Category: GATE

GATE 2021 Aerospace Engineering Previous Year Paper

General Aptitude (GA) 

Q.1 – Q.5 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong  answer: – 1/3).

Q.1	(i) Arun and Aparna are here.  (ii) Arun and Aparna is here.  (iii) Arun’s families is here.   (iv) Arun’s family is here.   Which of the above sentences are grammatically CORRECT?
(A)	(i) and (ii)
(B)	(i) and (iv)
(C)	(ii) and (iv)
(D)	(iii) and (iv)

Q.2	The mirror image of the above text about the x-axis is
(A)
(B)
(C)
(D)

Q.3	Two identical cube shaped dice each with faces numbered 1 to 6 are rolled  simultaneously. The probability that an even number is rolled out on each  dice is:
(A)	136
(B)	112
(C)	18
(D)	14

Q.4	⊕and ⊙ are two operators on numbers p and q such that  p ⊙ q = p − q, and p⊕ q=p × q Then, (9⊙ (6 ⊕ 7)) ⊙ (7 ⊕ (6 ⊙ 5))=
(A)	40
(B)	-26
(C)	-33
(D)	-40

Q.5	Four persons P, Q, R and S are to be seated in a row. R should not be seated  at the second position from the left end of the row. The number of distinct  seating arrangements possible is:
(A)	6
(B)	9
(C)	18
(D)	24

Q. 6 – Q. 10 Multiple Choice Question (MCQ), carry TWO marks each 

(for each wrong  answer: – 2/3).

Q.6	On a planar field, you travelled 3 units East from a point O. Next you  travelled 4 units South to arrive at point P. Then you travelled from P in the  North-East direction such that you arrive at a point that is 6 units East of  point O. Next, you travelled in the North-West direction, so that you arrive  at point Q that is 8 units North of point P.  The distance of point Q to point O, in the same units, should be _____
(A)	3
(B)	4
(C)	5
(D)	6

Q.7	The author said, “Musicians rehearse before their concerts. Actors rehearse  their roles before the opening of a new play. On the other hand, I find it  strange that many public speakers think they can just walk on to the stage  and start speaking. In my opinion, it is no less important for public speakers  to rehearse their talks.” Based on the above passage, which one of the following is TRUE?
(A)	The author is of the opinion that rehearsing is important for musicians, actors  and public speakers.
(B)	The author is of the opinion that rehearsing is less important for public speakers  than for musicians and actors.
(C)	The author is of the opinion that rehearsing is more important only for  musicians than public speakers.
(D)	The author is of the opinion that rehearsal is more important for actors than  musicians.

Q.8	1. Some football players play cricket.    2. All cricket players play hockey.  Among the options given below, the statement that logically follows from  the two statements 1 and 2 above, is:
(A)	No football player plays hockey.
(B)	Some football players play hockey.
(C)	All football players play hockey.
(D)	All hockey players play football.

Q.9	In the figure shown above, PQRS is a square. The shaded portion is formed  by the intersection of sectors of circles with radius equal to the side of the  square and centers at S and Q.  The probability that any point picked randomly within the square falls in the  shaded area is ______
(A)
(B)
(C)
(D)

Q.10	In an equilateral triangle PQR, side PQ is divided into four equal parts, side  QR is divided into six equal parts and side PR is divided into eight equal parts.  The length of each subdivided part in cm is an integer.  The minimum area of the triangle PQR possible, in cm2, is
(A)	18
(B)	24
(C)	48√3
(D)	144√3

Aerospace Engineering (AE) 

Q. 1 – Q. 13 Multiple Choice Question (MCQ), carry ONE marks each  (for each wrong  answer: – 1/3).

Q.1	Consider the differential equationand the boundary Conditions y(0)=1and The solution to this equation is:
(A)	y=(1+ 2x )e−4x
(B)	y =(1− 4x)e−4x
(C)	y =(1+8x )e−4x
(D)	y =  (1 +4x )e−4x

Q.2	u  (x,y)is governed by the following equation The nature of this equation is:
(A)	linear
(B)	elliptic
(C)	hyperbolic
(D)	parabolic

Q.3	Consider the velocity field V=(2x+ 3y)i+(3x +2 y)j. The field V is
(A)	divergence-free and curl-free
(B)	curl-free but not divergence-free
(C)	divergence-free but not curl-free
(D)	neither divergence-free nor curl-free

Q.4	The figure shows schematics of wave patterns at the exit of nozzles A and B  operating at different pressure ratios.            Nozzles A and B, respectively, are said to be operating in:
(A)	over-expanded mode and under-expanded mode
(B)	under-expanded mode and perfectly expanded mode
(C)	perfectly expanded mode and under-expanded mode
(D)	under-expanded mode and over-expanded mode

Q.5	The combustion process in a turbo-shaft engine during ideal operation is:
(A)	isentropic
(B)	isobaric
(C)	isochoric
(D)	isothermal

Q.6	How does the specific thrust of a turbojet engine change for a given flight  speed with increase in flight altitude?
(A)	Increases monotonically
(B)	Decreases monotonically
(C)	Remains constant
(D)	First increases and then decreases

Q.7	How does the propulsion efficiency of a turbofan engine, operating at a  given Mach number and a given altitude, change with increase in  compressor pressure ratio?
(A)	Remains constant
(B)	Increases monotonically
(C)	Decreases monotonically
(D)	First decreases and then increases

Q.8	A solid propellant rocket producing 25 MN thrust is fired for 150 seconds.The specific impulse of the rocket is 2980 Ns/kg. How much propellant is  burned during the rocket operation?
(A)	8390 kg
(B)	82300 kg
(C)	1.26 x 106kg
(D)	11.2 x 106 kg

Q.9	The shape of a supersonic diffuser that slows down a supersonic flow to  subsonic flow is
(A)	converging
(B)	diverging
(C)	diverging–converging
(D)	converging–diverging

Q.10	Uniaxial tension test (see the figure) is conducted on two different samples  prepared with homogeneous, isotropic materials. One of the materials is  brittle, whereas the other is ductile.    Assuming that there is no stress concentration at loading points, the failure  would initiate:
(A)	along x-x in both materials
(B)	along x-x in brittle material and along y-y in ductile material
(C)	along y-y in brittle material and along x-x in ductile material
(D)	along y-y in both materials

Q.11	For the state of stress as shown in the figure, what is the orientation of the  plane with maximum shear stress with respect to the x-axis?
(A)	45o
(B)	-45o
(C)	22.5o
(D)	-22.5o

Q.12	Let VTAS be the true airspeed of an aircraft flying at acertain altitude  where the density of air is ρ, and VEAS be the equivalent airspeed. If ρ0 is  the density of air at sea-level, what is the ratio VTAS/VEAS equal to?
(A)	ρ/ρ0
(B)	ρ0/ρ
(C)
(D)

Q.13	Cm − α variation for a certain aircraft is shown in the figure. Which one of  the following statements is true for this aircraft?
(A)	The aircraft can trim at a positive α and it is stable.
(B)	The aircraft can trim at a positive α, but it is unstable.
(C)	The aircraft can trim at a negative α and it is stable.
(D)	The aircraft can trim at a negative α, but it is unstable.

Q.14 – Q.16 Multiple Select Question (MSQ), carry ONE mark each (no negative  marks).

Q.14	Which of the following statement(s) is/are true across an obliqueshock (in  adiabatic conditions) over a wedge shown below?
(A)	Total pressure decreases
(B)	Mach number based on velocity tangential to the shock decreases
(C)	Total temperature remains constant
(D)	Mach number based on velocity tangential to the shock remains the same and  that based on velocity normal to the shock decreases

Q.15	Which of the following statement(s) is/are true with regards to Kutta condition for flow past airfoils?
(A)	It is utilized to determine the circulation on an airfoil.
(B)	It is applicable only to airfoils with sharp trailing edge.
(C)	The trailing edge of an airfoil is a stagnation point.
(D)	The flow leaves the trailing edge smoothly.

Q.16	According to the thin airfoil theory, which of the following statement(s)  is/are true for a cambered airfoil?
(A)	The lift coefficient for an airfoil is directly proportional to the absolute angle of  attack.
(B)	The aerodynamic center lies at quarter chord point.
(C)	The center of pressure lies at quarter chord point.
(D)	Drag coefficient is proportional to the square of lift coefficient.

Q.17 – Q.25 Numerical Answer Type (NAT), carry ONE mark each (no negative  marks).

Q.17	___________ (round off to nearest integer).

Q.18	Given that ςis the unit circle in the counter-clockwise direction with its  center at origin, the integral ∮Gz3/4z-i= _______ (round off to three decimal  place).

Q.19

A single degree of freedom spring-mass-damper system is designed to  ensure that the system returns to its original undisturbed position in  minimum possible time without overshooting. If the mass of the system is  10 kg, spring stiffness is 17400 N/m and the natural frequency is 13.2  rad/s, the coefficient of damping of the system in Ns/m is _________ (round  off to nearest integer).

Q.20	Two cantilever beams (Beam 1 and Beam 2) are made of same  homogenous material and have identical cross sections. Beam 1 has length  land Beam 2 has length 2.lRatio of the first natural frequency of Beam 1  to that of Beam 2 is ______ (round off to nearest integer).

Q.21	A free vortex filament (oriented along Z-axis) of strength K = 5 m2/s is placed at the origin as shown in the figure. The circulation around the  closed loop ABCDEFA for this flow is ________ .

