PUMEET 2026 Question Paper

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PUMEET 2026
Question Paper
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PUMEET 2026 Question Paper

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.
m .co s e m PUMEET 2026 Question Paper

s e l a
a ag [PU-MEET-2026]

MATHEMATICS (Q.No. 1-30)
1. Find the limit of the sequence 𝑠 = 2 + (−1) , if it exists.
(A) 1 (B) 3 (C) 2 (D) Limit does not exit
2. The series + + + ⋯ converges for following positive values of x:
(A) [1,2] (B) [1, ∞) only (C) (1, ∞) only (D) = 1 only
m
co
!
3. Find the radius of convergence of the series ∑ .
(A)
. c om(B) /2 (C) 3 (D) e/3
e m .
4. Find the summ
e of the series 1 + 2 + 3 + 4 + 5 + ⋯ , | | < 1
l as
(A) las (B) (C) (D) ag
a g ( ) ( ) ( )

5. If = sin [( + )/(√ + ) ], then the value of + is ________.
(A) ½ tan (B) tan (C) 0 (D) sec

6. If = sin , = ln , = , then is ________
(A) (cos + 2 sin ) (B) (sin − 2 cos )
(C) (sin + 2 cos ) (D) sin
m
7. If ( , , ) = + .co
+ − 8, then grad(f) , i.e., (∇ ) at (2,0,2) is
m
(A) 4 ̂ + e
(B) 3 ̂ − 4 ̂ + (C) 3 ̂ − ̂ + (D) −4 ̂ +
ssurface + = at the point (2,0,4) is
a
The equation of the tangent plane tolthe
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8.
(A) + − = 1 (B) 4x-z-4=0 (C) 2x+y-z=0 (D) -x-4y+1=0
9. A point of minima of ( , ) = + + 6 + 12 is _______
(A) (3,0) (B) (-3,0) (C) (0,3) (D) (0,-3)
10. Find the flux of the field ⃗ = ̂+ ̂+ outward through the surface of the cube
cut from the first octant by the planes x=1, y=1 and z=1.
(A) 2 (B) 3/4 (C) 3/2 (D) 0

m
.co
11. Find the divergence of the field ⃗ = ln ̂ + ln ̂ + ln .
m
c.12.o Evaluate the integral ∫ ∫ ( + )
(A) − ln( ) (B) ln( ) (C) ln ln ln (D) − ln ln ln

s em
s em .
l a
g la (A) 3/14 (B) 4/15 (C) 13/12
ag (D) 6/19
a 13. Evaluate the integral ∮ (√ + ) where C : The boundary of the circle + =3
(A) (B) - (C) 2 (D) 0
14. Evaluate the integral which is defined using spherical coordinates:
∫ ∫ ∫ sin .
(A) 36 (B) 12 (C) 0 (D)

m (1)
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c. o s e m
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15. Evaluate the integral ∫ ∫ ∫ .
(A) 6 (B) 12 (C) 4 (D) 2
16. Find a spherical coordinate equation for the cone z = + .
(A) = 2 (B) = 3 (C) = /4 (D) = /3

17. Find the integrating function for the differential equation + = .
(A) 1/ (B) 1/ (C) 1/ (D)
18. If is continuous on [a,b], then the length of the curve = ( ) over the interval [a,b] is
given by

(A) ∫ 1+ (B) ∫ 1+

(C) ∫ 1− (D) ∫ 1−

19. Find the general solution of the following differential equation
(ax+hy+g) dx+ (hx+by+f) dy=0
(A) + + + + =0
(B) + + + + =0
(C) ℎ + +2 + + + =0
(D) + + 2ℎ +2 +2 + =0
20. Find the general solution of the following differential equation
( +3 ) + (3 + ) =0
(A) +6 + = (B) − 6 + =
(C) +6 + =0 (D) ( + ) =
21. Find the particular integral of the differential equation ( + 1 ) = sin .
(A) – (B) (C) (D) −

22. Form the partial differential equation for = + + .
(A) = + + (B) − =0
(C) + + =0 (D) − =
23. Formulate the partial differential equation by eliminating the arbitrary function from
= ( + + ).
(A) − + =0 (B) + =0
(C) + = + (D) − =0
24. Find the general solution of the partial differential equation
( − ) + ( − ) = ( − ).
(A) ( + + , )=0 (B) ( + + ) =
(C) ( )= + + (D) ( ), ( ) ( ) are all general solutions
(2)

