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General Aptitude(10)Engineering Mathematics(9)Applied Mechanics and Design(16)Fluid Mechanics and Thermal Sciences(16)Materials, Manufacturing and Industrial Engineering(14)

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

The team scored more than 300 runs in 20 overs despite rains. However, some players needed to improve their batting skills. Choose the option with the correct sequence of words to fill the blanks.

(A)

score; despite

(B)

scoring; instead of

(C)

scored; despite

(D)

scoring; in spite of

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

If a positive real x satisfies the following equation $\log_{2}x+\log_{\sqrt{2}}x=48$, then the value of x is

(A)

2^{16}

(B)

4^{16}

(C)

2^{14}

(D)

4^{14}

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

The next figure (indicated by '?') in the sequence is

(A)

a

(B)

b

(C)

c

(D)

d

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q4

MCQ[1 Mark]

'All the mangoes in the basket are good.' If the above statement is false, then which one of the following statements is necessarily true?

(A)

All the mangoes in the basket are not good.

(B)

No mango in the basket is good.

(C)

In the basket, some of the mangoes are good and some are not good.

(D)

There exists at least one mango in the basket that is not good.

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

Consider the following statements about four numbers: (S1) The average of the four numbers is 25. (S2) Each number is at most 40. (S3) Each number is at least 20. Choose the option that is necessarily correct.

(A)

(S1) and (S2) together imply (S3)

(B)

(S2) and (S3) together imply (S1)

(C)

(S1) and (S3) together imply (S2)

(D)

(S1) implies (S3)

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

'People are crowding around **[1]** pit into which **[2]** elephant has fallen. I have never seen an elephant looking more bewildered **[3]** miserable. Here it is in a most undignified position, thrust into a pit and made to look up **[4]** a vast, curiosity-stricken crowd.' Choose the option with the correct sequence of words to fill the blanks.

(A)

an; a; at; and

(B)

a; an; and; at

(C)

and; a; an; at

(D)

at; a; an; and

Explanation

GATE→2026→General Aptitude→Data Interpretation

Q7

MCQ[2 Marks]

The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. Observations: (i) The quantity of S sold was twice that of T. (ii) The quantity of R sold was thrice that of T. (iii) The quantity of Q sold was four times that of T. | Product | Unit selling price (Rs.) | | --- | --- | | P | 50 | | Q | 100 | | R | 60 | | S | 60 | | T | 40 | \nWhat is the quantity of product P sold on that day?

(A)

40

(B)

50

(C)

60

(D)

70

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

Consider a string P of length $l$ that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length $x$ they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of $x/l$ is

(A)

\pi

(B)

\frac{\pi-1}{2\pi}

(C)

\frac{\pi}{2(\pi-1)}

(D)

\frac{\pi}{\pi-1}

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels. They are seated in rows and columns as shown in the figure with exactly one person sitting in each box. It is known that: (i) Meritorius' daughter and his brother are seated in the same column. (ii) His son is seated diagonally across the sibling of the worst orator. (iii) The best and worst orators are seated in the same row. \nWho is the best orator?

(A)

Meritorius

(B)

Meritorius' brother

(C)

Meritorius' son

(D)

Meritorius' daughter

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

Engineering Mathematics

9 Questions

GATE→2026→Engineering Mathematics→Calculus

Q11

MCQ[1 Mark]

Domain A is bounded by curve $x^{2}=4y$, ordinate $x=2$, and x-axis. The value of $\iint_{A}y~dxdy$ is

(A)

1/5

(B)

1/3

(C)

5/12

(D)

1/2

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q12

MCQ[1 Mark]

Let $\phi$ be a scalar function. Then, $\nabla\phi$ is

(A)

always perpendicular to the surface of constant $\phi$

(B)

always parallel to the surface of constant $\phi$

(C)

the minimum rate of change of scalar $\phi$

(D)

always zero

Explanation

GATE→2026→Engineering Mathematics→Differential Equations

Q13

MCQ[1 Mark]

The order and degree of the following differential equation are $m$ and $n$, respectively. $$\frac{\partial^{3}\varphi}{\partial x^{3}}+\frac{\partial^{2}\varphi}{\partial y^{2}}\frac{\partial\varphi}{\partial x}+(\frac{\partial^{2}\varphi}{\partial x^{2}})^{2}+\frac{\partial\varphi}{\partial y}=0$$\nThe value of $(m-n)$ is