Q.22

A thin-walled cylindrical tank with closed ends, made of homogeneous and  isotropic material, is pressurized internally. If the hoop (circumferential)  strain developed in the material is thrice the value of the axial strain then  the Poisson’s ratio of the material is __________ (correct up to one decimal  place).

Q.23

A jet aircraft has the following specifications: wing loading = 1800 N/m2,  wing area = 30 m2, drag polar CD= 0. 02+ 0.04CL2, and CLmax= 1.6.  Take density of air at sea level as 1.225 kg/m3. The speed at which the aircraft achieves maximum endurance in a steady  and level flight at sea level is _______ m/s (round off to two decimal places).

Q.24

An aircraft with twin jet engines has the following specifications: Thrust produced (per engine) = 8000 N Spanwise distance between the two engines = 10 m Wing area = 50 m2, Wing span = 10 m Rudder effectiveness, Cngr = −0.002 /deg Density of air at sea level = 1.225 kg/m3 The rudder deflection, in degrees, required to maintain zero sideslip at 100  m/s in steady and level flight at sea level with a non-functional right engine  is ________ (round off to two decimal places).

Q.25	The velocity required to launch a space shuttle from the surface of the  earth to achieve a circular orbit of 250 km altitude is _______ (round off to  two decimal places).  For earth, Gme = 398,600.4km3/s2 and surface radius Ro= 6378.14 km.

Q.26 – Q.30 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong  answer: – 2/3).

Q.26	A rigid massless rod pinned at one end has a mass mattached to its other  end.The rod is supported by a linear spring of stiffness k as shown in the  figure.The natural frequency of this system is:
(A)
(B)
(C)
(D)

Q.27	The figure shows three glasses P, Q and R with water and floating ice cube.  Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel  ball embedded in it and glass R has an ice cube with an air bubble. After  the ice cube melts, the level of water in glasses P, Q and R, respectively:
(A)	remains same, increases, and decreases
(B)	increases, decreases, and increases
(C)	remains same, decreases, and decreases
(D)	remains same, decreases, and increases

Q.28	To estimate aerodynamic loads on an aircraft flying at 100 km/h at  standard sea-level conditions, a one-fifth scale model is tested in a variable density wind tunnel ensuring similarity of inertial and viscous forces. The  pressure used in the wind tunnel is 10 times the atmospheric pressure.  Assuming ideal gas law to hold and the same temperature conditions in  model and prototype, the velocity needed in the wind tunnel test-section is  ______________.
(A)	25 km/h
(B)	50 km/h
(C)	100 km/h
(D)	20 km/h

Q.29	The figure shows schematic of a set-up for visualization of non-uniform  density field in the test section of a supersonic wind tunnel. This technique  of visualization of high speed flows is known as:
(A)	schlieren
(B)	interferometry
(C)	shadowgraph
(D)	holography

Q.30	For a conventional fixed-wing aircraft in a 360° inverted vertical loop  maneuver, what is the load factor (n) at the topmost point of the loop?  Assume the flight to be steady at the topmost point.
(A)	n =1
(B)	n <1
(C)	n =−1
(D)	n >−1

Q.31 – Q.36 Multiple Select Question (MSQ), carry TWO mark each (no negative  marks).

Q.31	Which of the following statement(s) is/are true about the function defined  asf (x)=e x − | cos | x for x > 0?
(A)	Differentiable at x= π/2
(B)	Differentiable at x = π
(C)	Differentiable at x= 3π/2
(D)	Continuous at x = 2π

Q.32	A two degree of freedom spring-mass system undergoing free vibration with generalized coordinates x1and x 2 has natural frequencies ω1=233.9 rad/s and ω2=324.5 rad/s, respectively. The corresponding mode shapes  are . If the system is disturbed with certain deflections and zero initial velocities, then which of the following  statement(s) is/are true?
(A)	An initial deflection of x1(0) 6.32 =cm and x2  (0) 3.16 = −cm would make the  system oscillate with only the second natural frequency.
(B)	An initial deflection of x1 (0) 2 =cm and x 2(0) 6.32 = −cmwould make the  system oscillate with only the first natural frequency.
(C)	An initial deflection of x1(0) 2 =cm and x2 (0) 2 = −cm would make the system oscillate with a linear combination of first and second natural frequencies.
(D)	An initial deflection of x1 (0) 1 =cm an x2 (0) 6.32 = −cm would make the system oscillate with only the first natural frequency.

Q.33	A shock moving into a stationary gas can be transformed to a stationary  shock by a change in reference frame, as shown in the figure. Which of the  following is/are true relating the flow properties in the two reference  frames?
(A)
(B)
(C)
(D)

Q.34	For a conventional fixed-wing aircraft, which of the following statements  are true?
(A)	Making Cma more negative leads to an increase in the frequency of its short period mode.
(B)	Making Cmq more negative leads to a decreased damping of the short-period  mode.
(C)	The primary contribution towards Cipis from the aircraft wing.
(D)	Increasing the size of the vertical fin leads to a higher yaw damping.

Q.35	Which of the following statement(s) is/are true?
(A)	Service ceiling is higher than absolute ceiling for a piston-propeller aircraft.
(B)	For a given aircraft, the stall speed increases with increase in altitude.
(C)	Everything else remaining the same, a tailwind increases the range of an  aircraft.
(D)	For a jet aircraft constrained to fly at constant altitude, there exists an altitude  where its range is maximum.

Q.36	A conventional fixed-wing aircraft, with a horizontal tail and vertical fin,  in steady and level flight is subjected to small perturbations. Which of the  following statement(s) is/are true?
(A)	Vertical fin has a stabilizing effect on the lateral stability of the aircraft.
(B)	Vertical fin has a destabilizing effect on the directional stability of the aircraft.
(C)	Presence of wing anhedral increases the lateral stability of the aircraft.
(D)	Horizontal tail has a stabilizing effect on the longitudinal static stability of the  aircraft.

Q.37 – Q.55 Numerical Answer Type (NAT), carry TWO mark each (no negative  marks).

Q.37	The ratio of the product of eigenvalues to the sum of the eigenvalues of the  given matrix   is ______ (round off to nearest integer).

Q.38	The definite integral is evaluated using four equal intervals by two  methods – first by the trapezoidal rule and then by the Simpson’s one third rule. The absolute value of the difference between the two  calculations is _______ (round off to two decimal places).

Q.39	The deflection y of a certain beam of length land uniform weight per unit length w, is given as where x is the distance from the point of support and EI is a constant. The non-dimensional  location x/l, where the deflection of the beam is maximum, is _____ (round  off to two decimal places).

Q.40

A large water tank is fixed on a cart with wheels and a vane (see figure).  The wheels of the cart provide negligible resistance for rolling on the fixed  support. The cart is tied to the fixed support with a thin horizontal rope.  There is a hole of diameter 5 cm on the side of the tank through which a  jet of constant velocity of 10 m/s emerges. The jet of water is deflected by  the attached vane by 60o(see figure). Assume that the jet velocity remains  constant at 10 m/s after emerging from the vane. Take density of water to  be 1000 kg/m3. The tension in the connecting rope is _____ N (round off to  one decimal place).

Q.41	A finite wing of elliptic planform with aspect ratio 10, whose section is a  symmetric airfoil, is placed in a uniform flow at 5 degrees angle of attack.  The induced drag coefficient for the wing is ______ (round off to three  decimal places).

Q.42	Consider a model of a boundary layer with the following velocity profile: The shape factor, defined as the ratio of the displacement thickness to  momentum thickness, for this profile is _____ (round off to 2 decimal  places).

Q.43

An aircraft with a turbojet engine is flying at 270 m/s. The enthalpy of the  incoming air at the intake is 260 kJ/kg and the enthalpy of the exhaust  gases at the nozzle exit is 912 kJ/kg. The ratio of mass flow rates of fuel  and air is equal to 0.019. The chemical energy (heating value) of fuel is  44.5 MJ/kg and the combustion process is ideal. The total loss of heat from  the engine to the ambient is 25 kJ per kg of air. The velocity of the exhaust  jet is __________m/s (round off to two decimal places).

Q.44

Hot gases are generated at a temperature of 2100 K and a pressure of 14  MPa in a rocket chamber. The hot gases are expanded ideally to the  ambient pressure of 0.1 MPa in a convergent-divergent nozzle having a  throat area of 0.1 m2. The molecular mass of the gas is 22 kg/kmol. The  ratio of specific heats (γ) of the gas is 1.32. The value of the universal gas  constant (R0) is 8314 J/kmol-K. The acceleration due to gravity, g, is 9.8  m/s2. The specific impulse of the rocket is _______ seconds (round off to  two decimal places).

Q.45

A twin-spool turbofan engine is operated at sea level (Pa = 1 bar, Ta = 288  K). The engine has separate cold and hot nozzles. During static thrust test  at sea level, the overall mass flow rate of air through the engine and the  cold exhaust temperature are measured to be 100 kg/s and 288 K,  respectively. The parameters for the engine are: Fan pressure ratio = 1.6 Overall pressure ratio = 20 Bypass ratio = 3.0 Turbine entry temperature = 1800 K. The specific heat at constant pressure (Cp) is 1.005 kJ/kg-K and the ratio of  specific heats (γ ) is 1.4 for air.  Assuming ideal fan and ideal expansion in the nozzle, the sea-level static  thrust from the cold nozzle is _____________ kN (round off to two decimal  places).

