AEEE Most Repeated Questions 2027: Important Questions with Answers

High Weightage Chapters of AEEE 2027

Focus on the following high-weightage chapters to prioritise your AEEE 2027 preparation and maximise your score.

Maths

Physics

Chemistry

AEEE Important Questions with Answers

The following section contains AEEE important questions with answers for Physics, Chemistry and Mathematics. Students can first attempt each question without looking at the solution and then check their answer.

AEEE Repeated Questions 2027 of Physics

Question 1: Which of the following has the dimensions of capacitance?

A. $M^{-1}L^{-2}T^4I^2$

B. $ML^2T^{-3}I^{-1}$

C. $ML^2T^{-2}I^{-1}$

D. $ML^3T^{-2}I^{-2}$

Correct answer: A

Solution:

Capacitance is defined as $C=\frac{Q}{V}$. Since $[Q]=IT$ and $[V]=ML^2T^{-3}I^{-1}$,

$[C]=M^{-1}L^{-2}T^4I^2$

Question 2: Choose the correct combination of the planet and its average orbital speed(in $\mathrm{km} \mathrm{s}^{-1}$ )

a) Earth (29.8); Saturn(9.65); Venus(35.0); Mars(24.2)

b) Earth (9.65); Saturn(29.8); Venus(35.0); Mars(24.2)

c) Earth (24.2); Saturn(9.65); Venus(35.0); Mars(29.8)

d) Earth (29.8); Saturn(9.65); Venus(24.2); Mars(35.0)

Correct answer: A

Solution:

The average orbital speed of a planet around the Sun is approximately given by

$v=\sqrt{\frac{GM}{r}}$

Thus, planets closer to the Sun generally have higher orbital speeds, while planets farther away have lower speeds.

The average orbital speeds are:

Earth = $29.8\ \mathrm{km,s^{-1}}$

Saturn = $9.65\ \mathrm{km,s^{-1}}$

Venus = $35.0\ \mathrm{km,s^{-1}}$

Mars = $24.2\ \mathrm{km,s^{-1}}$

Therefore, the correct combination is: Earth (29.8); Saturn(9.65); Venus(35.0); Mars(24.2)

Question 3: Two laser beams of wavelengths 640 nm and 400 nm have the same photon flux. What is the ratio of their powers?

A. $64:40$
B. $1:1$
C. $5:8$
D. $25:64$

Answer: C

Solution:

The energy of a photon is $E=\frac{hc}{\lambda}$.

For the same photon flux, power is proportional to photon energy.

Therefore,

$\frac{P_{640}}{P_{400}}=\frac{400}{640}=\frac{5}{8}$

Question 4: For an ideal gas undergoing an adiabatic process, which condition is true?

A. $Q=0$
B. $W=0$
C. $\Delta U=0$
D. $Q=W$

Answer: A

Solution:

In an adiabatic process, there is no heat exchange with the surroundings.

Therefore, $Q=0$.

Using the first law, $\Delta U=Q-W$,

so

$\Delta U=-W$.

Question 5: According to Poiseuille's law, the volume flow rate through a pipe is proportional to:

A. $r$
B. $r^2$
C. $r^3$
D. $r^4$

Answer: D

Solution: Poiseuille's law is:

$Q=\frac{\pi r^4\Delta P}{8\eta L}$

Therefore, $Q\propto r^4$.

If the radius is doubled,

the flow rate becomes $2^4=16$ times.

Question 6: If the charge stored in an isolated capacitor is doubled, how does its stored energy change?

A. It becomes half
B. It doubles
C. It becomes four times
D. It remains unchanged

Answer: C

Solution:

Energy stored in a capacitor is:

$U=\frac{Q^2}{2C}$

If charge becomes $2Q$:

$U'=\frac{(2Q)^2}{2C}=4U$

Therefore, the energy becomes four times.

Question 7: A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

A. The efficiency of a Carnot engine cannot be made larger than 50%

B. 1200 K

C. 750 K

D. 600 K

Answer: C

Solution:

The efficiency of a Carnot engine is given by:

$\eta = 1 - \frac{T_2}{T_1}$

where $T_1$ is the temperature of the source and $T_2$ is the temperature of the sink.

Case I:

Given:

$\eta = 0.4,\qquad T_1 = 500\,\mathrm{K},\qquad T_2 = \text{constant}$

Therefore,

$0.4 = 1 - \frac{T_2}{500}$

$\frac{T_2}{500} = 0.6$

$T_2 = 300\,\mathrm{K}$

Case II: If the efficiency becomes $0.6$, then

$0.6 = 1 - \frac{T_2}{T_1}$

Substituting $T_2 = 300\,\mathrm{K}$,

$0.6 = 1 - \frac{300}{T_1}$

$\frac{300}{T_1} = 0.4$

$T_1 = \frac{300}{0.4} = 750\,\mathrm{K}$

$\boxed{T_1 = 750\,\mathrm{K}}$

Question 8: A capacitor discharges through a resistance $R$. The time required for its charge to fall to half its initial value is:

A. $RC$
B. $RC\ln2$
C. $2RC$
D. $\frac{RC}{2}$

Answer: B

Solution:

During discharge:

$Q=Q_0e^{-t/RC}$

For 50% discharge:

$\frac{Q}{Q_0}=\frac{1}{2}$

Therefore,

$\frac{1}{2}=e^{-t/RC}$

Taking the logarithm:

$t=RC\ln2$

Question 9: A dielectric slab of dielectric constant 3 is placed in an electric field of $10\ Vm^{-1}$. What is the electric field inside the dielectric?

