2026

JEE Main 2026 (Online) 21st January Morning Shift

Paper Analysis Moderate to Difficult

JEE Main 2026 Analysis

Date: January 21 | Shift: 1

Overall Verdict: The overall difficulty level of the paper is reported as Moderate. While Physics and Chemistry were manageable, Mathematics proved to be the deciding factor for time management.

Physics Easy to Moderate

This section was generally considered the most scoring.

  • Questions were largely formula-based and conceptual, with strong alignment to the NCERT syllabus.
  • Key Topics: Modern Physics, Current Electricity, Fluids, and Mechanics.
  • Note: A few students noted a surprise question related to a microscope, which hasn't been asked recently.

Chemistry Moderate

Opinions varied slightly; some found it easy (direct NCERT questions), while others found it tricky (statement-based problems).

  • Balance: Equal weightage given to Organic and Inorganic Chemistry.
  • Physical Chemistry: Involved some numerical calculations but was manageable for those with clear concepts.

Mathematics Moderate to Difficult (Lengthy)

Consistently reported as the toughest section primarily due to its length.

  • Questions were calculation-intensive and time-consuming.
  • High-Weightage Topics: Vectors & 3D Geometry, Calculus (Integration and Differential Equations), and Algebra (Matrices and Determinants).

Summary based on student feedback and initial analysis.

Full Paper Analysis & Solutions

Physics

Multiple Choice Questions

1 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1144
Two capacitors $C$ and $2C$ charged to $V$ and $2V$ respectively are connected in parallel with opposite polarity. The common potential is:
(A)
$V$
(B)
$\frac{V}{2}$
(C)
$2V$
(D)
$3V$
MEDIUM
2 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1145
Ratio of de-Broglie wavelengths of a proton and an alpha particle accelerated through the same potential is:
(A)
$1:2$
(B)
$2\sqrt{2}:1$
(C)
$2:1$
(D)
$\sqrt{8}:1$
MEDIUM
3 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1153
Find dimensions of $\frac{A}{B}$ if $(P+\frac{A^{2}}{B})+\frac{1}{2}\rho V^{2}=$ constant, where $P\rightarrow$ pressure, $\rho\rightarrow$ density, $V$ speed.
(A)
$ML^{1}T^{-4}$
(B)
$ML^{-1}T^{-4}$
(C)
$ML^{2}T^{-4}$
(D)
$ML^{-1}T^{-2}$
HARD
4 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1157
Find the heat produced in the external circuit (AB) in one second (refer to circuit diagram).
(A)
$1181.25 J$
(B)
$1311.25 J$
(C)
$1207.50 J$
(D)
$1410.50 J$
HARD
5 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1161
An $\alpha$-particle having kinetic energy $7.7 MeV$ is approaching a fixed gold nucleus (atomic number $Z=79$). Find the distance of closest approach.
(A)
$1.72 nm$
(B)
$6.2 nm$
(C)
$16.8 nm$
(D)
$0.2 nm$
HARD
6 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1163
An $\alpha$-particle having kinetic energy $7.7 MeV$ is approaching a fixed gold nucleus (atomic number $Z=79$). Find the distance of closest approach. (Duplicate Question)
(A)
$1.72 nm$
(B)
$6.2 nm$
(C)
$16.8 nm$
(D)
$0.2 nm$
MEDIUM
