AMUEEE 2026 Question Paper with Answer Key

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AMUEEE 2026
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AMUEEE 2026 Question Paper

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m .co s e m AMUEEE 2026 Question Paper

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Question Paper — Series B
100 MCQs · Physics · Chemistry · Mathematics

Q1. Among Ar, HF, NH4Cl and HCl, the strength of interatomic/intermolecular forces follow the
order :
(A) HF > HCl > Ar > NH4Cl
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(B) NH4Cl > HF > HCl > Ar

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(C) HCl > Ar > NH4Cl > HF

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(D) Ar > NH4Cl > HF > HCl
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Q2. When copper is heated with concentrated HNO3, it produces :
(A) Cu(NO3)2, NO and NO2
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(B) Cu(NO3)2 and N2O
(C) Cu(NO3)2 and NO2
(D) Cu(NO3)2 and NO

Q3. Which of the following compound belongs to 'Monoclinic' crystal system ?
(A) Na2SO4.10H2O
(B) CuSO4.5H2O
(C) K2Cr2O7
(D) CaSO4

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Q4. Which of the following oxoacids of chlorine does not possess 'Cl = O' bond(s) ?

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(A) chlorous acid
(B) perchloric acid
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(C) chloric acid
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(D) hypochlorous acid
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Q5. The number of unshared pair of valence electrons in the Lewis dot structure of CO is :
(A) 0
(B) 1
(C) 2
(D) 3

Q6. The number of possible geometrical isomers of square planar MABXL (M = metal, A, B, X,
L – unidentate ligand) and Octahedral [Co(NH3)3(NO2)3] are, respectively :
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(A) 0 and 2
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(B) 2 and 1
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(C) 1 and 1

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Q7. Which one is used as bleaching agent for paper pulp and textile ?
a (A) ClO2
(B) Cl2O
(C) Cl2O5
(D) Cl2O7

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Q8. Nitrogen accepts electron and converts into N2^- when the electron goes to :
(A) Antibonding π molecular orbital
(B) Bonding π molecular orbital
(C) σ bonding molecular orbital
(D) σ antibonding molecular orbital

Q9. Which of the following chelating ligands is used to treat lead poisoning ?
(A) EDTA
(B) D-pencillamine
(C) desferrioxamine B
(D) dimethyl glyoxime

Q10. Which of the following does not exist for lanthanide (Ln) elements ?
(A) Ln2S3
(B) Ln2N3
(C) Ln2O3
(D) LnC2

Q11. The dihedral angles of H2O2 structure in gas phase and in solid phase (at 110 K) are,
respectively :
(A) 111.5° and 99.2°
(B) 99.2° and 90.2°
(C) 119.3° and 111.5°
(D) 111.5° and 90.2°

Q12. The IUPAC name of (cyclohexyl)—CONH—(phenyl) is :
(A) N-Cyclohexyl Benzamide
(B) N-Phenyl-N-Cyclohexyl Methanamide
(C) N-Phenyl Cyclohexane Carboxamide
(D) N-Cyclohexyl-N-Phenyl Methanamide

Q13. Ortho-nitrophenol is less soluble in water than p- and m-nitrophenols because :
(A) o-nitrophenol shows intramolecular H-bonding
(B) o-nitrophenol shows intermolecular H-bonding
(C) melting point of o-nitrophenol is lower than those of m- and p-nitrophenols
(D) o-nitrophenol is more volatile in steam than m- and p-nitrophenols

Q14. Which of the following is weakest acid ?
Options:

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Q15. Major product (X) of the following reaction is : phenyl benzoate (C6H5-COO-C6H5) +
HNO3 / H2SO4 -> X
Options:

Q16. The structure of β-D-ribose is :
Options:

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Q17. Which of the following is correct statement ?
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(A) OH⁻ is used as a 'nucleophile' in S_N1 reaction and 'base' in alkene formation reaction

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(dehydrohalogenation reaction i.e. β-elimination reaction).