(A)

2

(B)

3

(C)

1

(D)

0

Explanation

GATE→2026→Engineering Mathematics→Numerical Methods

Q14

MCQ[1 Mark]

Newton-Raphson method for solving algebraic equations is based on

(A)

Taylor series

(B)

Fourier series

(C)

Laurent series

(D)

Power series

Explanation

GATE→2026→Engineering Mathematics→Numerical Methods

Q15

MCQ[1 Mark]

The exact solution of $\int_{0}^{4}\frac{dx}{1+x}$ is represented as $n$. If $m$ represents numerically evaluated value of the above integral using Trapezoidal rule by considering four equal subintervals in the range of $x$, then $(m-n)$ is

(A)

-0.074

(B)

-0.003

(C)

0.074

(D)

0.003

Explanation

GATE→2026→Engineering Mathematics→Complex Variables

Q16

MCQ[2 Marks]

If $w=\log_{e}z=\log_{e}(x+iy)$, where $i=\sqrt{-1}$, then which one of the following statements is correct?

(A)

w is analytic everywhere except at z = 0

(B)

w is non-analytic everywhere

(C)

The conjugate functions of w are \log_e(x^2+y^2) and \log_e(x^2-y^2)

(D)

The conjugate functions of w are \tan^{-1}(x/y) and \tan^{-1}(y/x)

Explanation

GATE→2026→Engineering Mathematics→Differential Equations

Q17

MCQ[2 Marks]

Consider the following differential equation: $$\frac{\partial y}{\partial x}=3\frac{\partial y}{\partial t}+y$$\nIf $y(x,0)=10e^{-2x}$ then the solution of the differential equation is

(A)

y(x,t) = 10e^{-2x-t}

(B)

y(x,t) = 10e^{-2x+t}

(C)

y(x,t) = 10e^{-2x-2t}

(D)

y(x,t) = 10e^{-2x+2t}

Explanation

GATE→2026→Engineering Mathematics→Differential Equations

Q18

MCQ[2 Marks]

The Laplace transform of $f(t)=\sin 2t \sin 4t$ is

(A)

\frac{16s}{(s^{2}+4)(s^{2}+36)}

(B)

\frac{32s}{(s^{2}+4)(s^{2}+36)}

(C)

\frac{16}{(s^{2}+4)(s^{2}+36)}

(D)

\frac{32}{(s^{2}+4)(s^{2}+36)}

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q19

MCQ[2 Marks]

A student council of 10 members consists of two students from engineering school, three students from science school and five students from arts school. The university administration selects three students from the council at random. What is the chance that out of the selected students, two belong to the same school and the third belongs to different school?

(A)

\frac{79}{120}

(B)

\frac{2}{120}

(C)

\frac{89}{120}

(D)

\frac{69}{120}

Explanation

Applied Mechanics and Design

16 Questions

GATE→2026→Applied Mechanics and Design→Engineering Mechanics

Q20

MCQ[1 Mark]

A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular velocity of $3~rad/s$. If the block slides along the slot with a constant speed of $0.2~m/s$ relative to the slot, then the magnitude of Coriolis acceleration in $m/s^{2}$ is

(A)

1.2

(B)

0.6

(C)

2.4

(D)

0.3

Explanation

GATE→2026→Applied Mechanics and Design→Theory of Machines

Q21

MCQ[1 Mark]

A gear train with five gears is shown in the figure below. The number of teeth on each gear is $N_{1}$, $N_{2}$, $N_{3}$, $N_{4}$, and $N_{5}$. The idler gear in this gear train is

(A)

gear 4

(B)

gear 2

(C)

gear 3

(D)

gear 1

Explanation

GATE→2026→Applied Mechanics and Design→Vibrations

Q22

MCQ[1 Mark]

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is $350~N~s/m$ and the damping coefficient is $35~N~s/m$. The logarithmic decrement of the vibrating system is

(A)

0.63

(B)

1.26

(C)

0.32

(D)