Q.46

At the design conditions, the velocity triangle at the mean radius of a single  stage axial compressor is such that the blade angle at the rotor exit is equal  to 30°. The absolute velocities at the rotor inlet and exit are equal to 140  m/s and 240 m/s, respectively. The flow velocities relative to the rotor at inlet and exit of the rotor are equal to 240 m/s and 140 m/s, respectively.       The blade speed (U) at the mean radius of the rotor is __________ m/s  (round off to two decimal places).

Q.47

A single stage axial turbine has a mean blade speed of 340 m/s at design  condition with blade angles at inlet and exit of the rotor being 21° and 55°,  respectively. The degree of reaction at the mean radius of the rotor is  equal to 0.4. The annulus area at the rotor inlet is 0.08 m2 and the density  of gas at the rotor inlet is 0.9 kg/m3. The flow rate through the turbine at  these conditions is __________ kg/s (round off to two decimal places).

Q.48

The air flow rate through the gas generator of a turboprop engine is 100  kg/s. The stagnation temperatures at inlet and exit of the combustor are  600 K and 1200 K, respectively. The burner efficiency is 90% and the  heating value of the fuel is 40 MJ/kg. The specific heats at constant  pressure (Cp) for air and burned gases are 1000 J/kg-K and 1200 J/kg-K,  respectively. The flow rate of the fuel being used is _____________ kg/s  (round off to two decimal places). (Note: Do not neglect the fuel flow rate with respect to the air flow rate)

Q.49

A rigid horizontal bar ABC, with roller support at A, is pinned to the  columns BD and CE at points B and C, respectively as shown in figure.  The other end of the column BD is fixed at D, whereas the column CE is  pinned at E. A vertical load P is applied on the bar at a distance ‘a’ from  point B.  The two columns are made of steel with elastic modulus 200 GPa and have a cross section of 1.5 cm x 1.5 cm. The value of ‘a’ for which both columns  buckle simultaneously, is ____________ cm (round off to one decimal  place).

Q.50	A two-cell wing box is shown in the figure. The cell walls are 1.5 mm thick  and the shear modulus G = 27 GPa. If the structure is subjected to a  torque of 12 kNm, then the wall AD will experience a shear stress of magnitude _________ MPa (round off to one decimal place).

Q.51

Two cantilever beams AB and DC are in contact with each other at their  free ends through a roller as shown in the figure. Both beams have a  square cross section of 50 mm x 50 mm, and the elastic modulus E = 70  GPa. If beam AB is subjected to a uniformly distributed load of 20 kN/m,  then the compressive force experienced by the roller is ___________ kN  (round off to one decimal place).

Q.52

A 3 m x 1 m signboard is supported by a vertical hollow pole that is fixed  to the ground. The pole has a square cross section with outer dimension  250 mm. The yield strength of the pole material is 240 MPa. To sustain a  wind pressure of 7.5 kPa, the dimension d of the pole is _________ mm  (round off to nearest integer).  (Neglect the effect of transverse shear and load due to wind pressure  acting on the pole)

Q.53

An airplane weighing 5500 kg is in a steady level flight with a speed of 225  m/s. The pilot initiates a steady pull-up maneuver with a radius of  curvature of 775 m. The location of center of gravity (CG), center of  pressure on wing (CP) and point of action (T) of tail force are marked in  the figure. Use g = 9.81 m/s2. Neglect drag on the tail and assume that tail  force is vertical. Assuming the engine thrust and drag to be equal, opposite  and collinear, the tail force is_____________ kN (round off to one decimal  place).

Q.54

A jet aircraft weighing 10,000 kg has an elliptic wing with a span of 10 m  and area 30 m2. The CDofor the aircraft is 0.025. The maximum speed of  the aircraft in steady and level flight at sea level is 100 m/s. The density of  air at sea level is 1.225 kg/m3, and take g = 10 m/s2. The maximum thrust  developed by the engine at sea level is ______ N (round off to two decimal  places).

Answer Key 

Q. No.	Ans	Q. No.	Ans	Q. No.	Ans	Q. No.	Ans	Q. No.	Ans	Q. No.	Ans	Q. No.	Ans
1	B	1	D	11	D	21	0 to 0	31	B; D	41	0.005 to 0.009	51	2.2 to 2.6
2	B	2	B	12	C	22	0.2 to 0.2	32	B; C	42	4.8 to 5.2	52	232 to 238
3	D	3	B	13	B	23	64.30 to 64.60	33	D	43	605 to 607	53	14.8 to 15.2
4	D	4	A	14	A; B; C	24	6.50 to 6.60	34	A; C; D	44	216 to 220	54	9735 to 9797
5	C	5	B	15	A; B; D	25	7.75 to 7.77 OR  7750.00 to  7770.00	35	B; C; D	45	20 to 22	55	-0.025 to -0.023
6	C	6	A	16	A; B	26	A	36	A; D	46	274 to 282
7	A	7	D	17	0 to 0	27	C	37	8 to 8	47	18.0 to 19.5
8	B	8	C	18	0.02 to 0.03	28	B	38	0.66 to 0.68	48	2.35 to 2.50
9	C	9	D	19	264 to 264 OR  833 to 835	29	C	39	0.41 to 0.43	49	14.0 to 16.0
10	D	10	B	20	4 to 4	30	D	40	98.0 to 98.5	50	2.1 to 2.5

GATE 2020 Mechanical Engineering Previous Year Paper

General Aptitude 

Q1 – Q5 carry one mark each. 

Q. 1 He is known for his unscrupulous ways. He always sheds fox’s crocodile’s crocodile fox ___________ tears to deceive people

(A) fox’s

(B) crocodile’s

(C) crocodile

(D) fox

 

Q. 2 Jofra Archer, the England fast bowler, is______ than accurate. 

(A) more fast 

(B) faster 

(C) less fast 

(D) more faster 

 

Q. 3 Select the word that fits the analogy: 

Build : Building :: Grow : 

(A) Grown 

(B) Grew 

(C) Growth 

(D) Growed 

 

Q. 4 I do not think you know the case well enough to have opinions. Having said that, I agree with your other point. What does the phrase “having said that” mean in the given text? 

(A) as opposed to what I have said 

(B) despite what I have said 

(C) in addition to what I have said 

(D) contrary to what I have said 

 

Q. 5 Define [x] as the greatest integer less than or equal to x, for each x ∈ (-∞, ∞). If y = [x], then area under y for x ∈ [1,4] is_________ 

(A) 1 

(B) 3 

(C) 4 

(D) 6 

Q6 – Q10 carry two marks each. 

Q. 6 Crowd funding deals with mobilization of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project. 

Based on the above paragraph, which of the following is correct about crowd funding? 

(A) Funds raised through unwilling contributions on web-based platforms. 

(B) Funds raised through large contributions on web-based platforms.

(C) Funds raised through coerced contributions on web-based platforms. 

(D) Funds raised through voluntary contributions on web-based platforms.

 

Q. 7 P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as __________.

(A) βα and αβ 

(B) ββ and αα 

(C) αβ and ββ 

(D) βα and ββ 

 

Q. 8 The sum of the first n terms in the sequence 8, 88, 888, 8888, … is ___________

 

Q. 9 Select the graph that schematically represents BOTH y = x^m and y = x^1/m properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1. 

 

Q. 10 The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is ____________

(A) 58.5 % 

(B) 58.8 % 

(C) 59.0 % 

(D) 59.3 % 

Mechanical Engineering

Q1 – Q25 carry one mark each. 

Q. 1 Multiplication of real valued square matrices of same dimension is 

(A) associative 

(B) commutative 

(C) always positive definite 

(D) not always possible to compute 

 

Q. 2 The value of 

 

Q. 3 The Laplace transform of a function f(t) is . Then, f(t) is 

 

Q. 4 Which of the following function f(z), of the complex variable z, is NOT analytic at all the points of the complex plane? 

(A) f(z) = z² 

(B) f(3) = e^z 

(C) f(3) = sin^z 

(D) f(z) = log z 

 

Q. 5 The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load P >0 with no appreciable deformation of the truss (i.e. with no appreciable change in angles between the members), are 

(A) BF and DH only 

(B) BF, DH and GC only 

(C) BF, DH, GC, CD and DE only 

(D) BF, DH, GC, FG and GH only 

 

Q. 6 A single-degree-of-freedom oscillator is subjected to harmonic excitation F(t) = F₀ cos(wt) as shown in the figure. 

The non-zero value of w, for which the amplitude of the force transmitted to the ground will be F₀ is 

 

Q. 7 The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the σ-τ plane is 1 MPa, the Mohr’s circle representation of the state-of-stress is given by 

(A) a circle with a radius equal to principal stress and its center at the origin of the σ-τ plane 

(B) a point on the σ axis at a distance of 10 units from the origin 

(C) a circle with a radius of 10 units on the σ-τ plane 

(D) a point on the t axis at a distance of 10 units from the origin 

 

Q. 8 A four bar mechanism is shown below. 

For the mechanism to be a crank-rocker mechanism, the length of the link PQ can be 

(A) 80 mm 

(B) 200 mm 

(C) 300 mm 

(D) 350 mm 

 

Q. 9 A helical gear with 20° pressure angle and 30° helix angle mounted at the mid span of a shaft that is supported between two bearings at the ends. The nature of the stresses induced in the shaft is 

(A) normal stress due to bending only 

(B) normal stress due to bending in one plane and axial loading; shear stress due to torsion 

(C) normal stress due to bending in two planes and axial loading; shear stress due to torsion 

(D) normal stress due to bending in two planes; shear stress due to torsion 

 

Q. 10 The crystal structure of y iron (austenite phase) is 

(A) BCC 

(B) FCC 

(C) HCP 

(D) BCT 

 

Q. 11 Match the following. 

(A) P-2,0-3, R-4, S-1 

(B) P-1, Q-1, R-3, S-2 

(C) P-3, Q-3, R-1, S-3 

(D) P-4, Q-3, R-2, S-1 

 

Q. 12 The base of a brass bracket needs rough grinding. For this purpose, the most suitable grinding wheel grade specification is 

(A) C30Q12V 

(B) A50G8V 

(C) C90J4B 

(D) A30D12V 

 

Q. 13 In the Critical Path Method (CPM), the cost-time slope of an activity is given by 

 

Q. 14 Froude number is the ratio of 

(A) buoyancy forces to viscous forces 

(B) inertia forces to viscous forces 

(C) buoyancy forces to inertia forces 

(D) inertia forces to gravity forces 

 

Q. 15 Match the following non-dimensional numbers with the corresponding definitions: 

(A) P-1, Q-3, R-2, S-4 

(B) P-3, Q-1, R-2, S-4 

(C) P-4, Q-3, R-1, S-2 

(D) P-3, Q-1, R-4, S-2 

 

Q. 16 The velocity field of an incompressible flow in a Cartesian system is represented by 

Which one of the following expressions for v is valid? 