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(B) OH⁻ is used as a 'nucleophile' in S_N1 reaction and in alkene formation reaction
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(dehydrohalogenation reaction i.e. β-elimination reaction).
(C) OH⁻ is used as a 'base' in S_N1 reaction and in alkene formation reaction

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(dehydrohalogenation reaction i.e. β-elimination reaction).
(D) OH⁻ is used as a 'base' in S_N1 reaction and 'nucleophile' in alkene formation reaction
(dehydrohalogenation reaction i.e. β-elimination reaction).

Q18. Which of the following will not undergo haloform reaction ?
Options:

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Q19. Which of the following statement is wrong ?
(A) PVC stands for Polyvinyl chloride
(B) PTFE stands for teflon
(C) PMMA stands for polymethyl methacrylate
(D) Buna-S stands for natural rubber

Q20. Salicylaldehyde can be prepared from phenol using which of the following reaction ?
(A) Cannizaro's reaction
(B) Reimer-Tiemann reaction
(C) Kolbe's reaction
(D) Hell-Volhard Zelinsky reaction

Q21. Identify 'Y' in the following reaction : CH3-CH2-COOH --Red P/Br2--> X --(a) NaCN, (b)
H3O+--> Y
(A) H3C-CH(COOH)(COOH)
(B) H3C-CH(CN)-COOH
(C) H3C-CH(Br)-COOH
(D) H3C-CH(OH)-COOH

Q22. X —[(a) R−MgX/Dry Ether ; (b) H3O+]→ Y —[(a) NaHCO3 ; (b) NaOH and CaO,
heating]→ R−H. The starting material (X) is :
(A) CH3CN
(B) HC≡CH
(C) CO2
(D) H−C(=O)−H

Q23. The molal freezing point constant for water is 1.86 K kg mol^-1. Therefore the freezing
point of 0.1 molal NaCl solution in water is expected to be :
(A) − 1.86°C
(B) − 0.186°C
(C) − 0.372°C
(D) + 0.372°C

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Q24. 10 g of a gas at atmospheric pressure is cooled from 273°C to 0°C keeping the volume
constant, its pressure would become :
(A) 1/2 atm
(B) 1/278 atm
(C) 2 atm
(D) 273 atm

Q25. In electrolysis of CuCl2 solution, the mass of cathode increased by 6.4 g. What occurred
at Cu anode ?
(A) 0.224 L of Cl2 liberated
(B) 1.12 L of O2 liberated
(C) 0.05 mole of Cu^2+ passed into solution
(D) 0.1 mole of Cu^2+ passed into solution

Q26. Rate = Z_AB e^(-Ea/RT) . e^(-Ea/RT) represents :
(A) collision frequency of reactants.
(B) fraction of molecules with energies equal to or greater than activation energy.
(C) fraction of molecules with energies less than activation energy.
(D) proper orientation of the reacting molecules.

Q27. For a half order reaction ((1/2)A → Product), [A]^(1/2) vs t is represented as :
Options:

Q28. The variation of molar conductivity with (concentration)^(1/2) of electrolytes shows
straight line with negative slope. Which of the following statement is correct ?
(A) The slope is represented by limiting molar conductivity.
(B) The slope does not depends on charges of on the cation and anion.
(C) The electrolytes is acetic acid.
(D) The electrolytes is potassium chloride.

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Q29. On heating zinc oxide turns yellow. The reason is :
(A) metal excess defect due to the presence of extra Zn^2+.
(B) metal deficiency defect.
(C) metal-excess defect due to the anionic vacancies.
(D) impurity defects.