1.89

Explanation

GATE→2026→Applied Mechanics and Design→Machine Design

Q23

MCQ[1 Mark]

A closely coiled helical compression spring of mean coil diameter $D$ and wire diameter $d$, is loaded by an axial force $F$. The maximum shear stress developed in the wire is

(A)

\frac{8FD}{\pi d^{3}}+\frac{4F}{\pi d^{2}}

(B)

\frac{8FD}{\pi d^{3}}+\frac{2F}{\pi d^{2}}

(C)

\frac{16FD}{\pi d^{3}}+\frac{4F}{\pi d^{2}}

(D)

\frac{32FD}{\pi d^{3}}+\frac{4F}{\pi d^{2}}

Explanation

GATE→2026→Applied Mechanics and Design→Theory of Machines

Q24

MCQ[1 Mark]

The rotor of an aeroplane engine has a mass moment of inertia $1.0~kg~m^{2}$. The engine rotates at a speed of 500 RPM in the clockwise direction if viewed from the front of the aeroplane. If the aeroplane while flying at $1200~km/hr$ turns with a radius of $2~km$ at same elevation, then the magnitude of the gyroscopic moment exerted by the rotor on the aeroplane structure in $N~m$ is

(A)

8.73

(B)

17.46

(C)

4.37

(D)

26.19

Explanation

GATE→2026→Applied Mechanics and Design→Machine Design

Q25

MCQ[1 Mark]

A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is $l$ and the fillet weld leg size is $h$. The allowable shear strength of the weldment is $\tau_{all}$. A tensile force $P$ is applied on the plate in a direction parallel to the length of the weld. Assuming the throat of the weld as the weakest section, the critical load is

(A)

\sqrt{2}hl\tau_{all}

(B)

hl\tau_{all}

(C)

hl\tau_{all}/\sqrt{2}

(D)

hl\tau_{all}/2

Explanation

GATE→2026→Applied Mechanics and Design→Machine Design

Q26

MCQ[1 Mark]

Worm gearsets are used for transmitting rotary motion between

(A)

non-parallel and non-intersecting shafts

(B)

intersecting shafts

(C)

parallel shafts

(D)

non-parallel and intersecting shafts

Explanation

GATE→2026→Applied Mechanics and Design→Mechanics of Materials

Q27

NAT[1 Mark]

A steel plate having yield strength of $550~MPa$, is subjected to biaxial state of stress as $\sigma_{x}=\sigma$ and $\sigma_{y}=-2\sigma$. Using distortion energy theory and considering the factor of safety as 2, the permissible value of $\sigma$ that can be applied to the plate is ____ MPa (rounded off to 1 decimal place).

Explanation

GATE→2026→Applied Mechanics and Design→Mechanics of Materials

Q28

MCQ[2 Marks]

A cantilever beam of length L is subjected to a concentrated load P and a moment M as shown in the figure below. Neglecting the mass of the beam, which one of the following options is the correct representation of shear force diagram (SFD) and bending moment diagram (BMD)?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2026→Applied Mechanics and Design→Engineering Mechanics

Q29

MCQ[2 Marks]

Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecting the mass of the members, the magnitude of the vertical reaction force at C in kN is

(A)

5

(B)

10

(C)

20

(D)

15

Explanation

GATE→2026→Applied Mechanics and Design→Vibrations

Q30

MCQ[2 Marks]

A 5 kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young's modulus of the material of the beam is 200 GPa and area moment of inertia of the beam is $10^{-8}~m^{4}$. The natural frequency of the beam in rad/s is

(A)

10

(B)

10/3

(C)

5

(D)

20/3

Explanation

GATE→2026→Applied Mechanics and Design→Engineering Mechanics

Q31

NAT[2 Marks]

A block of $50~kg$ mass is on an inclined plane. The block is connected to another hanging mass $M$ by an inextensible massless string through two massless pulleys as shown in the figure below. The coefficient of static friction between the block and the inclined plane is $0.3$. Neglecting pulley friction, the minimum value of $M$ required to start the upward motion of the block is ____ kg (rounded off to 1 decimal place).

