [( ) ( ) , 2,2 x y ≡ ] is ____.

Accepted Answer

8

Question 39

The model of a conduit is scaled to 1/100 of the actual size. Seawater is used in the prototype and fresh water is used in the model. Velocity in the prototype is 0.5 m/s. Density and dynamic viscosity of the seawater are 1025 kg/m3 and 1.07 × 10-3 kg/m-s, respectively. Density and dynamic viscosity of fresh water are 1000 kg/m3 and 1 × 10-3 kg/m-s, respectively. Assume the viscous forces to be dominant. The velocity to be maintained in the model to ensure dynamic similarity is____ m/s.

Accepted Answer

47.52 to 48.50

Question 40

A fluid is flowing through a pipe of circular cross-section. Reynolds number of the flow is 1600. The head loss over a 45 m length of the pipe is 0.6 m. The average flow velocity of the fluid is 1 m/s and the acceleration due to gravity is 10 m/s2. The diameter of the pipe is ____ m. XE (GATE 2014)

Accepted Answer

0.145 to 0.155

Question 41

Consider a laminar flow over a flat plate of width w . At Section 1-1, the velocity profile is uniform as shown in the figure. The x -direction velocity profile at Section 2-2 is given by 2 2 , u y y U δ δ = − where δ is the boundary layer thickness. The volume flow rate through Section 2-2 is given by

Accepted Answer

2 3U wδ

Answer

1 2U wδ

Answer

1 3U wδ

Answer

U wδ

Question 42

A cube of weight W and side a falls at a constant speed in a medium as shown in the figure. If the medium is air (mass density =𝜌𝜌air ) let air U be the velocity of the cube. If the medium is water (mass density =𝜌𝜌water ) let water U be the velocity of the cube. Neglecting the buoyancy force and assuming drag coefficient to be same for both cases, the ratio of velocities, air water U U is given by

Accepted Answer

water air ρ ρ

Answer

air water ρ ρ

Answer

air water ρ ρ

Answer

1 δ 1 1 2 2 U U ( ) u y x y a W XE (GATE 2014)

Question 43

Water is flowing through a venturimeter having a diameter of 0.25 m at the entrance (Station 1) and 0.125 m at the throat (Station 2) as shown in the figure. A mercury manometer measures the piezometric head difference between Stations 1 and 2 as 1.3505 m. The loss of head between these two stations, is 1/7 times the velocity head at the Station 2. Assume the acceleration due to gravity to be 10 m/s2. The velocity of water at the throat is ____ m/s. • • 1 2 diameter 0.125 m diameter 0.25m Mercury Manometer XE (GATE 2014)

Accepted Answer

4.8 to 5.2

Question 44

A steel wire of diameter 5 mm is bent around a cylindrical drum of radius 0.5 m. The steel wire has modulus of elasticity of 200 GPa. Find the bending moment in the wire in N-m.

Accepted Answer

12.20 to 12.22

Question 45

A compressed air tank having an inner diameter of 480 mm and a wall thickness of 8 mm is formed by welding two steel hemispheres. If the allowable shear stress in the steel is 40 MPa, find the maximum permissible pressure (in MPa) inside the tank.

Accepted Answer

5.3 to 5.4

Question 46

A point in a body is subjected to a bi-axial state of stress, equal in magnitude but opposite in nature. On a plane inclined at an angle 45° with respect to x-axis (passing through the point), the

Accepted Answer

shear stress is maximum and normal stress is zero

Answer

shear and normal stresses are zero

Answer

normal stress is maximum and shear stress is zero

Answer

shear stress is maximum and normal stress is non-zero

Question 47

The Euler’s buckling load of a column fixed at both the ends is P. If one of the ends is made free, the buckling load shall change to

Accepted Answer

P/16

Answer

P/8

Answer

P/4

Answer

P/2 R = 0.5 m d = 5 mm XE (GATE 2014)

Question 48

For the pin jointed truss, find the axial force (in kN) in the member 2-5.

Accepted Answer

0

Question 49

A weightless beam subjected to two point loads is shown in the figure below. The shear force diagram of the beam is

Accepted Answer

Answer

10 kN 10 kN 2 m 1 m 1 m 10 kN 10 kN 10 kN 10 kN 5 kN 5 kN 5 kN 10 kN XE (GATE 2014)

Question 50

The supporting structure of a water tank is made of reinforced concrete (RC) with a tubular cross section of inner diameter di, outer diameter do, height l, and Young’s modulus E. The mass of the tank is m. If mass of the supporting structure is neglected, then the natural frequency of the water tank in transverse direction is