Q30. Calculate the equilibrium constant at 298 K for the synthesis of ozone from oxygen as
represented by the equation 3O2(g) → 2O3(g). The free energy of formation of O2 at 298 K is
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ΔG°f(298 K) = 163.4 kJ mol^-1.
(A) – 57.285
(B) 1.35 × 10^-25
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(C) 5.18 × 10^-58 m l as
a s
(D) 1.29 × 10^-7
a g
l liquid solution, which of the following expression represents the Raoult's
a g
Q31. For a binary
law ?
(A) p = p_1° x_1 + p_2° x_2
(B) p = p_1° x_1
(C) p = p_2° x_2
(D) p = p_1° x_2 + p_2° x_1

Q32. Arrange the following metals in the order in which they displace each other from the
solution of their salts : Al, Cu, Fe, Mg, Zn
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(A) Al, Mg, Zn, Cu, Ag, Fe
(B) Ag, Al, Mg, Zn, Fe, Cu
(C) Zn, Al, Mg, Ag, Cu, Fe
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(D) Mg, Al, Zn, Fe, Cu, Ag
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Q33. Vanishing cream is a example of : g
(A) Micelles
a
(B) Oil dispersed in water
(C) Water dispersed in oil
(D) Homogenous catalyst

Q34. A person lifts a 100 kg box to a height of 7.46 meters in 1 minute and 40 seconds. What
is the power used ? (Take g = 10 m/s^2)
(A) 746 watt
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(B) 100 watt

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(C) 74.6 watt

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(D) 10 HP
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Q35. A uniform disc of mass M and radius R has a moment of inertia Iaabout its central axis.
l central axis, is :
The moment of inertia about a tangent, to the disc, that is parallel togthe
l a a
ag (A) 3/2 MR^2
(B) 7/2 MR^2
(C) 5/2 MR^2
(D) 2/5 MR^2

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Q36. Two masses, 4 kg and 6 kg, are placed at distances 2 m and 5 m along a line from a
fixed point, respectively. What is the centre of mass of the system from the fixed point ?
(A) 2.0 m
(B) 3.5 m
(C) 3.8 m
(D) 5.0 m

Q37. The escape velocity of a planet having mass 6 times and radius 2 times that of the earth
is [Ve is the escape velocity of the earth] :
(A) 2√3 Ve
(B) √3 Ve
(C) √2 Ve
(D) 2 Ve

Q38. Two planets have the same average density, but their radii are r1 and r2. If acceleration
due to gravity on these planets is g1 and g2, respectively, then :
(A) g1/g2 = r1/r2
(B) g1/g2 = r2/r1
(C) g1/g2 = r1^2/r2^2
(D) g1/g2 = r2^2/r1^2

Q39. Two soap bubbles with radii r1 and r2 (r1 > r2) come in contact. Their common surface
has a radius of curvature r equals to :
(A) (r1 + r2)/2
(B) r1r2/(r1 - r2)
(C) r1r2/(r1 + r2)
(D) √(r1r2)

Q40. A liquid with a density of 0.88 kg/m^3 and viscosity of 0.1 Pa.s flows through a pipe of
radius 1 cm with a velocity gradient of 500 s^-1. What is the shear stress in the liquid ?
(A) 50 dyne/m^2
(B) 44 dyne/cm^2
(C) 50 N/m^2
(D) 44 N/m^2

Q41. A monoatomic gas at a pressure P, having a volume V, expands isothermally to a volume
2V and then adiabatically to a volume 16V. The final pressure of the gas is [Take r = 5/3] :
(A) P/4
(B) P/16
(C) P/32
(D) P/64

Q42. An ideal gas is taken through a cyclic process. During one complete cycle, the gas
absorbs 500 J of heat and does 200 J of work. The change in internal energy of the gas is :
(A) 700 J
(B) 0
(C) – 300 J
(D) 300 J

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Q43. The molar mass of oxygen is 83.14 g/mol and the universal gas constant R = 8.314 J/mol
K, the rms speed of an oxygen molecule at 7500 K is :
(A) 1000√2 m/s
(B) 1500 m/s
(C) 1500√2 m/s
(D) 750 m/s

Q44. A molecule of a gas has six degrees of freedom. Then the molar specific heat of the gas
at constant volume is :
(A) R/2
(B) R
(C) 3R
(D) 2R

Q45. Consider superposition of two waves y₁ = A₁sin (ωt − kx) and y₂ = A₂sin(ωt − kx + φ). The
ratio of the minimum and maximum resultant intensities (I_min/I_max) is :
(A) ((A₁ + A₂)/(A₁ − A₂))^2
(B) A₁^2/A₂^2
(C) √((A₁ − A₂)/(A₁ + A₂))
(D) ((A₁ − A₂)/(A₁ + A₂))^2