Explanation

GATE→2026→Applied Mechanics and Design→Mechanics of Materials

Q32

NAT[2 Marks]

A simply supported beam is subjected to an external point load $P$ as shown in the figure below. The beam has a rectangular cross-section of $20~mm \times 45~mm$. A is a pin support and B is a roller support. The shear stress developed at point C, lying on the neutral axis of the beam, is $3~MPa$. Neglecting the mass of the beam, the magnitude of the applied load is ____ kN (rounded off to 1 decimal place).

Explanation

GATE→2026→Applied Mechanics and Design→Engineering Mechanics

Q33

NAT[2 Marks]

A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown in the figure below. The velocity of A in the downward direction at a given instant is $6~m/s$. At that instant, the magnitude of absolute velocity of the midpoint G is ____ m/s (rounded off to 2 decimal places).

Explanation

GATE→2026→Applied Mechanics and Design→Mechanics of Materials

Q34

NAT[2 Marks]

A cylindrical pressure vessel made of steel has diameter of $3~m$ and wall thickness of $15~mm$. For steel, Young's modulus and Poisson's ratio are $210~GPa$ and $0.3$, respectively. The cylinder is designed such that the allowable normal strain at the outer cylindrical surface is equal to $0.00034$. The permissible pressure in the tank is ____ kPa (rounded off to 1 decimal place).

Explanation

GATE→2026→Applied Mechanics and Design→Machine Design

Q35

NAT[2 Marks]

A welded square plate of $1~m \times 1~m$ is subjected to biaxial stress of magnitude $6.5~MPa$ and $25~MPa$, as shown in the figure below. The ratio of the normal stress acting in the perpendicular direction of सरपंच the weld to the shear stress of the weld is ____ (rounded off to 2 decimal places).

Explanation

Fluid Mechanics and Thermal Sciences

16 Questions

GATE→2026→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q36

MCQ[1 Mark]

For an ideal gas, starting from state point 1, two different processes take place. The corresponding final states in these two processes are 2 and 3, lying on same isotherm. If P and h represent pressure and enthalpy, respectively, then which one of the following options is correct?

(A)

h_{2}=h_{3}

(B)

h_{2}>h_{3}

(C)

P_{2}h_{3}=P_{3}h_{2}

(D)

P_{3}h_{3}=P_{2}h_{2}

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q37

MCQ[1 Mark]

A steady incompressible laminar flow passes through a $90^{\circ}$ tube bend placed on a horizontal surface. In horizontal diametric plane, two pressure taps $P_{i}$ and $P_{o}$ are provided across the cross-section at inner and outer walls of the bend, respectively. Which one of the following options is correct?

(A)

P_{o}>P_{i}

(B)

P_{o}<P_{i}

(C)

(P_{o}-P_{i}) is directly proportional to bend radius

(D)

(P_{i}-P_{o}) is inversely proportional to average flow velocity

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q38

MCQ[1 Mark]

An ideal gas passes isothermally through a long horizontal uniform cross-section pipe under steady flow. Consider that the pressure gradient in the pipe is sufficient for a finite change in the density of the gas. If the flow of the gas is purely pressure driven and subsonic throughout, then the average flow velocity

(A)

increases along the flow

(B)

decreases along the flow

(C)

does not change throughout the pipe

(D)

increases in the hydrodynamic entrance region and then decreases thereafter

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q39

MCQ[1 Mark]

Bernoulli's equation CANNOT be applied between

(A)

any two arbitrary points in the flow field for steady incompressible rotational flow

(B)

any two arbitrary points in the flow field for steady incompressible irrotational flow

(C)

any two points along a streamline for steady incompressible flow

(D)

any two points along a streamline for steady incompressible rotational flow

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q40

MCQ[1 Mark]

A quiescent fluid at temperature $T_{3}$ is confined between two vertical parallel plates. While plate 1 is kept at temperature $T_{1}$ and plate 2 is maintained at temperature $T_{2}$, a velocity profile between the plates, as shown in the figure below, is generated due to heat transfer. Which one of the following options shows the correct relations among $T_{1}$, $T_{2}$, and $T_{3}$?