Accepted Answer

ට3𝜋𝜋𝜋𝜋൫𝑑𝑑𝑜𝑜 − 4 𝑑𝑑𝑖𝑖 4൯ 64𝑙𝑙3𝑚𝑚

Answer

ට𝜋𝜋𝜋𝜋൫𝑑𝑑𝑜𝑜 − 4 𝑑𝑑𝑖𝑖 4൯ 8𝑙𝑙3𝑚𝑚

Answer

) ට384𝜋𝜋𝜋𝜋൫𝑑𝑑𝑜𝑜 − 4 𝑑𝑑𝑖𝑖 4൯ 360𝑙𝑙3𝑚𝑚

Answer

ට𝜋𝜋𝜋𝜋൫𝑑𝑑𝑜𝑜 − 4 𝑑𝑑𝑖𝑖 4൯ 64𝑙𝑙3𝑚𝑚

Question 51

A mass is attached to a spring and placed horizontally in a frictionless surface. A simple pendulum has been pivoted to the mass. The degree of freedom of this system is

Accepted Answer

2

Answer

1

Answer

3

Answer

4 X y x l XE (GATE 2014)

Question 52

Consider the following two statements Statement 1: A body of weight W falls from a height h and strikes the ground. If the body starts from rest, the velocity with which it strikes the ground is ඥ2𝑔𝑔ℎ , where g is the acceleration due to gravity. Statement 2: If the same body (initially at rest) slides without friction along an inclined plane PQ (angle of inclination α) starting from an elevation h above point Q, then its velocity at point Q is ඥ2𝑔𝑔ℎ The correct option is

Accepted Answer

Both statements 1 and 2 are true

Answer

Statement 1 is true and 2 is false

Answer

Statement 1 is false and 2 is true

Answer

Both statements 1 and 2 are false W h h P Q W α XE (GATE 2014)

Question 53

A composite bar of length ‘L’ is made of a centrally placed steel plate (50 mm wide x 10 mm thick) with two copper plates (each 30 mm wide x 5 mm thick) connected rigidly on each side. If the temperature of the composite bar is raised by 50°C, find the stress developed in each copper plate in MPa. (For Steel: Es = 2x105 MPa and αs= 12x10-6 /°C; For Copper: Ec = 1x105 MPa and αc= 17x10-6 /°C)

Accepted Answer

19.1 to 19.3

Question 54

The vertical deflection at the free end of the cantilever beam as shown in figure is

Accepted Answer

1400/3EI

Answer

1400/EI

Answer

200/EI

Answer

100/EI

Question 55

A hollow shaft and a solid shaft have the same length and the same outer radius R. The inner radius of the hollow shaft is 0.6 R. Assuming that both the shafts are made of same material and are subjected to the same torque, find the ratio of shear stress in hollow shaft to that in solid shaft.

Accepted Answer

1.14 to 1.16

Question 56

A beam with overhangs carries one point load acting downwards and the other upward. The clockwise moment Pb is applied at each support. The bending moment at the midpoint of the beam is

Accepted Answer

0

Answer

PL/2

Answer

PL

Answer

PbL L Steel plate 5 mm 5 mm Copper plate Copper plate 10 mm 100 kN EI = flexural rigidity 1 m 2 m L P P b b Pb Pb XE (GATE 2014)

Question 57

A cantilever beam of length L supports a concentrated load P at the free end. The cross section of the beam is rectangular with constant width b and varying depth h. The depth h of this idealized cantilever beam varies in such a way that the maximum normal stress at every cross section remains equal to the allowable bending stress. Considering only the bending stresses, the depth hx of the fully stressed beam at any distance x from the free end shall vary

Accepted Answer

with square root of x

Answer

with square of x

Answer

linearly with x

Answer

with cube of x

Question 58

A cantilever beam is subjected to following three different loading conditions: (a) a concentrated load P at its free end, (b) a couple Mo at its free end and (c) both loads acting simultaneously (a) (b) (c) The flexural rigidity of the beam may be assumed as EI. The strain energy due to bending when both loads act simultaneously

Accepted Answer

cannot be determined by applying the principle of superposition and the strain energy is 𝑃𝑃2𝐿𝐿3 6𝐸𝐸𝐸𝐸+ 𝑀𝑀𝑜𝑜2𝐿𝐿 2𝐸𝐸𝐸𝐸+ 𝑃𝑃𝑀𝑀𝑜𝑜 𝐿𝐿2 2𝐸𝐸𝐸𝐸

Answer

can be determined by applying the principle of superposition and the strain energy is 𝑃𝑃2𝐿𝐿3 6𝐸𝐸𝐸𝐸+ 𝑀𝑀𝑜𝑜2𝐿𝐿 2𝐸𝐸𝐸𝐸