Q46. The ratio of electric force to gravitational force between two particles having charges a₁,
a₂ and masses m₁ and m₂ respectively is :
(A) 4π ε₀ m₁m₂G / (a₁ a₂)
(B) 4π ε₀ Gm₁m₂ / (a₁ a₂ r⁴)
(C) a₁ a₂ r⁴ / (4π ε₀ Gm₁m₂)
(D) a₁ a₂ / (4π ε₀ Gm₁m₂)

Q47. Two equal charges (+ Q) are placed on a line. Another charge q is placed at the mid-
point. What should be the ratio q/Q to maintain the system in equilibrium ?
(A) + 1/2
(B) − 1/2
(C) + 1/4
(D) − 1/4

Q48. Two identical 60 W, 120 V bulbs are connected in series across a 240 V supply. The total
power consumed will be :
(A) 60 W
(B) 240 W
(C) 120 W
(D) 480 W

Q49. Two particles having equal charges, after being accelerated through the same potential
difference, enter a region of uniform magnetic field. The particles then describe circular paths
of radius r₁ and r₂, respectively. What is the ratio of the masses of the two particles, in terms of
the radiuses ?
(A) √(r₁/r₂)
(B) r₁/r₂
(C) (r₁/r₂)^(3/2)
(D) (r₁/r₂)^2

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Q50. Two long, parallel wires are placed in free space along the x-axis and are separated by a
distance d. One wire carries a current I₁, while the other carries a current of −I₁. The force per
unit length between the wires, where μ₀ represents the permeability of free space, is given by :
(A) μ₀I₁²/(2πd), attract each other.
(B) attracting each other with an infinite force.
(C) μ₀I₁²/(2πd), repulse each other.
(D) 0, as the wires are effectively neutral.

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Q51. A periodic alternating current is given by : i(t) = 5sin(100t) + 12sin(300t) A The maximum

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and root-mean-square values of this current are :
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(A) 13 A and 13/√2

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(B) 12 A and 12/√2 m l a
as
(C) 17 A and 17/√2
l ag
g
(D) 30 A and 30/√2
a
Q52. Two coils have a mutual inductance of 0.01 H. The current in the first coil changes
according to equation I = 5sin(200πt). The maximum value of e.m.f. induced in the second coil
is :
(A) 10π volt
(B) π volt
(C) 0.1π volt
(D) 0.01π volt

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Q53. The equation of a progressive wave is y = 3sin[π((t/3) − (x/5)) + π/4], where x and y are
in metre and time in second. Which of the following is correct ?
(A) Velocity is 1.5 m/s
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(B) Amplitude is 3 cm
l as
ag
(C) Frequency is 0.2 Hz
(D) Wavelength is 10 m

Q54. The apparent flattening of sun at sunset and sunrise is due to :
(A) refraction
(B) diffraction
(C) total internal reflection
(D) interference

Q55. A concave mirror has a focal length of 50 cm. An object is placed 40 cm from the mirror.
Find the distance from the image and its nature :
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(A) 200 cm, Virtual, Upright and Magnified
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(B) 200 cm, Real, Inverted and Magnified
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(C) 200/9 cm, Virtual, Upright and Magnified
s (D) 200/9 cm, Real, Inverted and Magnified
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g la Q56. A particle with a mass of 10^-27 gm has a de Broglie wavelength
a of 10^5 picometer.
a What is the order of magnitude of the particle's velocity ?
(A) ~ 10^3 m/s
(B) ~ 10^4 m/s
(C) ~ 10^5 m/s
(D) ~ 10^6 m/s

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Q57. A metal surface is illuminated with a light wavelength of 662.6 nm. The work function of
the metal is 2 × 10^-12 ergs. The maximum kinetic energy of the emitted electrons is :
(A) 1.0 × 10^-12 ergs
(B) 662.6 ergs
(C) 1.0 eV
(D) 662.6 eV