7 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1164
An air-filled capacitor of capacitance $C$ is filled with a dielectric $(k=3)$ of width $\frac{d}{3}$, where $d$ is the separation between the plates. The new capacitance is:
(A)
$C$
(B)
$\frac{9}{7}C$
(C)
$\frac{12}{7}C$
(D)
$\frac{3}{7}C$
MEDIUM
8 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1168
Find the moment of inertia of the system formed using two identical rods about the given axis of rotation as shown in the figure. Each rod has mass M and length L.
(A)
$\frac{17}{12}ML^{2}$
(B)
$\frac{13}{12}ML^{2}$
(C)
$\frac{2}{3}ML^{2}$
(D)
$\frac{3}{4}ML^{2}$
MEDIUM
9 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1169
If the electric field of an EM wave is given by $60[\sin(3\times10^{14}t)+\sin(12\times10^{14}t)]$ at $x=0$ and it falls on a photosensitive material having work function $2.8 eV$, find the maximum kinetic energy (in eV) of the ejected electrons.
(A)
$2.52 eV$
(B)
$2.16 eV$
(C)
$2.00 eV$
(D)
$2.34 eV$
MEDIUM
10 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1175
Find the volume flow rate in the Venturi meter shown below in which water is flowing. Given $\frac{A}{a}=2$, $A=\sqrt{3}m^{2}$, difference in levels is 5 cm and $\rho=1000~kg~m^{-3}$.
(A)
$1$
(B)
$\sqrt{3}$
(C)
$2\sqrt{3}$
(D)
$\sqrt{2}$
MEDIUM
11 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1176
An ideal solenoid is kept with its axis vertical. A current $I_{0}$ is flowing in the solenoid. A charge q is thrown vertically downward inside the solenoid. The acceleration of the charged particle is:
(A)
$g$ downward
(B)
$g$ upward
(C)
Zero
(D)
Depends on current $I_{0}$
MEDIUM
12 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1182
A wave propagates whose electric field is given by $\vec{E}=69~\sin(\omega t-kx)\hat{j}$. Find the direction of the magnetic field.
(A)
$\hat{k}$
(B)
$-\hat{k}$
(C)
$\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
(D)
$\frac{\hat{i}-\hat{j}}{\sqrt{2}}$
MEDIUM
13 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1183
Two rods of equal length 60 cm each are joined together end to end. The coefficients of linear expansion are $24\times10^{-6\circ}C^{-1}$ and $1.2\times10^{-5\circ}C^{-1}$. Initial temperature $30^{\circ}C$ is increased to $100^{\circ}C$. Find final length (in cm).
(A)
$120.1321$
(B)
$120.1123$
(C)
$120.1512$
(D)
$120.1084$
MEDIUM
14 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1189
Two mechanical waves travel on strings of equal length L and equal tension T. The linear mass densities are in ratio $\frac{\mu_{1}}{\mu_{2}}=\frac{1}{2}$. Find the ratio of time taken for a wave pulse to travel from one end to the other.
(A)
$\frac{1}{2}$
(B)
$\frac{1}{\sqrt{2}}$
(C)
$\sqrt{2}$
(D)
$2$
MEDIUM
15 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1194
A potential energy curve U vs x is shown. If $F_{AB}, F_{BC}, F_{CD}, F_{DE}$ are forces in respective regions, arrange magnitudes in decreasing order.
(A)
$F_{BC}>F_{AB}>F_{CD}>F_{DE}$
(B)
$F_{BC}>F_{AB}>F_{DE}>F_{CD}$
(C)
$F_{AB}>F_{BC}>F_{DE}>F_{CD}$
(D)
$F_{BC}>F_{DE}>F_{AB}>F_{CD}$
MEDIUM

