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JEE Advanced 2023 · Paper 1

A full paper in the 2023 Paper 1 pattern: Physics, Chemistry and Mathematics, 17 questions each, one 180-minute clock. Take it as a timed mock or open it in learn mode and check every answer.

51questions

180 minone clock

180maximum marks

4/34/13easy / medium / hard

Start timed mock Study with solutions

Sections and marking

Each subject has the same 4 sections, 60 marks per subject.

Section	Type	Questions	Marking
Section 1	One or more correct	3	+4 all correct, partial +3/+2/+1, -2 otherwise
Section 2	Single correct	4	+3 / -1
Section 3	Integer answer	6	+4, no negative
Section 4	Matching lists	4	+3 / -1

Topics in this paper

Physics · 17 questions

Rotational dynamics1
Charged particle in parallel E and B fields1
Series LCR circuit and resonance1
Fluid buoyancy with spring1
Capacitors with charge sharing and dielectric1
Electromagnetic induction on an inclined rail1
Young's double slit with a glass sheet in a liquid1
Kinetic theory and adiabatic compression of a gas mixture1
Doppler effect with reflection and beats1
DC circuit with capacitor and cells in steady state1
Bohr model of He+ and photoelectric effect1
Gravitation1
Silvered lens1
Polytropic processes of an ideal gas1

Chemistry · 17 questions

p-block (boron family)1
Electrochemistry with complex equilibria1
Reactions of carbonyl compounds1
Chemical equilibrium and van't Hoff equation1
Enolate chemistry and stereoisomerism1
Salt analysis and stoichiometry1
Atomic structure and photoelectric effect1
Free radical halogenation and stereoisomerism1
Raoult's law and fractional distillation1
Eudiometry and mole concept1
Aldol condensation and symmetry1
Ionic equilibrium and selective precipitation1
Oxoacids of phosphorus1
Coordination compounds1

Mathematics · 17 questions

Monotonicity and extrema of ln x / x1
Complex numbers and roots of unity1
Lines in three dimensions1
Conditional probability and Bayes theorem1
Ellipse1
Differential equations (homogeneous)1
Matrices and determinants (circulant)1
Number theory1
Binomial coefficients and Lucas theorem1
Limits using series expansion1
Vector equations1
Recurrence relations and bounds1
Counting onto functions1
Circles and common tangents1

Sample question from this paper

Mathematics · Monotonicity and extrema of ln x / x · one or more options correct

Let

h(x)=\dfrac{\ln x}{x}

for

x>0

. Using properties of

h

, decide which of the following statements is/are correct.

A. $h$ attains its maximum value at $x=e$
B. $\pi^{e}<e^{\pi}$
C. The equation $2^{y}=y^{2}$ has a solution $y=4$ with $y\neq2$
D. $2023^{2024}<2024^{2023}$

Show answer and solution

Answer: A, B, C

h'(x)=\dfrac{1-\ln x}{x^2}

, so

h

increases on

(0,e)

, attains its maximum at

x=e

and decreases on

(e,\infty)

. Also

a^b>b^a\iff h(a)>h(b)

for

a,b>1

, because

b\ln a>a\ln b

is the same as

\frac{\ln a}{a}>\frac{\ln b}{b}

.
(A) True: maximum at

x=e

h(e)=\frac1e

.
(B) True:

h(e)>h(\pi)

gives

\frac{1}{e}>\frac{\ln\pi}{\pi}

, i.e.

\pi>e\ln\pi

, i.e.

e^\pi>\pi^e

(equivalently

\pi^e<e^\pi

).
(C) True:

h(2)=\frac{\ln2}{2}=\frac{2\ln2}{4}=h(4)

, and indeed

2^4=4^2=16

.
(D) False:

2023,2024>e

lie on the decreasing branch, so

h(2023)>h(2024)

, which means

2023^{2024}>2024^{2023}

, the opposite of the stated inequality.

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