Q58. Which of the following has highest proton to neutron ratio ?
(A) 8O^16
(B) 2He^4
(C) 26Fe^56
(D) 92U^235

Q59. Over what range of input voltage will the zener circuit shown in the figure maintain 30 V
across 2000 Ω load, assuming that series resistance R = 200 Ω and zener current rating is 25
mA ?
(A) 13 V to 18 V
(B) 23 V to 28 V
(C) 33 V to 38 V
(D) 43 V to 48 V

Q60. A physical quantity X is expressed as X = A^2B^0.5/CD^(1/3). Given that the percentage
errors in A, B, C and D are 2%, 4%, 1% and 3%, respectively, what is the percentage error in
X using the simpler average error formula ?
(A) 10%
(B) 6.68%
(C) 8%
(D) 4%

Q61. The dimensional formula of viscosity η is :
(A) [ML^-2T^-1]
(B) [MLT^-1]
(C) [ML^2T^-1]
(D) [ML^-1T^-1]

Q62. A boat is moving at a velocity of 12 m/s towards north, while the river flows at 5 m/s
towards east. The resultant velocity is :
(A) 13 m/s at tan^-1 (5/12) degree from east
(B) 13 m/s at tan^-1 (12/5) radian from east
(C) 13 m/s at tan^-1 (12/13) radian from east
(D) 13 m/s at tan^-1 (5/13) radian from east

Q63. Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The
ratio of the maximum height attained by the two projectiles respectively is :
(A) 2 : √3
(B) √3 : 1
(C) 1 : 3
(D) 1 : √3

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Q64. A rolling sphere moves on a rough horizontal surface without slipping. The work done by
friction is :
(A) zero
(B) mass of the rolling sphere × gravitational acceleration × height
(C) always negative
(D) depends on the radius of rolling sphere, mass, height and gravitational acceleration

Q65. A body of mass 10 kg is placed on a rough horizontal surface with a coefficient of kinetic
friction 0.4. What is the force of friction acting on the body ? (Take g = 10 m/s²)
(A) 4 × 10⁶ dyne
(B) 3.92 × 10⁶ dyne
(C) 4 × 10⁵ dyne
(D) 3.92 × 10⁵ dyne

Q66. A ball moving with velocity v strikes a smooth, fixed horizontal surface at an angle θ and
rebounds elastically. The coefficient of restitution e for this collision is :
(A) 0
(B) sin θ
(C) cos θ
(D) 1

Q67. If A and B are two square matrices of order 3 × 3, which satisfy AB = A and BA = B, then
(A + B)^9 equals :
(A) 9 (A + B)
(B) 9I_3×3, where I_3×3 is the identity matrix of order 3 × 3
(C) 256 (A + B)
(D) 256I_3×3

Q68. The total number of solutions of 16^(cos^2 x) + 16^(sin^2 x) = 10 in x ∈ [0, 3π] is equal to
:
(A) 4
(B) 8
(C) 12
(D) 16

Q69. A box contains 6 red, 4 white and 5 black balls. A person draws 4 balls from the box at
random. The probability that, among the balls drawn there is at least one ball of each colour,
will be :
(A) 48/91
(B) 38/91
(C) 28/91
(D) 18/91

Q70. The value of sin(π/n) · sin(2π/n) · sin(3π/n) · .... sin((n−1)π/n), where n ∈ N, n ≥ 2, is :
(A) 2^(n−1)/n
(B) n/2^(n−1)
(C) n · 2^(n−1)
(D) n/2^(n+1)