A. $1.1\ Vm^{-1}$
B. $3.33\ Vm^{-1}$
C. $10\ Vm^{-1}$
D. $30\ Vm^{-1}$

Answer: B

Solution:

Electric field inside the dielectric is:

$E=\frac{E_0}{K}$

Therefore,

$E=\frac{10}{3}=3.33\ Vm^{-1}$

Question 10: A parallel-plate capacitor remains connected to a battery. If the separation between its plates is increased, what happens?

A. Electric field and charge both decrease
B. Electric field decreases and charge increases
C. Electric field increases and charge decreases
D. Both electric field and charge increase

Answer: A

Solution:

Since the capacitor remains connected to the battery, $V$ remains constant.

Electric field is:

$E=\frac{V}{d}$

Therefore, increasing $d$ decreases $E$.

Also,

$C=\frac{\epsilon A}{d}$

So, capacitance decreases. Since $Q=CV$ and $V$ is constant, charge also decreases.

AEEE Repeated Questions 2027 of Chemistry

Question 1: A solution contains 20 g of a solute having molar mass 100 g/mol. If the mass of the solvent is 1 kg, what is its molality?

A. $0.02\ m$
B. $0.20\ m$
C. $2.0\ m$
D. $20\ m$

Answer: B

Solution:

Number of moles of solute:

$n=\frac{20}{100}=0.2\ mol$

Molality is:

$m=\frac{\text{moles of solute}}{\text{mass of solvent in kg}}$

$m=\frac{0.2}{1}=0.2\ m$

Question 2: What is the ratio of the speed of infrared radiation to ultraviolet radiation in vacuum?

A. 2
B. $\frac{1}{2}$
C. 1
D. 4

Answer: C

Solution:

All electromagnetic radiation travels at the same speed in vacuum:

$c=3\times10^8\ m/s$

Therefore,

$\frac{v_{IR}}{v_{UV}}=1$

Question 3: Which statement correctly distinguishes an orbit from an orbital?

A. An orbit can hold a maximum of 2 electrons
B. An orbital is a definite circular path of an electron
C. An orbital is a region of high probability of finding an electron
D. An orbit and orbital are exactly the same

Answer: C

Solution:

An orbital represents a three-dimensional region around the nucleus where the probability of finding an electron is high.

Question 4: Which element has an electronic configuration that is an exception to the expected Aufbau filling order?

A. Calcium
B. Titanium
C. Chromium
D. Manganese

Answer: C

Solution: Chromium has the configuration:

$Cr=[Ar]3d^5 4s^1$

instead of the expected $[Ar]3d^4 4s^2$. The half-filled $3d^5$ subshell provides additional stability.

Question 5: Which of the following can be a spontaneous process under suitable conditions?

A. Burning of a matchstick after ignition
B. Evaporation of petrol in an open container
C. Both A and B
D. Neither A nor B

Answer: C

Solution:

Burning of a matchstick after ignition and evaporation of petrol are processes that can proceed spontaneously under suitable conditions.

Question 6: If the dissociation constants for two successive steps are $5\times10^{-5}$ and $1\times10^{-9}$, what is the overall equilibrium constant?

A. $5\times10^4$
B. $2\times10^{-5}$
C. $4\times10^{-4}$
D. $5\times10^{-14}$

Answer: D

Solution:

For successive reactions, the overall equilibrium constant is the product of the individual constants.

$K=K_1K_2$

$K=(5\times10^{-5})(1\times10^{-9})$

$K=5\times10^{-14}$

Question 7: What happens to the melting point of ice when pressure is increased?

A. It increases
B. It decreases
C. It remains unchanged
D. It first increases and then decreases

Answer: B

Solution:

Ice has a larger volume than liquid water. Increasing pressure favours the phase with lower volume, so ice melts at a lower temperature.

Question 8: Which equation is used to calculate electrode potential at a non-standard concentration?

A. Arrhenius equation
B. Nernst equation
C. Henderson-Hasselbalch equation
D. Raoult's law

Answer: B

Solution:

The Nernst equation relates electrode potential to the concentration of ions:

$E=E^\circ-\frac{0.0591}{n}\log Q$

at $25^\circ C$.

Question 9: Which law is used to calculate the quantity of hydrogen required to generate a given amount of electrical charge in a fuel cell?

A. Boyle's law
B. Faraday's law of electrolysis
C. Charles' law
D. Henry's law

Answer: B

Solution:

The amount of substance involved in an electrochemical reaction is related to the quantity of electricity passed through the cell by Faraday's laws.

Question 10: The rate of a reaction becomes four times when the concentration of reactant $X$ is doubled. What is the order of reaction with respect to $X$?