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m .co s e m PUMEET 2026 Question Paper

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a ag [PU-MEET-2026]

25. Find ( )
.
(A) (B) (C) (D)
26. Find the Laplace transform of unit Impulse function ( − ).
(A) (B) (C) /s (D) /𝑠

27. The value of in the Fourier series expansion of cos in (− , ) is
m
(A) 1
om
(B) 1/2 (C) /2 (D) 0
. co
28. . c
Find the fundamental period of the function ( ) = sin( ) + sin (2 ). em
(A)
e m (B) 2
l as
(C) 3 a s (D) Fundamental period does not exist
lof the following periodic function with period p is even? ag
29. a g
Which
(I) ( )= , 0 < < 2; = 2
(II) ( ) = , −1 < < 1; = 2
(A) Only (I) is even (B) Only (II) is even
(C) Both (I) and (II) are even (D) Neither (I) nor (II) is even
30. The Fourier series for ( ) = cos ,− ≤ ≤ (with period p= 2 ) is
(A) (B) (C) (D)
m
PHYSICS (Q.No. 31-50)
m .co
31. e
In an electrical oscillator such as an LC circuit, the analogue of the spring constant
s
l a
(stiffness) k in a mechanical oscillator is:
g
32.
(A) L (B) R
a (C) 1/C (D) 1/L
At resonance, the phase difference between driving force and velocity is:
o
(A) (B) 45o (C) 90o (D) 180o
33. The logarithmic decrement for weak damping is related to quality factor by:
(A) = (B) = (C) = (D) =

34. The fractional change in resonant frequency of a damped harmonic oscillator is
(A) 4 2 (B) 1/4 2 (C) 8 2 (D) 1/8 2
m
m .co
.co
35. In a Michelson interferometer, moving one mirror by a distance d changes the path length
by
s em
s em (A) d (B) d/2 (C) 2d
g l a
(D) 4d

g la 36. a the plano-convex lens
When a liquid of refractive index , ( > 1) is introduced between
a and the glass plate, the ring diameters shrink by a factor of
(A) shrink by a factor of (B) shrink by a factor of
√
(C) expand by a factor of (D) expand by a factor of
37. The coherence length of a laser beam primarily depends on:
(A) The spectral bandwidth of the source (B) The intensity of the emitted light
(C) The diameter of the laser beam (D) The state of polarization of light

m (3)
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c. o s e m
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38. When unpolarized light of intensity I0 passes through an ideal polarizer, the transmitted
intensity is:
(A) I0 (B) I0/2 (C) I0/4 (D) I0/8
39. If a particle moves at 0.8c relative to a spaceship moving at 0.7c relative to earth, its speed
relative to earth is:
(A) 1.5c (B) 0.96c (C) 0.99c (D) c
40. A spacecraft receding from the earth at 0.97c transmits data at the rate of 10 4 pulses/sec. At
what rate are they received?
(A) 1.23 × 104 pulses/sec (B) 1.0 × 103 pulses/sec
(C) 1.0 × 104 pulses/sec (D) 1.23 × 103 pulses/sec
41. The energy of a photon with momentum 2 MeV/c, where c is the speed of light, is given
by:
(A) 2.50 MeV (B) 2.96 MeV (C) 0.66MeV (D) 2MeV
42. A body initially at rest explodes into two equal fragments, each having a rest mass of 1 kg.
If the fragments move in opposite directions with speed 0.6c relative to the original body,
the rest mass of the original body is:
(A) 2.5 kg (B) 2.0 kg (C) 1.65 kg (D) 1.2 kg
43. Which of the following processes is responsible for the production of characteristic X-
rays?
(A) Sudden deceleration of high-speed electrons
(B) Transitions occurring within the atomic nucleus
(C) Electronic transitions between inner atomic shells
(D) Vibrational motion of molecules
44. For a particle confined in a one-dimensional box of width L, the expectation value of its
position ⟨x⟩ is:
(A) L/2 (B) L (C) 1/L (D) 2/L
45. Momentum operator in one dimension is:
ħ ħ ħ ħ
(A) (B) (C) (D)