Answer

can be determined by applying the principle of superposition and the strain energy is 𝑃𝑃2𝐿𝐿2 6𝐸𝐸𝐸𝐸+ 𝑀𝑀𝑜𝑜𝐿𝐿3 2𝐸𝐸𝐸𝐸

Answer

cannot be determined by applying the principle of superposition and the strain energy is 𝑃𝑃2𝐿𝐿2 6𝐸𝐸𝐸𝐸+ 𝑀𝑀𝑜𝑜𝐿𝐿3 2𝐸𝐸𝐸𝐸+ 𝑃𝑃𝑀𝑀𝑜𝑜 𝐿𝐿2 2𝐸𝐸𝐸𝐸 P L P L Mo L Mo L P XE (GATE 2014)

Question 59

A tapered rod has diameter d1 at one end which reduces uniformly to a diameter d2 over the length (L). If the modulus of elasticity of the material is E, the change in the length of the rod due to the application of axial force (P) is

Accepted Answer

4𝑃𝑃𝑃𝑃 𝜋𝜋𝜋𝜋𝑑𝑑1𝑑𝑑2

Answer

4𝑃𝑃𝑃𝑃 𝜋𝜋𝜋𝜋൫𝑑𝑑12−𝑑𝑑22൯

Answer

𝑃𝑃𝑃𝑃 𝜋𝜋𝜋𝜋𝑑𝑑1𝑑𝑑2

Answer

2𝑃𝑃𝑃𝑃 𝜋𝜋𝜋𝜋൫𝑑𝑑12−𝑑𝑑22൯

Question 60

For a point in a body subjected to a plane stress condition (σx= 100 MPa, σy= 50 MPa and τxy = τyx = 25 MPa), the maximum principal stress in MPa is_____________

Accepted Answer

110.3 to 110.5

Question 61

An isotropic body is subjected to a state of stress given by: σx= 10 MPa and τxy = τyx = −20 MPa. Assuming G = 0.4E, the volumetric strain is

Accepted Answer

5/E

Answer

7.5/E

Answer

10/E

Answer

15/E

Question 62

A block of weight Q rests on an inclined plane and it is attached to a string which runs over a frictionless pulley to carry a block of weight P at its other end. The coefficient of friction between the block of weight Q and the inclined plane is µ. Consider the following cases: Case I: weight Q starts moving down the inclined plane Case II: weight P starts falling down The limiting values of ratio P/Q for Case I and Case II respectively are

Accepted Answer

(sin 𝛼𝛼−𝜇𝜇cos𝛼𝛼) and (sin𝛼𝛼+ 𝜇𝜇cos 𝛼𝛼)

Answer

(𝜇𝜇sin 𝛼𝛼−cos 𝛼𝛼) and (𝜇𝜇sin 𝛼𝛼+ cos 𝛼𝛼)

Answer

(sin 𝛼𝛼+ 𝜇𝜇cos𝛼𝛼) and (sin𝛼𝛼−𝜇𝜇cos 𝛼𝛼)

Answer

(𝜇𝜇sin 𝛼𝛼+ cos 𝛼𝛼) and 𝜇𝜇(sin 𝛼𝛼−cos 𝛼𝛼) XE (GATE 2014)

Question 63

To unload an item from a truck a crane boom is raised with a constant angular velocity of 1 rad/s relative to the cab and then the cab is rotated about a vertical axis with constant angular velocity of 0.5 rad/s. If the length of the boom (OP) is 10 m, the velocity of the tip (P) of the boom in m/s is

Accepted Answer

5 √2 ൫−𝑖𝑖 ො−2 𝑗𝑗̂ + 2𝑘𝑘෠൯

Answer

√2 5 ൫−2𝑖𝑖 ො− 𝑗𝑗̂ + 2𝑘𝑘෠൯

Answer

√2 5 ൫−𝑖𝑖 ො− 2𝑗𝑗̂ + 𝑘𝑘෠൯

Answer

5 √2 ൫−2𝑖𝑖 ො− 𝑗𝑗̂ + 2𝑘𝑘෠൯

Question 64

A block of mass 5 kg moves up on a smooth inclined plane with a velocity of 10 m/s in the direction shown. A bullet of mass 60 g travelling at 500 m/s strikes the block centrally and gets embedded in it. The velocity of the block and embedded bullet in m/s immediately after the impact is

Accepted Answer

13.84 at 51.78°

Answer

12.54 at 30°

Answer

13.84 at 30°

Answer

15.62 at 51.78° Z X Y Cab Boom 45° O P 30° x y 500 m/s 10 m/s XE (GATE 2014)

GATE XE (Engineering Sciences) 2014 Question Paper & Solutions

General Aptitude

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Engineering Mathematics

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Question 11

Fluid Mechanics

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Question 22

Solid Mechanics

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Question 22

Thermodynamics

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Question 9