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Q71. A water tank has the shape of an inverted right circular cone with its axis vertical and
vertex lowermost. Its semi-vertical angle is tan^-1(0.5). Water is poured into it at a constant
rate of 5 cubic meter per hour. The rate at which the level of the water is rising at the instant,
when the depth of the water in the tank is 4 m, will be :
(A) 15/88 m/hour
(B) 25/44 m/hour
(C) 35/88 m/hour
(D) 45/88 m/hour
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Q72. The least perimeter of an isosceles triangle circumscribed about a circle of radius r is : . co
. c e m
s
(A) 5√3 r
(B) 6√3 r
e m l a
(C) 7√3 r
l as ag
g
(D) 8√3 r
a
Q73. The equation of a tangent to the curve y = cos (x + y); −2π ≤ x ≤ 2π, which is parallel to
the line x + 2y = 0, is :
(A) 2x + 4y + 3π = 0
(B) 2x + 4y + π = 0
(C) 2x + 4y + 5π = 0
(D) 2x + 4y + 7π = 0

Q74. The area of the segment cut off from the parabola y^2 = 2x by the straight line y = 4x − 1,
m
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is :
(A) 7/32
(B) 9/32
e m
(C) 11/32
l as
agx dx / (sin^4(2x) + cos^4(2x)) equals :
(D) 13/32

Q75. The value of the integral ∫_0^(π/4)
(A) √2 π^2 / 8
(B) √2 π^2 / 16
(C) √2 π^2 / 32
(D) √2 π^2 / 64

Q76. Let P(X) denotes the power set of X, where X is any non-empty set. For non-empty sets
A and B, which of the following is incorrect ?
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(A) P(A) ⊆ P(B) ⇒ A ⊆ B
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(B) P(A ∩ B) ⊆ P(A) ∩ P(B)

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(C) P(A) ∪ P(B) ⊆ P(A ∪ B)
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(D) P(A ∪ B) ⊆ P(A) ∪ P(B)
s g l
g la 11, .... and Y be the set consisting of the first 2018 terms of the arithmetic
Q77. Let X be the set consisting of the first 2018 terms of the
a
arithmetic

a 23,....... . Then the number of elements in the set X ∪Y is :
progression 9, 16,

(A) 3478
(B) 3748
(C) 4384
(D) 3847

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Q78. If a root of the equation a_1x^2 + b_1x + c_1 = 0 is the reciprocal of a root of the
equation a_2x^2 + b_2x + c_2 = 0, then :
(A) (a_1a_2 − c_1c_2)^2 = (a_1b_2 − b_1c_2)(a_2b_1 − b_2c_1)
(B) (a_1a_2 − b_1b_2)^2 = (a_1b_2 − b_1c_2)(a_2b_1 − b_2c_1)
(C) (b_1c_2 − b_2c_1)^2 = (a_1b_2 − b_1c_2)(a_2b_1 + b_2c_1)
(D) (b_1c_2 − b_2c_1)^2 = (a_1b_2 + b_1c_2)(a_2b_1 − b_2c_1)

Q79. Four persons independently solve a certain problem correctly with probabilities 1/2, 3/4,
1/4, 1/8. Then the probability that the problem is solved correctly by at least one of them is :
(A) 235/256
(B) 21/256
(C) 3/256
(D) 253/256

Q80. Let a, b, c, d be in geometric progression. Then which one of the following is incorrect ?
(A) a^n + b^n, b^n + c^n, c^n + d^n are in geometric progression, where n is any positive integer
(B) (d + b)(b + c) = (c + a)(c + d)
(C) (b − c)^2 + (c − a)^2 + (d − b)^2 = (a − d)^2
(D) (ab + bc + cd)^2 = (a^2 + b^2)(c^2 + d^2)

Q81. Solution of the inequality x − 3 < √(x^2 + 4x − 5) is :
(A) (−∞, −5] ∪ [1, ∞)
(B) (−5, 3]
(C) (−∞, −5] ∪ (7/5, ∞)
(D) (7/5, ∞)

Q82. The sum of all five-digit numbers that can be formed using the digits 3, 4, 5, 6, 7 (without
repetition) is :
(A) 66600
(B) 666600
(C) 6666600
(D) 6600

Q83. Let f(x) and g(x) be real valued functions of a real variable x. Suppose that f′(x) = g(x) and
g′(x) = −f(x) for all x ∈ ℝ. If f(5) = 2 = f′(5), then (f(10))^2 + (g(10))^2 is equal to :
(A) 2
(B) 4
(C) 8
(D) 10