(A) – 4xz + 6xy 

(B) – 4xy – 4xz 

(C) 4x² – 6xy 

(D) 4xy + 4xz 

 

Q. 17 For an ideal gas, the value of the Joule-Thomson coefficient is 

(A) positive 

(B) negative 

(C) zero 

(D) indeterminate 

 

Q. 18 For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature (1) versus specific entropy (s) diagram. C_p is the specific heat at constant pressure and C_V is the specific heat at constant volume. The ratio of the slopes of the constant pressure and constant volume lines at the point of intersection is 

 

Q. 19 For three vectors are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system, the value of is _____________.

 

Q. 20 A flywheel is attached to an engine to keep its rotational speed between 100 rad/s and 110 rad/s. If the energy fluctuation in the flywheel between these two speeds is 1.05 kJ then the moment of inertia of the flywheel is _____________ (round off to 2 decimal places). kg.m² 

 

Q. 21 A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of 10 grams, attached to four points on the 100 mm radius circle shown in the figure. 

The rotor is driven by a motor at uniform angular speed of 10 rad/s. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is _____________ N (round off to 2 decimal places). 

 

Q. 22 A sheet metal with a stock hardness of 250 HRC has to be sheared using a punch and a die having a clearance of 1 mm between them. If the stock hardness of the sheet metal increases to 400 HRC, the clearance between the punch and the die should be _________ mm. 

 

Q. 23 A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is___________(round off to 2 decimal places). 

 

Q. 24 The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of 6 in a two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the inlet temperature of the first stage, before its entry to the second stage. Air enters the compressor at 300 K and 100 kPa. If the properties of gas are constant, the intercooling pressure for minimum compressor work is _________ kPa (round off to 2 decimal places). 

 

Q. 25 In a concentric tube counter-flow heat exchanger, hot oil enters at 102°C and leaves at 65°C. Cold water enters at 25°C and leaves at 42°C. The log mean temperature difference (LMTD) is ___________ °C (round off to one decimal place). 

Q26 – Q55 carry two marks each. 

Q. 26 The evaluation of the definite integral -11.4x|x|dx by using Simpson’s 1/3^rd (one third) rule with step size h = 0.6 yields 

(A) 0.914 

(B) 1.248 

(C) 0.581 

(D) 0.592 

 

Q. 27 A vector field is defined as 

where, are unit vectors along the axes of a right-handed rectangular /Cartesian coordinate system. The surface integral (where is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the center, and internal and external radii of 1 and 2, respectively, is 

(A) 0 

(B) 2π 

(C) 4π

(D) 8π

 

Q. 28 Bars of square and circular cross-section with 0.5 m length are made of a material with shear strength of 20 MPa. The square bar cross-section dimension is 4 cm × 4 cm and the cylindrical bar cross-section diameter is 4 cm. The specimens are loaded as shown in the figure. 

Which specimen(s) will fail due to the applied load as per maximum shear stress theory? 

(A) Tensile and compressive load specimens 

(B) Torsional load specimen 

(C) Bending load specimen 

(D) None of the specimens 

 

Q. 29 The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness 5 N/m. 

The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity ν of 1.5 m/s perpendicular to the cord. The magnitude of velocity in m/s of the block at the instant the cord is stretched by 0.4 m is 

(A) 0.83 

(B) 1.07 

(C) 1.36 

(D) 1.50 

 

Q. 30 The truss shown in the figure has four members of length 1 and flexural rigidity EI, and one member of length 1/2 and flexural rigidity 4E1. The truss is loaded by a pair of forces of magnitude P, as shown in the figure. 

The smallest value of P, at which any of the truss members will buckle is 

 

Q. 31 A rigid massless rod of length L is connected to a disc (pulley) of mass m and radius r = L/4 through a friction-less revolute joint. The other end of that rod is attached to a wall through a frictionless hinge. A spring of stiffness 2k is attached to the rod at its mid-span. An inextensible rope passes over half the disc periphery and is securely tied to a spring of stiffness k at point C as shown in the figure. There is no slip between the rope and the pulley. The system is in static equilibrium in the configuration shown in the figure and the rope is always taut. 

Neglecting the influence of gravity, the natural frequency of the system for small amplitude vibration is 

 

Q. 32 A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and arc length in mm, respectively are 

(A) 0.45 and 38.84 

(B) 0.39 and 38.84 

(C) 0.39 and 44.72 

(D) 0.45 and 44.72 

 

Q. 33 For an assembly line, the production rate was 4 pieces per hour and the average processing time was 60 minutes. The WIP inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by 30 percent. As a result of this change in the processing time, the WIP inventory 

(A) decreases by 25% 

(B) increases by 25% 

(C) decreases by 30% 

(D) increases by 30% 

 

Q. 34 A small metal bead (radius 0.5 mm), initially at 100°C, when placed in a stream of fluid at 20°C, attains a temperature of 28°C in 4.35 seconds. The density and specific heat of the metal are 8500 kg/m³ and 400 J/kg.K, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in W/m².K) between the metal bead and the fluid stream is 

(A) 283.3 

(B) 299.8 

(C) 149.9 

(D) 449.7 

 

Q. 35 Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is _________ (round off to 2 decimal places). 

 

Q. No. 36 An analytic function of a complex variable z = x + iy (i = √-1) is defined as 

f(z) = x² – y² + i ψ (x, y), 

where ψ(x,y) is a real function. The value of the imaginary part of f(z) at z = (1 + i) is ____________ (round off to 2 decimal places). 

 

Q. 37 In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm, respectively. An axial force F₁ is needed to transmit a torque by a new clutch. However, to transmit the same torque, one needs an axial force F₂ when the clutch wears out. If contact pressure remains uniform during operation of a new clutch while the wear is assumed to be uniform for an old clutch, and the coefficient of friction does not change, then the ratio F₁/F₂ is __________ (round off to 2 decimal places). 

 

Q. 38 A cam with a translating flat-face follower is desired to have the follower motion 

Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than 40 mm anywhere. The minimum permissible base circle radius is ___________ mm (round off to one decimal place). 

 

Q. 39 A rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts, as shown. 

For an external load of 10 kN applied at the tip of the steel bar, the resultant shear load on the bolt at B, is __________ kN (round off to one decimal place). 

 

Q. 40 The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modeled as a cantilever. 

Taking the density of water as 1000 kg/m³, and the acceleration due to gravity as 10 m/s², the maximum absolute bending moment developed in the cantilever is _________ kN·m (round off to the nearest integer). 

 

Q. 41 The magnitude of reaction force at joint C of the hinge-beam shown in the figure is ________ KN (round off to 2 decimal places). 

 

Q. 42 A slot of 25 mm × 25 mm is to be milled in a workpiece of 300 mm length using a side and face milling cutter of diameter 100 mm, width 25 mm and having 20 teeth. For a depth of cut 5 mm, feed per tooth 0.1 mm, cutting speed 35 m/min and approach and over travel distance of 5 mm each, the time required for milling the slot is __________ minutes (round off to one decimal place). 

 

Q. 43 The following data applies to basic shaft system: 

tolerance for hole = 0.002 mm, 

tolerance for shaft = 0.001 mm, 

allowance = 0.003 mm, 

basic size = 50 mm. 

The maximum hole size is ________ mm (round off to 3 decimal places). 

 

Q. 44 A steel part with surface area of 125 cm² is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation: 

1 = 12 + 0.2t 

where, I = current (A) and t = time (minutes). The part is submerged in the plating solution for a duration of 20 minutes for plating purpose. Assuming the cathode efficiency of chromium to be 15% and the plating constant of chromium acid sulphate to be 2.50 × 10^-2 mm/A’s, the resulting coating thickness on the part surface is _________ μm (round off to one decimal place). 

 

Q. 45 In a turning process using orthogonal tool geometry, a chip length of 100 mm is obtained for an uncut chip length of 250 mm. 

The cutting conditions are: cutting speed = 30 m/min, rake angle = 20°. 

The shear plane angle is _________ degrees (round off to one decimal place). 

 

Q. 46 The thickness of a steel plate with material strength coefficient of 210 MPa, has to be reduced from 20 mm to 15 mm in a single pass in a two-high rolling mill with a roll radius of 450 mm and rolling velocity of 28 m/min. If the plate has a width of 200 mm and its strain hardening exponent, n is 0.25, the rolling force required for the operation is _________ kN (round off to 2 decimal places). 