(A)

T_{1}>T_{3} \text{ and } T_{3}>T_{2}

(B)

T_{1}>T_{3} \text{ and } T_{3}<T_{2}

(C)

T_{1}<T_{3} \text{ and } T_{3}<T_{2}

(D)

T_{1}<T_{3} \text{ and } T_{3}>T_{2}

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q41

MCQ[1 Mark]

For the isothermal expansion of an ideal gas in a piston cylinder system, the net heat supplied during the process is equal to the net work. Which one of the following statements is correct for the given process?

(A)

The process is possible.

(B)

The process is not possible as it violates the second law of thermodynamics.

(C)

The process is not possible as it violates the first law of thermodynamics.

(D)

The process is possible, however, it violates the second law of thermodynamics.

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q42

MCQ[1 Mark]

A hydraulic crane supports a mass of $500~kg$ with its piston-cylinder actuator, inclined at $60^{\circ}$ with horizontal, as shown in the figure below. The diameter of the piston is $30~cm$ and gravitational acceleration is $10~m/s^{2}$. Neglecting mass of the piston, the reading of the pressure gage in kPa (gage) is

(A)

61.26

(B)

6.13

(C)

35.35

(D)

70.71

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q43

NAT[1 Mark]

A sphere of radius $5~mm$ is initially in equilibrium at $400^{\circ}C$ in a furnace. It is suddenly removed from the furnace and dipped in a well-stirred water bath at $20^{\circ}C$, with a convection heat transfer coefficient of $500~W/(m^{2}K)$. For the given range of temperatures, the thermophysical properties of the material of the sphere are: density $\rho=3000~kg/m^{3}$, thermal conductivity $k=10~W/(m~K)$, and specific heat $c=1000~J/(kg~K)$. Neglecting radiation heat transfer, the time required for the centre of the sphere to cool from $400^{\circ}C$ to $50^{\circ}C$ is ____ seconds (rounded off to 2 decimal places).

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q44

MCQ[2 Marks]

A very long fin of a uniform square cross-section is replaced by another very long fin of a uniform circular cross-section of the same material. Assume uniform and identical heat transfer coefficient for both the fins. If the diameter of ket circular fin is equal to the side length of the square fin, then the ratio of heat transfer rates before and after the replacement is

(A)

\frac{4}{\pi}

(B)

\frac{16}{\pi^{2}}

(C)

\frac{1}{\pi}

(D)

\frac{1}{\pi^{2}}

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Applications (Power Engineering, I.C. Engines, Refrigeration, Turbomachinery)

Q45

MCQ[2 Marks]

For an ideal regenerative Rankine cycle, as shown in the figure below, which one of the following options is the correct representation of temperature-entropy (T-s) diagram?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Fluid Mechanics

Q46

NAT[2 Marks]

Water with a density of $1000~kg/m^{3}$ comes out of an industrial condenser through a horizontal pipe of $15~cm$ radius at the flow rate of $4.5~m^{3}/min$. The outlet of the pipe is connected to a coaxial diffuser of $0.5~m$ length using a flange to raise the pressure of water to atmospheric condition without any backflow. The inner radius ($r$, in $m$) of the diffuser cross-section is expressed as $r=0.15+0.4~x^{2}$ where, $x$ represents the axial distance of the diffuser in m, from its inlet. Considering frictionless flow, the magnitude of the force exerted by the diffuser on the flange is ____ N (rounded off to 2 decimal places).

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q47

NAT[2 Marks]

Two rectangular surfaces both having $1~m^{2}$ area are placed perpendicular to each other with a common edge. One surface is hot, having a temperature of $1000~K$ and emissivity of $0.4$, while the other is insulated and in radiant balance with a large surrounding room at $300~K$. If the fraction of radiation leaving the hot surface which reaches the cold surface is $0.2$, then the equivalent overall resistance for the radiation heat loss from the hot surface is ____ $m^{-2}$ (rounded off to 2 decimal places).

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Heat Transfer

Q48

NAT[2 Marks]

Convective heat transfer coefficients for Fluid 1 and Fluid 2 in a heat exchanger, as shown in the figure below, are $50~W/(m^{2}K)$ and $80~W/(m^{2}K)$, respectively. The inner tube is made of a material which has a thermal conductivity $386~W/(m~K)$ for the given range of temperatures in the heat exchanger. The length of the heat exchanging surface, the inside radius of the inner tube, and thickness of the inner tube are $1~m$, $10~mm$, and $1~mm$, respectively. Considering no heat exchange between the outer tube and the surrounding, the heat transfer rate for the heat exchanger is ____ W (rounded off to 1 decimal place).