Q84. If the vector 5î + 4 is decomposed into the vectors →u and →v, where →u and →v are
respectively parallel and perpendicular to the vector î − ĵ + , then |→u|^2 + |→v|^2 equals :
(A) 41
(B) 42
(C) 43
(D) 44

Q85. ∫ dx/(3 sin x + 4 cos x) equals :
(A) ln |(2 + tan(x/2))/(4 − tan(x/2))| + C
(B) (1/5) ln |(2 + tan(x/2))/(4 + 2 tan(x/2))| + C
(C) (3/5) ln |(1 + 2 tan(x/2))/(4 − 2 tan(x/2))| + C
(D) (1/5) ln |(1 + 2 tan(x/2))/(4 − 2 tan(x/2))| + C

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Q86. If the system of linear equations x + ky + 3z = 0 3x + ky − 2z = 0 2x + 4y − 3z = 0 has a
non-zero solution (a, b, c), then (a^2 + c^2)/b^2 equals :
(A) 26
(B) 27
(C) 28
(D) 29

Q87. Let Δ be the "relation of equality" in the set ℝ, of real numbers i.e., Δ = {(a,a) | a ∈ ℝ}
and R be any arbitrary relation in ℝ. Then which one of the following statements is incorrect ?
(A) Δ is an equivalence relation.
(B) Δ ⊆ R if R is a reflexive relation.
(C) Δ ⊆ R if R is a symmetric relation.
(D) Δ is also a function from ℝ to ℝ.

Q88. If the lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0 are concurrent, where a ≠ b ≠ c
≠ 1, then 1/(1−a) + 1/(1−b) + 1/(1−c) equals :
(A) − 1
(B) 1
(C) 1/2
(D) − 1/2

Q89. The differential equation of all circles of radius 5 units is :
(A) 25[1 + (dy/dx)^2]^3 = [d^2y/dx^2]^2
(B) [1 + (dy/dx)^2]^3 = 25[d^2y/dx^2]^2
(C) 25[1 + (dy/dx)^3]^2 = [d^2y/dx^2]^3
(D) [1 + (dy/dx)^2]^3 = [d^2y/dx^2]^2

Q90. The value of cos^4 π/8 + cos^4 3π/8 + cos^4 5π/8 + cos^4 7π/8 is :
(A) 1
(B) 1/2
(C) 5/2
(D) 3/2

Q91. The minimum value of z = 2x_1 + 3x_2 subject to the constraints 2x_1 + 7x_2 ≥ 22, x_1
+ x_2 ≥ 6, 5x_1 + x_2 ≥ 10 and x_1, x_2 ≥ 0 is :
(A) 14
(B) 20
(C) 10
(D) 16

Q92. The value of sin^-1(12/13) + cos^-1(4/5) + tan^-1(63/16) is equal to :
(A) 4π/3
(B) π/2
(C) π
(D) π/3

Q93. The r^th term from the end in the expansion of (x + a)^n is :
(A) nC_(n-r) x^(r-1) · a^(n-r+1)
(B) nC_r x^(r-2) · a^(n-r+2)
(C) nC_(n-r+1) x^(r-1) · a^(n-r+1)
(D) nC_(r-1) x^(n-r+1) · a^(r-1)

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.
m .co s e m AMUEEE 2026 Question Paper

e l a
as a g AMU B.Tech (Engineering) Admission Test 2026

Q94. Let f(x) = x^135 + x^125 - x^115 + x^5 + 1. If f(x) is divided by x^3 - x, then the remainder
is some function of x, say g(x). Then g(x) is :
(A) surjective but not injective
(B) injective but not surjective
(C) neither injective nor surjective
(D) Option not available

Q95. The locus of a point, which moves such that the sum of the squares of its distances from
m
co
the vertices of a triangle is constant, is a/an :
(A) Circle
(B) Parabola
. c om e m .
(C) Ellipse
e m l as
a
(D) Hyperbola
l s a g
Q96. If Z_k, kg= 1, 2, 3, ....6 are the roots of the equation Z^6 = 1, then the area of the figure
a
formed by joining the points represented by Z_k, is :
(A) √3/2 sq units
(B) 5√3/2 sq units
(C) 3√3/2 sq units
(D) 4√3/5 sq units