Note: Average Flow Stress = Material Strength Coefficient True Strainn1 + n

 

Q. 47 Two business owners Shveta and Ashok run their businesses in two different states. Each of them, independent of the other, produces two products A and B, sells them at Rs. 2,000 per kg and Rs. 3,000 per kg, respectively, and uses Linear Programming to determine the optimal quantity of A and B to maximize their respective daily revenue. Their constraints are as follows: i) for each business owner, the production process is such that the daily production of A has to be at least as much as B, and the upper limit for production of B is 10 kg per day, and ii) the respective state regulations restrict Shveta’s production of A to less than 20 kg per day, and Ashok’s production of A to less than 15 kg per day. The demand of both A and B in both the states is very high and everything produced is sold. 

The absolute value of the difference in daily (optimal) revenue of Shveta and Ashok is ____________ thousand Rupees (round off to 2 decimal places). 

 

Q. 48 Consider two cases as below. 

Case 1: A company buys 1000 pieces per year of a certain part from vendor ‘X’. The changeover time is 2 hours and the price is Rs. 10 per piece. The holding cost rate per part is 10% per year. 

Case 2: For the same part, another vendor ‘Y’ offers a design where the changeover time is 6 minutes, with a price of Rs. 5 per piece, and a holding cost rate per part of 100% per year. The order size is 800 pieces per year from ‘X’ and 200 pieces per year from ‘Y’. 

Assume the cost of downtime as Rs. 200 per hour. The percentage reduction in the annual cost for Case 2, as compared to Case 1 is ________ (round off to 2 decimal places). 

 

Q. 49 Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter D. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: m/s, where C is a constant. The rate of kinetic energy in J/s) at the control surface A-B, as shown in the figure, is proportional to Dⁿ. The value of n is __________

 

Q. 50 Air discharges steadily through a horizontal nozzle and impinges on a stationary vertical plate as shown in figure. 

The inlet and outlet areas of the nozzle are 0.1 m² and 0.02 m², respectively. Take air density as constant and equal to 1.2 kg/m³. If the inlet gauge pressure of air is 0.36 kPa, the gauge pressure at point 0 on the plate is _______ kPa (round off to two decimal places). 

 

Q. 51 Air (ideal gas) enters a perfectly insulated compressor at a temperature of 310 K. The pressure ratio of the compressor is 6. Specific heat at constant pressure for air is 1005 J/kg.K and ratio of specific heats at constant pressure and constant volume is 1.4. Assume that specific heats of air are constant. If the isentropic efficiency of the compressor is 85 percent, the difference in enthalpies of air between the exit and the inlet of the compressor is ________ kJ/kg (round off to nearest integer). 

 

Q. 52 One kg of air, initially at a temperature of 127°C, expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is 287 J/kg.K, the magnitude of work transfer is ___________ kJ (round off to 2 decimal places). 

 

Q. 53 For an ideal Rankine cycle operating between pressures of 30 bar and 0.04 bar, the work output from the turbine is 903 kJ/kg and the work input to the feed pump is 3 kJ/kg. The specific steam consumption is _________ kg/kW.h (round off to 2 decimal places). 

 

Q. 54 For a Kaplan (axial flow) turbine, the outlet blade velocity diagram at a section is shown in figure. 

The diameter at this section is 3 m. The hub and tip diameters of the blade are 2 m and 4 m, respectively. The water volume flow rate is 100 m³s. The rotational speed of the turbine is 300 rpm. The blade outlet angle β is ________ degrees (round off to one decimal place). 

 

Q. No. 55 The indicated power developed by an engine with compression ratio of 8, is calculated using an air-standard Otto cycle (constant properties). The rate of heat addition is 10 kW. The ratio of specific heats at constant pressure and constant volume is 1.4. The mechanical efficiency of the engine is 80 percent. 

The brake power output of the engine is ________ kW (round off to one decimal place). 

Answer Key

Que.	1	2	3	4	5	6	7	8	9	10
Ans.	C	A	C	B	D	D	D	D	A	C
Que.	1	2	3	4	5	6	7	8	9	10
Ans.	A	C	C	D	C	C	B	A	A OR C	B
Que.	11	12	13	14	15	16	17	18	19	20
Ans.	A	A	D	D	D	B	C	D	6 TO 6	0.98 TO 1.02
Que.	21	22	23	24	25	26	27	28	29	30
Ans.	1.0 TO 0.11	1.0 TO 1.3	0.90 TO 0.95	MTA	48.8 TO 49.8	D	A	A	C	C
Que.	31	32	33	34	35	36	37	38	39	40
Ans.	C	D	C	B	-1.00 TO 0.98	1.99 TO 2.01	0.85 TO 0.89	47.9 to 48.1	15.9 to 16.1	104 to 106
Que.	41	42	43	44	45	46	47	48	49	50
Ans.	19.95 to 20.05	7 to 9	50.005 to 50.005	0 to 0	22 to 25	1164 to 1168	9.90 to 10.10	8.19 to 8.23	8 to 8	0.37 to 0.45
Que.	51	52	53	54	55
Ans.	244 to 246	114.6 to 115.0	3.98 to 4.02	11.0 to 14.0	4.4 to 4.6

GATE 2020 Statistics Previous Year Paper 

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q.No. 1 Rajiv Gandhi Khel Ratna Award was conferred Mary Kom, a six-time world champion in boxing, recently in a ceremony the Rashtrapati Bhawan (the President’s official residence) in New Delhi. 

(A)with,

(B)at on,

(C)on, at

(D)to, at

 

Q.No. 2 Despite a string of poor performances, the chances of K. L. Rahul’s selection in the team are 

(A) slim

(B) bright

(C) obvious

(D) uncertain

 

Q.No. 3 Select the word that fits the analogy: 

Cover : Uncover :: Associate : 

(A) Unassociate

(B) Inassociate 

(C) Misassociate

(D) Dissociate

 

Q.No. 4 Hit by floods, the kharif (summer sown) crops in various parts of the country have been affected. Officials believe that the loss in production of the kharif crops can be recovered in the output of the rabi (winter sown) crops so that the country can achieve its food-grain production target of 291 million tons in the crop year 2019-20 (July-June). They are hopeful that good rains in July-August will help the soil retain moisture for a longer period, helping winter sown crops such as wheat and pulses during the November-February period. 

Which of the following statements can be inferred from the given passage?

(A)Officials declared that the food-grain production target will be met due to good rains.

(B)Officials want the food-grain production target to be met by the November-February period.

(C)Officials feel that the food-grain production target cannot be met due to floods.

(D)Officials hope that the food-grain production target will be met due to a good rabi produce.

 

Q.No. 5 The difference between the sum of the first 2n natural numbers and the sum of the first n odd natural numbers is _____________

(A) n²

(B) n² + n

(C) 2n² – n

(D) 2n² +n

Q6 – Q10 carry two marks each. 

Q.No. 6 Repo rate is the rate at which Reserve Bank of India (RBI) lends commercial banks, and reverse repo rate is the rate at which RBI borrows money from commercial banks. 

Which of the following statements can be inferred from the above passage? 

(A)Decrease in repo rate will increase cost of borrowing and decrease lending by commercial banks. 

(B)Increase in repo rate will decrease cost of borrowing and increase lending by commercial banks. 

(C)Increase in repo rate will decrease cost of borrowing and decrease lending by commercial banks. 

(D)Decrease in repo rate will decrease cost of borrowing and increase lending by commercial banks.

 

Q.No. 7 P, Q, R, S, T, U, V, and W are seated around a circular table. 

I. S is seated opposite to W. 

II. U is seated at the second place to the right of R. 

III. T is seated at the third place to the left of R. 

IV. V is a neighbour of S. 

Which of the following must be true? 

(A) P is a neighbour of R.

(B) Q is a neighbour of R.

(C) P is not seated opposite to Q. 

(D) R is the left neighbour of S.

 

Q.No. 8 The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car started. Both cars were travelling at constant speed. The speed of car P was 10 km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other? 

(A) 66.6

(B) 75.2

(C) 88.2

(D) 116.5

 

Q. No. 9 For a matrix M = [m_ij]; i, j = 1,2,3,4, the diagonal elements are all zero and m_ij = -m_ij: The minimum number of elements required to fully specify the matrix is______ 

(A) 0

(B) 6

(C) 12

(D) 16

 

Q.No. 10 The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 – 2018 is Company P Company Q 

(A) 15:17

(B) 16:17

(C) 17:15

(D) 17:16

Q1 – Q25 carry one mark each. 

Q.No. 1 Let M be a 3 × 3 non-zero idempotent matrix and let I₃ denote the 3 × 3 identity matrix. Then which of the following statements is FALSE? 

(A) The eigenvalues of M are 0 and 1

(B) Rank(M) = Trace(M)

(C) I₃ – M^-1 is idempotent

(D) (I₃ + M)^-1 = I₃ – 2M

 

Q.No.2 Let C denote the set of all complex numbers. Consider the vector space 

V = {(a,b,c): a,b,c e C, a + 5 = 0, b + c = 0}, 

over the field of real numbers, where for any complex number z, z denotes its complex conjugate. If i = √-1, then a basis of V is 

(A){(1,-1,1),(i,i,i)}

(B){(1,-1,1), (i, -i,i)}

(C){(1, -i, 1), (i,1,1)}

(D){(1, -i,1),(i,1,-1)}

 

Q.No. 3 Let S = {(x, y) E R R: x² – y² = 4} and f: S ⟶ R be defined by f(x,y) = 6 x + y2, where R denotes the set of all real numbers. Then 

(A) f is bounded on S

(B) the maximum value off on S is 13

(C) the minimum value of f on S is -14

(D) the minimum value off on S is -13

 

Q.No. 4 Let f: R XR → R be defined by 

Where R denotes the set of all real numbers and c E R is a fixed constant. Then, which of the following statements is TRUE? 

