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Chemical Engineering GATE 2023 Questions with Answer

Ques 27 Engineering Mathematics

Which one of the following is the CORRECT value of 𝑦, as defined by the expression given below?

A

1

B

2

C

0

D

∞


Ques 28 Engineering Mathematics

The vector 𝒗 βƒ—βƒ— is defined as

Which one of the following is the CORRECT value of divergence of 𝒗 βƒ—βƒ— , evaluated at the point (π‘₯,𝑦,𝑧)=(3,2,1) ?

A

0

B

3

C

14

D

13


Ques 29 Engineering Mathematics

Given that

where 𝑧1=2+3𝑖 and 𝑧2=βˆ’2+3𝑖 with 𝑖=βˆšβˆ’1 , which one of the following options is CORRECT?

A

F<0

B

F<1

C

F>1

D

F=1


Ques 30 Engineering Mathematics

For a two-dimensional plane, the unit vectors, (π‘’π‘Ÿ,π‘’πœƒ) of the polar coordinate system and (𝑖,𝑗) of the cartesian coordinate system, are related by the following two equations.

Which one of the following is the CORRECT value of

A

1

B

ΓͺΞΈ

C

Γͺr+ΓͺΞΈ

D

-Γͺr+ΓͺΞΈ


Ques 31 Engineering Mathematics

The position x(t) of a particle, at constant ω, is described by the equation:
d2x/dt2 = −ω2x.
The initial conditions are x(t = 0) = 1 and (dx/dt)|t=0 = 0.
The position of the particle at t = (3π/ω) is __________ (in integer).

-1 is the correct answer.


Ques 32 Engineering Mathematics

An exhibition was held in a hall on 15 August 2022 between 3 PM and 4 PM during which any person was allowed to enter only once. Visitors who entered before 3:40 PM exited the hall exactly after 20 minutes from their time of entry. Visitors who entered at or after 3:40 PM, exited exactly at 4 PM. The probability distribution of the arrival time of any visitor is uniform between 3 PM and 4 PM. Two persons X and π‘Œ entered the exhibition hall independent of each other. Which one of the following values is the probability that their visits to the exhibition overlapped with each other?

A

5/9

B

4/9

C

2/9

D

7/9


Ques 33 Engineering Mathematics

Simpson’s one-third rule is used to estimate the definite integral

with an interval length of 0.5. Which one of the following is the CORRECT estimate of 𝐼 obtained using this rule?

A

1/3-1/√3

B

1/3+2/√3

C

1/3+1/√3

D

1/3-2/√3


Ques 34 Engineering Mathematics

If a matrix 𝑀 is defined as the sum of all the eigenvalues of 𝑀3 is equal to __________ (in integer).

13264 is the correct answer.


Ques 35 Engineering Mathematics

The first derivative of the function evaluated at π‘Ÿ=1 is ______ (in integer).

0 is the correct answer.


Ques 36 Fluid Mechanics

For a packed-bed comprising of uniform-sized spherical particles of diameter 𝐷p, the pressure drop across the bed is given by the Kozeny-Carman equation when the particle Reynolds number (Rep)<1. Under this condition, minimum fluidization velocity is proportional to 𝐷p𝑛. Which one of the following is the CORRECT value of exponent 𝑛 ?

A

2

B

-1

C

-2

D

1


Ques 37 Fluid Mechanics

Which one of the following quantities of a flowing fluid is measured using a rotameter?

A

Static pressure

B

Dynamic pressure

C

Volumetric flow rate

D

Viscosity


Ques 38 Fluid Mechanics

For a fully developed turbulent flow of an incompressible Newtonian fluid through a pipe of constant diameter, which of the following statements is/are CORRECT?

A

Reynolds stress, averaged over a sufficiently long time, is zero everywhere inside the pipe.

B

Reynolds stress at the pipe wall is zero.

C

Average velocity of the fluid is half of its center-line velocity.

D

Average pressure gradient in the flow direction is constant.


Ques 39 Fluid Mechanics

The viscosity of an incompressible Newtonian fluid is measured using a capillary tube of diameter 0.5 mm and length 1.5 m. The fluid flow is laminar, steady and fully developed. For a flow rate of 1 cm3s−1, the pressure drop across the length of the tube is 1 MPa. If the viscosity of the fluid is k × 10−3 Pa.s, the value of k is ___________ (rounded off to two decimal places).

1.06 is the correct answer.


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