A. 2
B. 4
C. 1
D. 0

Answer: A

Solution:

Let the rate law be:

$r=k[X]^n$

When concentration is doubled:

$4r=k(2[X])^n$

Therefore:

$4=2^n$

So:

$n=2$

Hence, the reaction is second order with respect to $X$.

AEEE Repeated Questions: Mathematics

Question 1: If $z=3+4i$, what is $|z|$?

A. 3
B. 4
C. 5
D. 7

Answer: C

Solution:

$|z|=\sqrt{3^2+4^2}$

$|z|=\sqrt{25}=5$

Question 2: If $z=3-4i$, which statement is correct?

A. Real part = 4
B. Imaginary part = 3
C. Real part = 3 and imaginary part = $-4$
D. Both parts are positive

Answer: C

Solution:

Comparing $z=3-4i$ with the standard form $z=a+ib$:

$Re(z)=3$

and

$Im(z)=-4$

Question 3: If $z=x+iy$ and $x^2+y^2=25$, what is the value of $|z|$?

A. 5
B. 10
C. 25
D. 50

Answer: A

Solution:

$|z|=\sqrt{x^2+y^2}$

Given $x^2+y^2=25$:

$|z|=\sqrt{25}=5$

Question 4: If $\omega$ is a non-real cube root of unity, which relation is correct?

A. $1+\omega+\omega^2=0$
B. $1+\omega+\omega^2=1$
C. $\omega^2=1$
D. $\omega=1$

Answer: A

Solution:

For the non-real cube roots of unity:

$1+\omega+\omega^2=0$

Question 5: Find the range of:

$f(x)=\frac{10^x-10^{-x}}{10^x+10^{-x}}$

A. $(-1,1)$
B. $[0,1]$
C. $(1,\infty)$
D. $(-\infty,\infty)$

Answer: A

Solution:

Let $t=10^x$, where $t>0$.

Then:

$f(x)=\frac{t^2-1}{t^2+1}$

For every positive value of $t$, this expression lies between $-1$ and $1$.

Therefore, the range is:

$(-1,1)$

Question 6: How many triangles can be formed by choosing any 3 vertices of a regular polygon having $n$ sides?

A. $n^2$
B. $n(n-1)$
C. $\binom{n}{3}$
D. $3n$

Answer: C

Solution:

A triangle is formed by selecting any 3 vertices from $n$ vertices.

Therefore:

$^nC_3=\frac{n(n-1)(n-2)}{6}$

Question 7: Find the inverse of the function:

$f(x)=\log_{10}(2-x)$

A. $f^{-1}(x)=2-10^x$
B. $f^{-1}(x)=10^x-2$
C. $f^{-1}(x)=\log_{10}(2+x)$
D. $f^{-1}(x)=2+x$

Answer: A

Solution:

Let:

$y=\log_{10}(2-x)$

Therefore:

$10^y=2-x$

So:

$x=2-10^y$

Replacing $y$ with $x$:

$f^{-1}(x)=2-10^x$

Question 8: What is the sum of the first $n$ natural numbers?

A. $n^2$
B. $\frac{n(n+1)}{2}$
C. $\frac{n(n-1)}{2}$
D. $2n$

Answer: B

Solution:

The sum is:

$1+2+3+\cdots+n$

Using the standard formula:

$S_n=\frac{n(n+1)}{2}$

Question 9: The numbers $2x$, $2x+1$ and $2x+2$ are in arithmetic progression. What is the value of $x$?

A. 0
B. 1
C. 2
D. Any real value

Answer: D

Solution:

For three numbers to be in A.P.:

$2b=a+c$

Here:

$a=2x$, $b=2x+1$, $c=2x+2$

Therefore:

$2(2x+1)=2x+(2x+2)$

$4x+2=4x+2$

This equation is true for every real value of $x$.

Question 10: What is the arithmetic mean of the first $n$ odd natural numbers?

A. $\frac{n}{2}$
B. $n$
C. $n^2$
D. $2n$

Answer: B

Solution:

The first $n$ odd natural numbers are:

$1,3,5,\ldots,(2n-1)$

Their sum is $n^2$.

Therefore, their arithmetic mean is:

$\frac{n^2}{n}=n$

AEEE Most Scoring Topics in Physics

Focus on these topics first to get a good score in the AEEE exam. Questions from these topics are asked frequently.

AEEE Most Scoring Topics in Chemistry

Complete these high-scoring AEEE Chemistry topics first to cover the most important concepts, improve accuracy, and maximise your potential score in the exam.

AEEE Most Scoring Topics in Mathematics

Given below in the table are some high-scoring mathematics topics that can help you enhance your AEEE preparation and make your revision more focused and effective.

AEEE 2027 Exam Pattern

The exam pattern of AEEE is given in the table below. The AEEE exam consists of 100 questions. The questions are MCQ-based. The exam will be conducted in online mode with a duration of 2 hours 30 minutes.

AEEE Mock Test 2027

Solving mock tests helps candidates get familiar with actual exam conditions. Aspirants should practise mock tests to enhance their preparation.