(A) There does NOT exist a value of c for which f is continuous at (0,0)

(B) f is continuous at (0,0) if c = 0 

(C) f is continuous at (0,0) if c = 10

(D) f is continuous at (0,0) if c = 16

 

Q.No. 5 The moment generating function of a random variable X is given by 

Then P(X ≤ 2) equals 

(A) 1/3

(B) 1/6

(C) 1/2

(D)5/6

 

Q.No. 6 Consider the following two-way fixed effects analysis of variance model 

Where ε_ijk‘s are independently and identically distributed N(0,0%) random variables, .

Let SSE denote the sum of squares due to error. For any positive integer v and any ∝ € (0,1), let X_V²∝ denote the (1 – ∝)-th quantile of the central chi-square distribution with v degrees of freedom. Then a 95% confidence interval for σ² is given by SSE x? 

 

Q.No. 7 Let X₁,…,X₂₀ be independent and identically distributed random variables with the common probability density function 

Then the distribution of the random variable is

(A) central chi-square with 10 degrees of freedom 

(B) central chi-square with 20 degrees of freedom 

(C) central chi-square with 30 degrees of freedom 

(D) central chi-square with 40 degrees of freedom 

 

Q.No. 8 Let X₁, …, X₁₀ be a random sample from a Weibull distribution with the probability density function 

where For any positive integer v and any a the quantile of the central chi-square distribution with v degrees of freedom. Then, a 90% confidence interval for θ is 

 

Q.No. 9 Let X₁, …, X_n be a random sample of size n (≥ 2) from a uniform distribution on the interval [-θ, θ], where θ ε (θ,∞). A minimal sufficient statistic for θ is 

 

Q.No. 10 Let X₁, …, X_n be a random sample of size n (≥ 2) from N(θ,2θ²) distribution, where θ ε (0,∞). Which of the following statements is TRUE? 

 

Q.No. 11 Let be a Poisson process with rate λ= 2. Given that N(3) = 1, the expected arrival time of the first event of the process is 

(A) 1

(B) 3/2 

(C) 2/3

(D) 3

 

Q.No. 12 Consider the regression model 

where β₀ and β₁ are unknown parameters and εi’s are random errors. Let y_i be the observed value of Y_i, i = 1, …, n. Using the method of ordinary least squares, the estimate of β₁ is 

 

Q.No. 13 Let In be a random sample of size n (≥2) from N_p (0, Σ) distribution, where is a positive definite matrix. Define 

where for any column vector U, U^t denotes its transpose. Then the distribution of the statistic is 

 

Q.No. 14 Consider a two-way fixed effects analysis of variance model without interaction effect and one observation per cell. If there are 5 factors and 4 columns, then the degrees of freedom for the error sum of squares is 

(A) 20

(B) 19

(C) 12

(D) 11

 

Q.No. 15 Let X₁, …, X_n be a random sample of size n (≥2) from an exponential distribution with the probability density function 

where Consider the problem of testing against based on X₁, …, X_n. Which of the following statements is TRUE? 

(A) Likelihood ratio test at level leads to the same critical region as the corresponding most powerful test at the same level. 

(B) Critical region of level likelihood ratio test is is the a-th quantile of the central chi-square distribution with 2n degrees of freedom 

(C) Likelihood ratio test for testing H₀ against H₁ does not exist 

(D) At any fixed level , the power of the likelihood ratio test is lower than that of the most powerful test 

 

Q.No. 16 The characteristic function of a random variable X is given by 

 

Q.No. 17 Let the random vector X = (X₁, X₂, X₃, X₄) follow N₄(μ, ∑) distribution, where 

Then P(X₁ + X₂ + X₃ + X₄ > 0) = _______________ (correct up to one decimal place).

 

Q.No. 18 Let {X_n}_n≥0 be a homogeneous Markov chain with state space {0,1} and one 

step transition probability matrix , then 27 × E(X₂) ______________= (correct up to two decimal places). 

 

Q. No. 19 Let E, F and G be mutually independent events with P(E) = 1/2, P(F) = 1/3 and P(G) = 1/4. Let p be the probability that at least two of the events among E,F and G occur. Then 12 × p = __________ (correct up to one decimal place). 

 

Q.No. 20 Let the joint probability mass function of (X,Y,Z) be 

where k = 10 – x – y – z; x, y, z = 0,1, … , 10; x + y + z ≤ 10. Then the variance of the random variable Y + Z equals _____________ (correct up to one decimal place). 

 

Q.No. 21 The total number of standard 4 X 4 Latin squares is___________

 

Q.No. 22 Let X be a 4 × 1 random vector with E(X) = 0 and variance-covariance matrix 

Let Y be the 4 × 1 random vector of principal components derived from ∑. The proportion of total variation explained by the first two principal components equals __________ (correct up to two decimal places). 

 

Q.No. 23 Let X₁, …,X_n be a random sample of size n (≥2) from an exponential distribution with the probability density function 

 

Q.No. 24 Let where x_i‘s are fixed covariates and εi’s are independent and identically distributed random variables with mean zero and finite variance. Suppose that α and β are the least squares estimators of α and β, respectively. Given the following data: 

where y_i is the observed value of Y_i, i = 1, …, 7. Then the correlation coefficient between and equals 

 

Q.No. 25 Let {0,1,2,3} be an observed sample of size 4 from N(θ,5) distribution, where θ ε [2,∞). Then the maximum likelihood estimate of θ based on the observed sample is _________.

Q26 – Q55 carry two marks each. 

Q.No. 26 Let f: × → be defined by 

where denotes the set of all real numbers. Then 

 

Q.No. 27 Consider the linear transformation T: ³ → ³ defined by 

Where is the set of all complex numbers and ³ = × × . Which of the following statements is TRUE? 

(A) There exists a non-zero vector X such that T(X) = -X 

(B) There exist a non-zero vector Y and a real number λ ≠ 1 such that T(Y) = λY 

(C) T is diagonalizable 

(D) T² = I₃, where I₃ is the 3 × 3 identity matrix 

 

Q.No. 28 For real numbers a, b and c, let 

Then, which of the following statements is TRUE? 

(A) Rank(M) = 3 for every a, b, c ∈

(B) If a + c = 0 then M is diagonalizable for every b ∈

(C) M has a pair of orthogonal eigenvectors for every a,b,c ∈

(D) If b = 0 and a + c = 1 then M is NOT idempotent 

 

Q.No. 29 Let M be a 4 × 4 matrix with (x – 1)²(x – 3)² as its minimal polynomial. Then, which of the following statements is FALSE? 

(A) The eigenvalues of M are 1 and 3 

(B) The algebraic multiplicity of the eigenvalue 1 is 3 

(C) M is NOT diagonalizable 

(D) Trace(M) = 8 

 

Q.No. 30 Let f: × → be defined by 

f(x.y)=|y-2||x-1|,      (x,y) ×

where denotes the set of all real numbers. Then which of the following statements is TRUE? 

(A) f is differentiable at (1,2) 

(B) f is continuous at (1,2) but NOT differentiable at (1,2) 

(C) The partial derivative of f, with respect to x, at (1,2) does NOT exist 

(D) The directional derivative of f at (1,2) along u=12,12equals 1

 

Q.No. 31 Which of the following functions is uniformly continuous on the specified domain? 

 

Q.No. 32 Let the random vector X = (X₁, X₂,X₃) have the joint probability density 

function 

Which of the following statements is TRUE? 

(A) X₁, X₂ and X₃ are mutually independent 

(B) X₁, X₂, and X₃ are pairwise independent 

(C) (X₁, X₂) and X₃ are independently distributed 

(D) Variance of X₁ + X₂ is π² 

 

Q.No. 33 Suppose that P₁ and P₂ are two populations having bivariate normal distributions with mean vectors respectively, and the same variance-covariance matrix be two new observations. If the prior probabilities for P₁ and P₂ are assumed to be equal and the misclassification costs are also assumed to be equal then, according to linear discriminant rule, 

(A) Z₁ is assigned to P₁ and Z₂, is assigned to P₂ 

(B) Z₁ is assigned to P₂ and Z₂ is assigned to P₁ 

(C) both Z₁ and Z₂ are assigned to P₁ 

(D) both Z₁ and Z₂ are assigned to P₂ 

 

Q.No. 34 Let X₁, …, X_n be a random sample of size n (≥2) from an exponential distribution with the probability density function 

where Which of the following statements is TRUE?

Q.No. 35. Let the joint distribution of (X, Y) be bivariate normal with mean vector and variance-covariance matrix where -1 < p < 1. Then E[max (X , Y)] equals 

 

Q.No. 36 Let X₁, X₂, …, X₁₀ be independent and identically distributed N₃(0,I₃) random vectors, where I₃ is the 3 × 3 identity matrix. Let 

where J₃ is the 3 × 3 matrix with each entry 1 and for any column vector U, U^t denotes its transpose. Then the distribution of T is 

(A) central chi-square with 5 degrees of freedom 

(B) central chi-square with 10 degrees of freedom 

(C) central chi-square with 20 degrees of freedom 

(D) central chi-square with 30 degrees of freedom 

 

Q.No. 37 Let be independent and identically distributed random vectors, where is a positive definite matrix. Further, let matrix, where for any matrix M, M^t denotes its transpose. If W_m(n, ∑) denotes a Wishart distribution of order m with n degrees of freedom and variance covariance matrix 2, then which of the following statements is TRUE? 