46. In a photoelectric experiment, a graph is plotted between the stopping potential Vo and the
frequency ν of the incident radiation. The slope of the graph is equal to:
(A) h/e (B) e/h (C) he (D) 1/h
47. Which type of bonding generally produces the most brittle materials?
(A) Metallic bonding (B) Ionic bonding
(C) Van der Waals bonding (D) Hydrogen bonding
48. The ideal c/a ratio for hexagonal close packed structure is approximately:
(A) 1.414 (B) 1.633 (C) 1.732 (D) 2.121
49. In a face-centered cubic (FCC) crystal structure, the plane having the highest planar atomic
density is:
(A) (100) (B) (110) (C) (111) (D) (210)
(4)

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m .co s e m PUMEET 2026 Question Paper

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a ag [PU-MEET-2026]

50. The wavelength of X-rays used in crystallography is typically of the order of:
(A) 10−3m (B) 10−6m (C) 10−10m (D) 10−15m
CHEMISTRY (Q.No. 51-70)
51. According to molecular orbital theory, the bond orders of O2, O2+ and O2- are
(A) 1.5, 2.0 and 2.5 respectively (B) 2.0, 2.5 and 1.5 respectively
(C) 2.5, 1.5 and 2.0 respectively (D) 2.0, 1.5 and 2.5 respectively
m
52.
om
The correct molecular orbital electronic configuration of CN molecule is
. co
c
(A) KK (σ2s)2 (σ*2s)2 (π2px)2 (π2py)2 (σ2pz)2
. e m
m
(B) KK (σ2s)2 (σ*2s)2 (σ2pz)2 (π2px)2 (π2py)2
e l as
as
(C) KK (σ2s)2 (σ*2s)2 (π2px)2 (π2py)2 (σ2pz)1
l ag
g
(D) KK (σ2s)2 (σ*2s)2 (σ2pz)2 (π2px)2 (π2py)1
a
53. Among the followings, which is the true statement about oxygen molecule?
(A) It is paramagnetic with one unpaired electron in the bonding molecular orbital
(B) It is paramagnetic with two unpaired electrons in the bonding molecular orbital
(C) It is paramagnetic with one unpaired electron in the anti-bonding molecular orbital
(D) It is paramagnetic with two unpaired electrons in the anti-bonding molecular orbital
54. In a unit cell of zinc blende,
(A) Zn2+ ions are present at the corners and S2- ions have fcc arrangement
m
(B) Zn2+ ions are present at the corners and S2- ions have bcc arrangement
.co
(C) Zn2+ ions have fcc arrangement and S2- ions occupy alternate tetrahedral sites
m
e
(D) Zn2+ ions occupy alternate tetrahedral sites and S 2- ions have fcc arrangement
sin the crystal structures of NaCl and ZnS?
55. l a
What is the true statement about defects
g ZnS shows Schottky defect
a
(A) NaCl shows Frenkel defect and
(B) NaCl shows Schottky defect and ZnS shows Frenkel defect
(C) Both show Schottky defect
(D) Both show Frenkel defect
56. The hybridization and geometry of Ni(CO)4 complex is
(A) dsp2 and tetrahedral respectively (B) dsp2 and square planar respectively
(C) sp3 and tetrahedral respectively (D) sp3 and square planar respectively
57. What is the correct energy order of d-orbitals when a metal ion is placed in a square planar
m
m field?
.co
.co em
(A) dxz = dyz < dxy < dz2 < dx2-y2 (B) dxz = dyz < dz2 < dxy < dx2-y2

em58.
(C) dxy < dxz = dyz < dz2 < dx2-y2 s
(D) dx2-y2 < dz2 < dxy < dxz = dyz
a
s Number of unpaired electrons in the case of [Fe(CN) ] is/are gl
la a (D) three
3-
6

ag (A) zero (B) one (C) two
59. CFSE in the case of d5 octahedral low spin complex is
(A) -2.0 Δo (B) zero (C) – 2.0 Δo + 2P (D) – 2.0 Δo + 1P
60. For a reversible engine working at two different temperatures T 1 and T2 (T2 > T1), the
efficiency (η) of the engine can be given as
(A) η = T2 / (T2 – T1) (B) η = T1 / (T1 – T2)
(C) η = (T1 – T2) / T1 (D) η = (T2 – T1) / T2

m (5)
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c. o s e m
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PUMEET 2026 Question Paper