Q97. Let P_1 : ·(2î + ĵ − ) − 3 = 0 and P_2 : ·(î + 2ĵ + ) − 2 = 0 be two planes. Then, which
one of the following statements is incorrect ?
m
.co
(A) The vector equation of the line of intersection of P_1 and P_2 is = (4/3)î + (1/3)ĵ + λ(î − ĵ + ),
where λ ∈ R.
(B) The acute angle between P_1 and P_2 is 60°.
e m
as
(C) The line (x−4)/1 = (y−5)/(−1) = (z−6)/(−2) is perpendicular to the line of intersection of P_1 and
l
ag
P_2.
(D) If P_3 is the plane passing through the point (4, 2, −2) and perpendicular to the line of
intersection of P_1 and P_2, then the distance of the point (2, 1, 1) from the plane P_3 is √3.

Q98. Consider the vectors u→ = 2i^ - j^ + k^, v→ = i^ - 2j^ + k^ and w→ = i^ - j^ + 2k^. Then
which one of the following statements is correct regarding u→, v→ and w→ ?
(A) There exist scalars α, β, γ, not all zero such that α u→ + β v→ + γ w→ = 0→.
(B) Each one of these vectors can be written as a linear combination of the remaining two.
(C) The projection vector of u→ on the vector v→ is 1/6 (i^ - 2j^ + k^).
(D) If a u→ + b v→ + c w→ = 0→, for same scalars a, b, c, then a = b = c = 0.
m
m .co
Q99. The equation of the normal to the plane r→ = (i^ - j^ + k^) + λ(2i^ - 2j^ + 2k^) + μ(i^ + 2j^

c. (A)o (x-1)/5 = (y-3)/2 = (z-2)/(-3)
+ 3k^), where λ, μ ∈ ℝ, which passes through the point with position vector i^ + 3j^ + 2k^, is :
s e m
e m (B) (x-1)/2 = (y-3)/5 = (z-2)/3 la
las (C) (x-1)/3 = (y-3)/5 = (z-2)/(-2)
ag
ag (D) (x-1)/3 = (y-3)/(-2) = (z-2)/5

Q100. Let the coordinates of the foot of perpendicular, drawn from the origin to the line r→·(i^
+ 2j^ + 3k^) + 4 = 0, r→·(2i^ + 3j^ + 4k^) + 5 = 0 be (α, β, γ), Then γ^2 equals :
(A) 4/9
(B) 1/9
(C) 16/9
(D) 1

m . c
c. o Page 16
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Answer Key — Series B
Official answer key published by Aligarh Muslim University, Aligarh — B.Tech Admission Test 2026-27, SERIES: B (dated
20.04.2026).

Q.No. Ans Q.No. Ans Q.No. Ans Q.No. Ans Q.No. Ans
1 B 21 A 41 D 61 D 81 A
2 C 22 C 42 B 62 B 82 C
3 A 23 C 43 B 63 C 83 C
4 D 24 A 44 C 64 A 84 A
5 C 25 D 45 D 65 A 85 D
6 D 26 B 46 D 66 D 86 D
7 A 27 B 47 D 67 C 87 C
8 A 28 D 48 C 68 C 88 B
9 A 29 A 49 D 69 A 89 B
10 B 30 C 50 C 70 B 90 D
11 D 31 A 51 A 71 C 91 A
12 C 32 D 52 A 72 B 92 C
13 A 33 B 53 D 73 A 93 C
14 A 34 C 54 A 74 B 94 D
15 C 35 A 55 A 75 C 95 A
16 B 36 C 56 A 76 D 96 C
17 A 37 B 57 A 77 B 97 D
18 A 38 A 58 D 78 A 98 D
19 D 39 B 59 C 79 A 99 A
20 B 40 C 60 C 80 D 100 C

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