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q49

NAT[2 Marks]

A liquid comes out of the reactor of a chemical plant at $250^{\circ}C$ temperature with a flow rate of $100~LPM$. The ambient temperature is $25^{\circ}C$. Density and specific heat of the liquid remain constant at $1000~kg/m^{3}$ and $4.18~kJ/(kg~K)$, respectively, for the given range of temperature. The rate of exergy associated with the hot liquid stream at the exit of the plant is ____ kW (rounded off to 2 decimal places).

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Thermodynamics

Q50

NAT[2 Marks]

A rigid closed vertical cylindrical vessel of $15~cm$ diameter contains $5~kg$ water at $80^{\circ}C$ with $10\%$ quality. The water is heated till its temperature reaches $130^{\circ}C$. Considering only a horizontal separated interface between liquid and vapor, the dip in the liquid level after heating process is ____ cm (rounded off to 2 decimal places).

Explanation

GATE→2026→Fluid Mechanics and Thermal Sciences→Applications (Power Engineering, I.C. Engines, Refrigeration, Turbomachinery)

Q51

NAT[2 Marks]

An inward flow reaction turbine, having an outer diameter of $1~m$, runs at $600~RPM$. The normal component of absolute velocity at the inlet is $10~m/s$. If the guide blade angle is $15^{\circ}$, then the inlet vane angle of the runner is ____ degree (rounded off to 1 decimal place).

Explanation

Materials, Manufacturing and Industrial Engineering

14 Questions

GATE→2026→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q52

MCQ[1 Mark]

In relation to metal casting defects, match the following: | Description | Defect | | --- | --- | | P: Shallow blow found on a flat casting surface | I: Dross | | Q: Lighter impurities appearing on the top surface of a casting | II: Scab | | R: A rough, thin layer of metal, protruding above the casting surface, on top of a thin layer of sand | III: Scar | \nOptions:

(A)

P-II, Q-III, R-I

(B)

P-II, Q-I, R-III

(C)

P-III, Q-I, R-II

(D)

P-III, Q-II, R-I

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Additive Manufacturing

Q53

MCQ[1 Mark]

Which one of the following options is NOT an error associated with STereoLithography (STL) file in additive manufacturing?

(A)

Staircase effect

(B)

Missing facet

(C)

Non-manifold topology conditions

(D)

Degenerate facets

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q54

MCQ[1 Mark]

A work piece is to be firmly held in a fixture. It is to be machined by using a plain slab milling cutter as shown in the figure below. Which one of the following options is the most suitable value of height H of the fixture in mm?

(A)

200

(B)

210

(C)

150

(D)

70

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Metrology and Inspection

Q55

MCQ[1 Mark]

A two-dimensional surface profile is obtained over a sampling length by using a contact type stylus profilometer as shown in the figure below. A line AA parallel to the general lay of the trace is considered. The true heights from AA to the peaks and valleys $(in~\mu m)$ in the trace are also shown in the figure. The ten-point height average in $\mu m$ is

(A)

6.7

(B)

5.99

(C)

3.09

(D)

2.90

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Computer Aided Manufacturing and Automation

Q56

MCQ[2 Marks]

Consider the Euler variables of polyhedral objects namely, P1, P2, P3, and P4 given in the table below. | Polyhedral objects | Faces (F) | Edges (E) | Vertices (V) | Faces' inner loops (L) | Bodies (B) | Genus (G) | | --- | --- | --- | --- | --- | --- | --- | | P1 | 6 | 12 | 8 | 0 | 1 | 0 | | P2 | 5 | 8 | 5 | 0 | 1 | 0 | | P3 | 8 | 12 | 6 | 0 | 1 | 2 | | P4 | 10 | 24 | 16 | 0 | 1 | 0 | \nWhich one of the following options is NOT a topologically valid closed polyhedral object as per Euler's law?