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61. Mathematically, first law of thermodynamics can be expressed as
(A) ΔH = q + w (B) ΔH = q - w (C) ΔE = q + w (D) ΔE = q - w
62. Which one of the followings led to the concept of Third law of thermodynamics?
(A) Nernst Heat Theorem (B) Carnot Theorem
(C) Kirchhoff’s equation (D) Gibb’s equation
63. Heat capacity at constant pressure is greater than heat capacity at constant volume by
(A) 4 calories (B) 2 calories (C) 4 joules (D) 2 joules
64. On the basis of configuration, polymers can be classified as
(A) isotactic, syndiotactic and atactic (B) linear, branched and cross-linked
(C) homo-polymer and co-polymer (D) thermoplastic and thermoset
65. Out of followings, which one can be used to measure molecular weight distribution in
polymers?
(A) Number-average molecular weight (B) Weight-average molecular weight
(C) Polydispersity index (D) Degree of polymerization
66. A polymer having aromatic amide functional group is
(A) Nylon 6 (B) Nylon 6,6 (C) Kevlar (D) Teflon
67. Epoxy resin is an example of
(A) polyether (B) polyester (C) polyamide (D) polyamine
68. The liquid mixtures which can be distilled with a change in composition are called
(A) azeotropic mixtures (B) equilibrium mixtures
(C) non-equilibrium mixtures (D) zeotropic mixtures
69. Corrosion is an example of
(A) oxidation (B) reduction (C) electrolysis (D) erosion
70. Which one of the followings is not regarded as a pollutant?
(A) NO2 (B) CO2 (C) SO2 (D) CO
GENERAL ENGINEERING (Q.No. 71-90)
71. Which of the following conditions is true for both series and parallel resonance?
(A) Impedance is minimum (B) Power factor is unity
(C) Power factor is nearly zero (D) Power is extremely low
72. The ratio of the readings of two wattmeters connected to measure power in a balanced
3-phase load is 5 : 3 and the load is inductive. The power factor of the load is
(A) 0.917 lead (B) 0.917 lag (C) 0.6 lead (D) 0.6 lag
73. During open circuit test of a transformer
(A) Primary is supplied rated voltage
(B) Primary is supplied full-load current
(C) Primary is supplied current at reduced voltage
(D) Primary is supplied rated kVA

(6)

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m .co s e m PUMEET 2026 Question Paper

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a ag [PU-MEET-2026]

74. The effect of increasing the air-gap length in a 3 phase induction motor is to
1. reduce the pulsation loss
2. improve the power factor
3. reduce the air-gap flux
4. worsen the power factor
5. reduce the torque
6. increase the efficiency m
om
From these, the correct statements are . co
(A) 1,4,5 . c (B) 1,3,4,5,6 (C) 2,3,5,6 (D) 1,3,4,5 e m
m
e of 10Ω is connected in series with a combination of two resistances arrangedl as
75. s
A resistance
a
l each of value 20Ω. Determine the resistance R which should be shuntedaacross g
g
in parallel
theaparallel combination so that current drawn by the circuit is 1.5A with applied voltage of
20 V.
(A) 3.33 Ω (B) 40 Ω (C) 5 Ω (D) 6.66 Ω
76. A 220-V dc machine has an armature resistance of 1 Ω. If the full-load current is 20 A, the
difference in the induced voltages when the machine is running as a motor and as a
generator is
(A) 20V (B) Zero (C) 40V (D) 50V
m
77.
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Following statements are made regarding the open-circuit test on a 1-phase transformer :
1. It is performed on l.v. side
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s e
2. It is performed at rated current
l a
ag
3. It helps in the calculation of equivalent leakage impedance
4. It is performed on h.v. side
5. It is performed at rated voltage
6. It gives magnetizing current and core loss
7. It helps in determination of voltage regulation
8. It gives turns ratio
From these, the correct answer is
(A) 1,5,6,8 (B) 2,4,6,8 (C) 3,4,5,6,8 (D) 1,5,7,8

o m
78.
m
3FA516 is equals to octal number system
. c
c.79.o When the transistor is operated in cut off and(C)
(A) 37665 (B) 37645 37946
m
(D) 37964
saturation, it acts like as
e
e m l a(D) Switch
s
la 80. A digital circuit that can store only one bit of information is called
(A) Linear amplifier (B) Photodiode (C) LED
a g
ag
(A) Encoder (B) Flip flop (C) XOR gate (D) Shift register
81. A body of mass m moving with velocity u collides elastically with another identical
stationary body. After collision, the first body will:
(A) Continue with velocity u (B) Stop completely
(C) Move with velocity u/2 (D) Reverse its direction

m (7)
. c
c. o s e m
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PUMEET 2026 Question Paper