Q.No. 38 Let the joint distribution of the random variables where 

Then which of the following statements is TRUE? 

(A) X₁ – X₂ + X₃ and X₁ are independent 

(B) X₁ + X₂ and X₃ – X₁ are independent 

(C) X₁ – X₂ + X₃ and X₁ + X₂ are independent 

(D) X₁ – 2X₂ and 2X₁ + X₂ are independent 

 

Q.No. 39 Consider the following one-way fixed effects analysis of variance model 

 

Q.No. 40 Let X₁, …, X_n be a random sample of size from N(θ,1) distribution, where θ∈ (-∞,∞). Consider the problem of testing Ho: θ ∈ [1,2] against H:θ <1 or θ > 2, based on X₁, …,X_n. Which of the following statements is TRUE? 

 

Q.No. 41 In a pure birth process with birth rates λ_n = 2ⁿ, n ≥ 0, let the random variable T denote the time taken for the population size to grow from 0 to 5. If Var(T) denotes the variance of the random variable T, then 256 ×Var(T) = _____________

 

Q.No. 42 Let {X_n]_n≥0 be a homogeneous Markov chain whose state space is {0,1,2} and TO 1 01 whose one-step transition probability matrix is Then nP(X2n=2|X0=2)= ________________(correct up to one decimal place). 

 

Q.No. 43 Let (X,Y) be a random vector such that, for any y > 0, the conditional probability density function of X given Y = y is 

If the marginal probability density function of Y is 

then E(Y|X = 1) = ________  (correct up to one decimal place). 

 

Q.No. 44 Let (X,Y) be a random vector with the joint moment generating function 

Let Φ(.) denote the distribution function of the standard normal distribution and and Φ (1.5) = 0.9332 then the value of 2 p + 1 (round off to two decimal places) equals _______

 

Q.No. 45 Consider a homogeneous Markov chain {X_n}_n≥0 with state space {0,1,2,3} and one-step transition probability matrix 

Assume that P(X₀ = 1) = 1. Let p be the probability that state 0 will be visited before state 3. Then 6 × p = __________

 

Q.No. 46 Let (X,Y) be a random vector with joint probability mass function 

where Then the variance of Y equals ____________

 

Q.No. 47 Let X be a discrete random variable with probability mass function f ∈{f₀, f₁}, 

where 

The power of the most powerful level α = 0.1 test for testing H₀: X ~ f₀ against H₁:X ~ f₁, based on X, equals ___________ (correct up to two decimal places). 

 

Q.No. 48 Let X = (X₁,X₂,X₃) be a random vector following N₃ (0, ∑) distribution, 

where . Then the partial correlation coefficient between X₂ and X₃, with fixed X₁, equals _______ (correct up to two decimal places). 

 

Q.No. 49 Let X₁, X₂, X₃ and X₄ be a random sample from a population having probability density function and f(-x) = f(x), for all For testing H₀: θ = 0 against H₁ : θ <0, let T⁺ denote the Wilcoxon Signed-rank statistic. Then under H₀, 

 

Q.No. 50 A simple linear regression model with unknown intercept and unknown slope is fitted to the following data 

using the method of ordinary least squares. Then the predicted value of y corresponding to x = 5 is _________

 

Q.No. 51 Let where denotes the set of all real numbers. If then 84 × 1 = _____________________________

Q.No. 52 Let the random vector (X,Y) have the joint distribution function 

Let Var(X) and Var(Y) denote the variances of random variables X and Y, respectively. Then 16 Var(x) + 32 Var(Y) = _________________

 

Q.No. 53 Let {X_n}_n≥1 be a sequence of independent and identically distributed random variables with Further, let 

where Φ (.) denotes the cumulative distribution function of the standard normal distribution, then c² = _______________(correct up to one decimal place). 

 

Q.No. 54 Let the random vector X = (X₁, X₂, X₃) have the joint probability density function 

Then the variance of the random variable X₁ + X₂ + X₃ equals _____________. (correct up to one decimal place). 

 

Q.No. 55 Let X₁, …,X₅ be a random sample from a distribution with the probability density function 

where For testing H₀: θ = 0 against   the sign test statistic, where 

 otherwise Then the size of the test, which rejects H, if and only if equals _______________ (correct up to one decimal place). 

 

GATE 2020 Textile Engineering and Fibre Science Previous Year Paper

GA – General Aptitude 

Q1 – Q5 carry one mark each. 

Q.1 This book, including all its chapters____interesting. The students as well as the, instructor __________in agreement about it. 

(A)is, was

(B)are, are

(C)is, are

(D)were, was

Q.2 their vehicles near the entrance of the main administrative People were prohibited building 

(A)to park

(B)from parking

(C)parking

(D)to have parked

 

Q.No.3 Select the word that fits the analogy: 

Do: Undo :: Trust : 

(A)Entrust

(B)Intrust

(C)Distrust

(D)Untrust

 

Q.No.4 Stock markets ________ at the news of the coup. 

(A) poised

(B) plunged

(C) plugged

(D) probed

 

Q.5 If P,Q,R,S are four individuals, how many teams of size exceeding one can be formed, with Q as a member? 

(A) 5

(B) 6

(C) 7

(D) 8

 Q6 – Q10 carry two marks each. 

Q.No.6 Non-performing Assets (NPAs) of a bank in India is defined as an asset, which remains unpaid by a borrower for a certain period of time in terms of interest, principal, or both. Reserve Bank of India (RBI) has changed the definition of NPA thrice during 1993-2004, in terms of the holding period of loans. The holding period was reduced by one quarter each time. In 1993, the holding period was four quarters (360 days).

 

(A) √2

(B) √3

(C) 2

(D) 3

 

Q.10 The revenue and expenditure of four different companies P, Q, R and S in 2015 are shown in the figure. If the revenue of company Q in 2015 was 20% more than that in 2014, and company Q had earned a profit of 10% on expenditure in 2014, then its expenditure (in million rupees) in 2014 was _______

(A) 32.7
(B) 33.7
(C) 34.1
(D) 35.1

TF: Textile Engineering and Fibre Science 

Q1-Q25 carry one mark each. 

 

Q.1 For the matrix , the eigenvalues of the matrix AP are

(A)1,0,1

(B)1,0,0

(C)1, 1,0

(D)1,1,1

Q.2 The integrating factor of the differential equation dy/dx + y = e-x is 

(A)ex

(B)e-x

(C)xe-x

(D)xex

Q.3 Laplace transform of cosh(t) is 

(A)1/S2 – 1

(B)S/S-1

(C)S/S2 – 1

(D)S/S2+1

 

Q.4 In wool, the sulfur containing amino acid is 

(A)Alanine

(B)Cystine

(C)Glycine

(D)Serine

Q.5 Viscose rayon is soluble in 

(A) Acetone

(B) Chloroform

(C) Formic 85% (v/v)

(D) acid Sulfuric acid 59% (w/w)

Q.6 In carding, the highest draft is kept between 

(A) Lap roller and feed roller

(B) Feed roller and licker-in

(C) Licker-in and cylinder

(D) Cylinder and doffer

  

Q.7 The spinning system in which one revolution of twisting element imparts several turns to the fibre strand is 

(A) Ring

(B) Rotor

(C) Friction

(D) Wrap

    

Q.8 The technology that does NOT produce a nonwoven fabric is 

(A) Spunbonding

(B) Hydroentangling

(C) Melt Blowing

(D) Braiding

Q.9 For the same yarn and fabric sett, the weave that gives the maximum tearing strength is 

(A) Plain

(B) 2×2 matt

(C) 5-end satin

(D) 2/1 twill 

 

Q.10 Two yarns have variance of strength as V1 and V2. If Vi< V2, the variance ratio F would be 

(A)V2 /V1

(B)V1 /V2

(C)V12 /V22

(D)V22 /V12

 

Q.11 Cotton fibre length parameter that CANNOT be obtained from Baer Sorter diagram is 

(A) Mean length

(B) Dispersion

(C) Uniformity ratio

(D) Modal length

Q.12 The purpose of carbonization of wool fibres is to remove 

(A) Waxy matter

(B) Surface scales

(C) Vegetable matter

(D) Ortho-cortex

 

Q.13 Biopolishing of cotton fabrics is done using 

(A) Cellulase

(B) Amylase

(C) Proteinase

(D) Esterase

 

Q.14 For the given system of linear equations, 2x -z = 1; 5x + y = 7; y + 3z = 5, the sum of x, y and z is _______________.

 

Q.15 If F = xi + yj + zk, then the magnitude of 7x F is ______________.

 

Q.16 A polypropylene filament is drawn in two stages with draw ratios of 1.5 and 2 respectively. The overall draw ratio is ___________.