(A)

P3

(B)

P1

(C)

P4

(D)

P2

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Operations Research

Q57

MCQ[2 Marks]

An objective function Z of primal variables ($x_{1}$ and $x_{2}$) is described below:\nMinimize $Z=0.07~x_{1}+0.05~x_{2}$\nsubject to $0.1~x_{1}\ge0.4$ $0.1~x_{2}\ge0.6$ $0.1~x_{1}+0.2~x_{2}\ge2.0$ $0.2~x_{1}+0.1~x_{2}\ge1.8$ $x_{1},x_{2}\ge0$ $W$ is the objective function of the dual of $Z$. $k_{1}, k_{2}, k_{3},$ and $k_{4}$ represent the corresponding dual variables. Which one of the following options represents the correct form of $W$?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q58

MCQ[2 Marks]

Four jobs are on order in a factory. As on day 20 of the production calendar, corresponding due date and work remaining to complete these jobs (in days) are given in the table below. | Job | Due date | Work remaining (in days) | | --- | --- | --- | | M | 26 | 5 | | N | 24 | 10 | | O | 28 | 10 | | P | 31 | 5 | \nWhich job(s) has/have critical ratio less than unity?

(A)

Job N and Job O

(B)

Job M and Job N

(C)

Job P

(D)

Job O and Job P

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Casting, Forming and Joining Processes

Q59

NAT[2 Marks]

In a deep drawing operation of a rectangular sheet metal, $30\%$ stretching in length results in $15\%$ reduction in thickness. Assuming volume constancy, the normal anisotropy of the sheet metal is ____ (rounded off to 2 decimal places).

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q60

NAT[2 Marks]

The actual demand for castings in a factory is 500 units and 635 units for the months of January 2026 and February 2026, respectively. The forecasted demand for January 2026 is 250 units and smoothing constant is $0.7$. Using the exponential smoothing method, the forecast of the demand for castings in March 2026 is ____ units (in integer).

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Production Planning and Control

Q61

NAT[2 Marks]

The inventory holding cost of an item is $0.50 per unit per month and the ordering cost per order is$550. A stockist needs to supply 10000 units of the item per year to the customers. Assume demand is fixed and shortage cost is infinite. Using classical economic order quantity (EOQ) model, the optimal lot size is ____ units per order (rounded off to nearest integer).

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Engineering Materials

Q62

NAT[2 Marks]

A metal has FCC crystal structure with $2.71~g/cm^{3}$ of density and $26.98~g/mol$ of atomic weight. Avogadro's number is $6.023 \times 10^{23}$. The atomic radius of the metal is ____ nm (rounded off to 2 decimal places).

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q63

NAT[2 Marks]

During orthogonal turning by using a single point cutting tool, feed rate is $0.24~mm/rev$. The uncut chip thickness is $0.23~mm$. The shear angle, tangential force component, and radial force component are $20^{\circ}$, $800~N$, and $150~N$, respectively. The value of shear force is ____ N (rounded off to 2 decimal places).

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Machining and Machine Tool Operations

Q64

NAT[2 Marks]

A drill bit during its lifetime can produce 150 through holes in a plate at a drill-speed of $200~RPM$. If the drill-speed increases to $300~RPM$, then it can produce 60 through holes in the same plate before the drill bit fails. Assume all other parameters remain constant. The value of the exponent in Taylor's tool life equation is ____ (rounded off to 2 decimal places).

Explanation

GATE→2026→Materials, Manufacturing and Industrial Engineering→Operations Research

Q65

NAT[2 Marks]

The activities of a PERT network and their corresponding activity time estimates (in weeks) i.e., optimistic ($t_{o}$), most likely ($t_{m}$), and pessimistic ($t_{p}$) are given in the table below. | Activity | $t_{o}$ | $t_{m}$ | $t_{p}$ | | --- | --- | --- | --- | | 1-2 | 2 | 4 | 12 | | 1-3 | 2 | 4 | 6 | | 1-4 | 3 | 4 | 11 | | 2-5 | 3 | 6 | 9 | | 3-4 | 2 | 5 | 14 | | 3-5 | 3 | 3 | 3 | | 4-5 | 3 | 6 | 15 | | 5-6 | 2 | 5 | 8 | \nThe expected project length is ____ weeks (in integer).

Explanation