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82. A couple acting on a body produces:
(A) Only translational motion (B) Only rotational effect
(C) Both translation and rotation (D) No effect if forces are equal
83. During tensile testing of mild steel, the point beyond which permanent deformation begins is
called:
(A) Elastic limit (B) Ultimate stress point
(C) Breaking point (D) Proportional limit
84. Which welding defect is most strongly associated with rapid cooling and excessive hardness
in the Heat Affected Zone (HAZ)?
(A) Porosity (B) Slag inclusion (C) Hydrogen cracking (D) Undercutting
85. In orthographic projection, if the object is placed in the first quadrant, then
(A) Top view appears above XY line (B) Front view appears below XY line
(C) Top view appears below XY line (D) Both views appear above XY line
86. Pure carbon is burnt in oxygen. The flue gas analysis is 70% CO 2, 20% CO and 10% O2.
The percent excess oxygen used is:
(A) 20 (B) 12.5 (C) 0 (D) 10
87. Four cars, with a mass of 1500 Kg are loaded on a 6m wide, 12 m long small car ferry. How
far in cm, will it sink in the water
(A) 15.2 (B) 11.5 (C) 10.2 (D) 8.3
88. One mole of methane contains
(A) 6.023 × 1023 atoms of carbon (B) 6.023 × 1023 atoms of hydrogen
(C) 4 gm atom of methane (D) 24.092 × 1023 molecules of methane
89. Vapour free gas means
(A) 0 % humidity (B) 100 % humidity
(C) 1% humidity (D) Between 0 and 100 % humidity
90. Ideal gas law is applicable at
(A) Low T, Low P (B) High T, High P (C) Low T, High P (D) High T, Low P
COMMUNICATION SKILLS (Q.No. 91-100)
91. Rearrange the following parts of the sentence in the correct order:
If the research team
P: had analyzed the data thoroughly
Q: before publishing the report
R: it would not have attracted criticism
S: from international scholars
(A) PQRS (B) PRQS (C) QPRS (D) PSRQ
92. Rearrange the following parts of the sentence in the correct order:
The principal
P: instructed the participants
Q: before the commencement of the seminar
R: to maintain silence
S: throughout the presentation
The proper sequence is:
(A) PQRS (B) PRSQ (C) QPRS (D) PSRQ
(8)

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m .co s e m PUMEET 2026 Question Paper

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93. Neither of the proposals __________ suitable for immediate implementation.
(A) are (B) were (C) is (D) have been
94. Hardly had the guests entered the auditorium when they realized that they __________ the
invitation cards at home.
(A) leave (B) had left (C) have left (D) were leaving
95. Choose the correct passive voice:
m
om
People consider her one of the finest classical dancers.
. co
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(A) She is considered one of the finest classical dancers.
e m
m
(B) One of the finest classical dancers is considered by people.
e l as
as
(C) It is considered that she was a classical dancer.
l ag
g
(D) She has been considered by people as finest classical dancer
a
96. Identify the grammatically correct sentence.
(A) Each of the students have submitted their assignments.
(B) Neither the teacher nor the students was aware of the change.
(C) The criteria for selection are clearly mentioned in the notice.
(D) One of the player were absent yesterday.

97. Choose the correct use of articles:
m
.co
________ university professor delivered ________ inspiring lecture on postcolonial
literature.
e m
(A) An, an (B) A, an
l as (C) A, a (D) An, a
Which of the following sentences g
98.
a contains the correct use of pronoun?
(A) Between you and I, the decision seems unreasonable.
(B) Neither of the boys have completed their assignment.
(C) Each candidate must present his or her identification card.
(D) Whom do you think will be selected for the position?

99. Identify the sentence with the correct sequence of tenses.
(A) He said that he is working on a new project.
(B) She informed me that the train had arrived at six o’clock daily. m
m (C) The scientist explained that water boils at 100°C. .co
.co (D) I knew that he has already submitted the application.
s e m
s em100. Which of the following sentences is grammatically correct? gla
g la (A) No sooner did the lecture begin when the students started ataking notes.
a (B) Hardly had the match started than it began to rain heavily.
(C) Scarcely had she completed the assignment when the supervisor called her.
(D) Barely had he entered the room than the lights went out.
x-x-x

m (9)
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ROUGH WORK

(10)

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m .co s e m PUMEET 2026 Question Paper

s e l a
a ag [PU-MEET-2026]

ROUGH WORK

m
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m
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s e g la
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m (11)
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ROUGH WORK

(12)

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