 

Q.17 The refractive indices of a filament in axial and radial directions are 1.58 and 1.52 respectively. The birefringence of the filament (correct up to 2 decimal places) is._____________

 

Q.18 A twin-delivery drawframe, running at a delivery speed of 800 m/min with an efficiency of 95%, is producing 5.9 ktex sliver. The rate of production of the draw frame in kg/h (rounded off to 2 decimal places) is _____________

 

Q.19 The diameter (mm) of a yarn having twist of 700 turns per meter and surface twist angle of 20° (rounded off to 2 decimal places) is _________________

 

Q.20 A magazine creel has 800 package holders. The effective creel capacity (number) is ___________

 

Q.21 A shuttle loom is running at 180 picks per minute. The angular velocity of crank shaft (degree/second) is _____________

Q.22 The length (km) of 5 kg of 30 Ne yarn (rounded off to the nearest integer) is __________

 

Q.23 The limit irregularity and measured irregularity of a yarn are 8.4% and 9.6%, 

respectively. The Index of Irregularity (rounded off to 2 decimal places) is __________

 

Q.24 A padding mangle is processing a fabric at 1320 m/h. The bottom bowl of the mangle is rotating at 25 rpm. Assuming zero slippage at the nip, the diameter (cm) of this bowl is ___________

 

Q.25 A Procion H (monochlorotriazine based) reactive dye used for printing of cotton has a molecular weight of 471. Taking the atomic weight of H=1, C=12, N=14, O=16, CI=35.5, the molecular weight of the fully hydrolyzed dye (correct up to 1 decimal place) would be ____________

 

Q26 – Q55 carry two marks each. 

Q.26 Let L = lim(sin x) tanx. The value of L is 

(A) 0

(B) 1

(C) 2

(D) ∞

Q.27 The solution of the differential equation = 0, which satisfies the conditions, y(0) = 0, y'(0) = 3 is

(A) e-x 

(B) ex

(C) ex + e-2x 

(D) ex – e-2x

 

Q.28 In melt spinning of poly(ethylene terephthalate), pre-drying of polymer chips is essential to avoid 

(A) Hydrolytic degradation

(B) Oxidative degradation

(C) Microbial degradation

(D) Photo-induced degradation

 

Q.29 Determine the correctness or otherwise of the following Assertion (a) and Reason 

[a]: Caprolactam is polymerized in the presence of a small amount of water to produce fibre grade nylon 6. 

Im I 

[r]: Water acts as a catalyst and converts caprolactam to aminocaproic acid. 

(A) Both [a] and [1] are true and [7] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(C) Both [a] and [r] are false 

(D) [a] is true but [r] is false 

 

Q.30 Determine the correctness or otherwise of the following Assertion [a] and Reason 

[r] 

[a]: Melting point of nylon 66 fibre is much higher than that of polyethylene fibre. 

[r]: The molecular weight of nylon 66 fibre is significantly higher than that of polyethylene fibre. 

(A) Both [a] and [r] are true and [r] is the correct reason for [a]

(B) Both [a] and [r] are true but [r] is not the correct reason for [a]

(C) Both [a] and [1] are false

(D) [a] is true but [r] is false

 

Q.31 Carding of polyester fibres requires that the values of wire-point density 

(points/inch2) of 

(P) Licker-in 

(Q) Cylinder 

(R) Flat 

follow the order 

(A) P<Q R 

(B) P<R<Q 

(C) Q<R<P

(D) Q<P<R

 

Q.32 For combing with forward feed, the given parameters are: Detachment setting = 15 mm, Length of feed per combing cycle=6 mm, Longest fiber length = 30 mm. According to Gégauff’s theory, the noil (%) would be 

(A) 9

(B) 16

(C) 30

(D) 49

Q.33 Determine the correctness or otherwise of the following Assertion (a) and Reason 

[r] 

[a]: Open-loop auto levelling system needs a signal storage device with time delay 

function. 

[r]: The signal must be stored until the material reaches the adjusting point. 

(A) Both [a] and [r] are true and [r] is the correct reason for [a] 

(B) Both [a] and [1] are true but [r] is not the correct reason for [a] 

(C) Both [a] and [r] are false

(D) [a] is true but [r] is false

Q.34 If both the concentration (%, w/w) of size paste and target add-on are 12%, the total wet pick-up (kg) by 12 kg bone-dry warp sheet is 

(A) 6

(B) 12

(C) 18

(D) 24

 

Q.35 At front centre (0°) and at back centre (180°) of a shuttle loom, 

(A)The sley velocities are the same but accelerations are different.

(B)The sley velocities are different but accelerations are the same.

(C)The sley velocities are the same and also accelerations are the same.

(D)The sley velocities are different and also accelerations are different. 

 

Q.36 Match the looms listed in Group I with the corresponding components given in Group II. The correct option is 

Group I                                         Group II 

P. Multiphase                         1. Matched cam 

Q. Projectile                            2. Profile reed 

R. Air-jet                                    3. Crank shaft 

S. Shuttle 4. Weaving rotor

(A) P-1, Q-4, R-2, S-3

(B) P-1, Q-2, R-4, S-3

(C) P-4, Q-1, R-2, S-3

(D) P-3, Q-1, R-2, S-4

Q.37 Consider two yarns, one 100% wool and the other 100% cotton, each containing 100 fibres in the yarn cross-section. The respective limit irregularities (%) of wool and cotton yarns will approximately be 

(A) 11.2 and 10.6

(B) 10.6 and 11.2

(C) 11.8 and 11.2

(D) 11.8 and 10.6

 

Q.38 If the numerical value X of yarn linear density, expressed in denier is the same as that expressed in English (Ne) system, then X approximately is 

(A) 24.3

(B) 48.6

(C) 72.9

(D) 97.2

Q.39 Determine the correctness or otherwise of the following Assertion [a] and Reason 

[r] 

[a]: Sodium chlorite is a bleaching agent for cotton. 

[r]: Sodium chlorite is an effective reducing agent. 

(A)Both [a] and [] are true and [r] is the correct reason for [a] 

(B)Both [a] and [r) are true but [r] is not the correct reason for [a]

(C)Both [a] and [r] are false

(D)[a] is true but [r] is false

Q.40 Determine the correctness or otherwise of the following Assertion (a) and Reason 

[a]: Acrylic fibres are dyed with basic dyes in acidic medium. 

[r]: In acidic medium the acrylic fibre acquires positive charge. 

(A) Both [a] and [r] are true and [r] is the correct reason for [a] 

(B)Both [a] and [r] are true but [r] is not the correct reason for [a] 

(C) Both (a) and rare false

(D) [a] is true but [r] is false

 

Q.41 Determine the correctness or otherwise of the following Assertion (a) and Reason 

[a]: Foam finishing significantly reduces the energy consumed in drying. 

[r]: The specific heat of air is significantly lower than that of water. 

(A) Both [a] and [f] are true and [r] is the correct reason for [a] 

(B) Both [a] and [r] are true but [r] is not the correct reason for [a] 

(C) Both [a] and [r] are false

(D) [a] is true but [7] is false

Q.42 If the probability density function of a continuous random variable X is given by f(x) = e-*, 0<x<co, the mean of random variable X is _____________

 

Q.43 Assuming the step size h = 1, the numerical value of the definite integral r2 x2 Jo 1+x3 dx obtained using Trapezoidal rule (rounded off to 2 decimal places) is_____

 

Q.44 In the production of PET, diglycol terephthalate (DGT) is an intermediate. Taking the atomic weights of H=1, C=12, 0=16, the molecular weight of DGT is _____

 

Q.45 In wet spinning of acrylic filament yarn, the volumetric flow rate of the spinning dope per spinneret hole is 0.1 cm3/min. If the surface speed at the first take up roller is 1.5 m/min and the diameter of spinneret hole is 0.02 cm, then the jet stretch (rounded off to 2 decimal places) is _____________

 

Q.46 Two types of polyester staple fibers of fineness 3 and 6 denier and having the  same length are mixed in a ratio of 2:3 by weight. The mean fibre fineness (denier) of the mix (rounded off to 2 decimal places) is ______________

 

Q.47 Two rovings, each with a mass CV of 10%, are fed to a ring spinning machine that adds a mass CV of 20%. The mass CV (%) of the yarn (rounded off to 2 decimal places) is ________________

 

Q.48 In a drum-driven winder, the grooved drum having a width of 20 cm is rotating at 1000 rpm. If the drum makes 5 revolutions per double traverse, the traverse speed (m/min) is _____________

 

Q.49 The whale constant and course constant are 4.2 and 5.04 respectively. If the loop length is 4.2 mm, then stitch density (number/cm’) is _________

 

Q.50 A cotton fibre has a degree of cell wall thickening (O) of 0.9 and perimeter of 40 um. The actual cross-sectional area of the wall (um) of the fibre (rounded off to 1 decimal place) is __________

 

Q.51 A fabric with mass per unit area of 250 g/m2 has flexural rigidity of 275 uN-m. The bending length (mm) of the fabric (rounded off to 2 decimal places) is _______

 

Q.52 The ‘standard machine rate of loading of a tensile tester, working on pendulum lever principle, is 440 N/cm. As the pendulum lever swings from 30° 10 45°, the *machine rate of loading’ (N/cm), reduces by___________ (rounded off to 2 decimal places) 

 

Q.53 Under a load of 500 cN, the extension of a yarn of 300 mm length is 10%. If the elastic recovery is 90%, then the length (mm) of the yarn after removal of load is_____ 

 

Q.54 Given that one gram mole of a gas occupies 22.4 L of volume at STP, the atomic weights of H=1, and that of O=16, the concentration (g/L) of hydrogen peroxide solution of 25 volume strength (rounded off to 2 decimal places) is ______________

 

Q.55 The work of adhesion (Ws) depends on the surface tension (Ylv) of the liquid and the contact angle (6) formed on a surface and is expressed as Yuv(1 + cose). The Wsz for a given fabric and a liquid is reduced to 1/3rd of the original value after oil repellent treatment. If the measured contact angle of the untreated fabric is 60°, the percent change in the contact angle after the treatment is ____________

 

ANSWER KEY