Mathematics

Multiple Choice Questions

1 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1141
Evaluate the limit: $\lim_{x\to 0} \frac{\sin(2x) - 2 \sin x}{x^3}$
(A)
1
(B)
$-1$
(C)
$0$
(D)
2
MEDIUM
2 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1142
The value of $\csc 10^{\circ} - \sqrt{3} \sec 10^{\circ}$ is:
(A)
1
(B)
2
(C)
4
(D)
None of these
MEDIUM
3 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1143
7. If $y=y(x)$ and
$$(1+x^2) dy + (1-\tan^{-1} x) dx = 0$$
and $y(0)=1$, then $y(1)$ is equal to:
(A)
$$\frac{\pi^2}{32}+\frac{\pi}{4}+1$$
(B)
$$\frac{\pi^2}{32}-\frac{\pi}{4}+1$$
(C)
$$\frac{\pi^2}{32}-\frac{\pi}{2}-1$$
(D)
$$\frac{\pi^2}{32}-\frac{\pi}{2}+1$$
MEDIUM
4 REMEMBER MCQ_SINGLE 4 Mark(s) 2026
#1147
Evaluate the limit: $\lim_{x\rightarrow0}\frac{sin(2x)-2~sin~x}{x^{3}}$
(A)
$1$
(B)
$-1$
(C)
$0$
(D)
$2$
EASY
5 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1148
The value of $\csc 10^{\circ} - \sqrt{3} \sec 10^{\circ}$ is:
(A)
$1$
(B)
$2$
(C)
$4$
(D)
None of these
MEDIUM
6 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1150
If $y=y(x)$ and $(1+x^{2})dy+(1-\tan^{-1}x)dx=0$ and $y(0)=1$ then $y(1)$ is equal to:
(A)
$\frac{\pi^{2}}{32}+\frac{\pi}{4}+1$
(B)
$\frac{\pi^{2}}{32}-\frac{\pi}{4}+1$
(C)
$\frac{\pi^{2}}{32}-\frac{\pi}{2}-1$
(D)
$\frac{\pi^{2}}{32}-\frac{\pi}{2}+1$
MEDIUM
7 REMEMBER MCQ_SINGLE 4 Mark(s) 2026
#1154
If $L_{1}$ and $L_{2}$ are two parallel lines and $\triangle ABC$ is an equilateral triangle as shown in the figure, then the area of triangle ABC is:
(A)
$7\sqrt{3}$
(B)
$4\sqrt{3}$
(C)
$21\sqrt{3}$
(D)
$84$
EASY
8 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1156
Consider a set $S=\{a,b,c,d\}$. Then the number of reflexive as well as symmetric relations from $S\rightarrow S$ is:
(A)
$1024$
(B)
$256$
(C)
$16$
(D)
$64$
MEDIUM
9 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1159
The locus of the point of intersection of tangents drawn to the circle $(x-2)^{2}+(y-3)^{2}=16$ which subtends an angle of $120^{\circ}$ is:
(A)
$3x^{2}+3y^{2}-12x-18y-25=0$
(B)
$x^{2}+y^{2}-12x-18y-25=0$
(C)
$3x^{2}+3y^{2}+12x+18y-25=0$
(D)
$x^{2}+y^{2}+12x+18y-25=0$
HARD
10 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1160
If $a_{1}, a_{2}, a_3,...$ are in increasing geometric progression such that $a_{1}+a_{3}+a_{5}=21$ and $a_{1}a_{3}a_{5}=64$, then $a_{1}+a_{2}+a_{3}$ is:
(A)
$5$
(B)
$7$
(C)
$10$
(D)
$15$
HARD
11 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1162
If O is the vertex of the parabola $x^{2}=4y$, Q is a point on the parabola. If C is the locus of a point which divides OQ in the ratio 2:3, then the equation of the chord of C which is bisected at the point (1,2) is:
(A)
$5x+4y+3=0$
(B)
$5x-4y-3=0$
(C)
$5x-4y+3=0$
(D)
$5x+4y-3=0$
HARD
12 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1172
Ellipse E: $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$. A hyperbola is confocal with the ellipse and the eccentricity of the hyperbola is equal to 5. If the principal axis of the hyperbola is the x-axis, then the length of the latus rectum of the hyperbola is:
(A)
$\frac{96}{\sqrt{5}}$
(B)
$24\sqrt{5}$
(C)
$18\sqrt{5}$
(D)
$12\sqrt{5}$
HARD
13 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1173
If the mean and variance of observations $x, y, 12, 14, 4, 10, 2$ is 8 and 16 respectively, where $x>y$, then the value of $3x-y$ is:
(A)
$18$
(B)
$20$
(C)
$22$
(D)
$24$
HARD
14 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1179
If O is the vertex of the parabola $x^{2}=4y,$ Q is a point on the parabola. If C is the locus of the point which divides OQ in the ratio $2:3,$ then the equation of the chord of C which is bisected at the point (1,2) is: (Duplicate Question)
(A)
$5x+4y+3=0$
(B)
$5x-4y-3=0$
(C)
$5x-4y+3=0$
(D)
$5x+4y-3=0$
HARD
15 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1180
The value of $\int_{\frac{\pi}{6}}^{\pi}\frac{\pi+4x^{11}}{1-\sin(|x|+\frac{\pi}{6})}dx$ is:
(A)
$3\pi$
(B)
$4\pi$
(C)
$6\pi$
(D)
$12\pi$
HARD
16 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1181
If $f(3)=18$, $f'(3)=0$ and $f''(3)=4$ then the value of $\lim_{x\rightarrow1}\ln(\frac{f(x+2)}{f(3)})^{\frac{18}{(x-1)^{2}}}$ is:
(A)
$2$
(B)
$4$
(C)
$6$
(D)
$8$
HARD
17 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1186
If the domain of the function $\cos^{-1}(\frac{2x-5}{11x-7})+\sin^{-1}(2x^{2}-3x+1)$ is $[a,b]$, then the value of $\frac{1}{ab}$ is:
(A)
$-3$
(B)
$3$
(C)
$2$
(D)
$4$
HARD
18 REMEMBER MCQ_SINGLE 4 Mark(s) 2026
#1187
In the binomial expansion of $(ax^{2}+bx+c)(1-2x)^{26}$, the coefficients of $x$, $x^{2}$, $x^{3}$ are 56, 0 and 0 respectively. Then the value of $(a+b+c)$ is:
(A)
$1500$
(B)
$1403$
(C)
$1300$
(D)
$1483$
EASY
19 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1193
The area enclosed by $x^{2}+4y^{2}\le4$, $y\le|x|-1$, $y\ge1-|x|$ is equal to:
(A)
$4~sin^{-1}(\frac{3}{5})+\frac{6}{5}$
(B)
$sin^{-1}(\frac{3}{5})-\frac{6}{5}$
(C)
$4~sin^{-1}(\frac{3}{5})+\frac{12}{5}$
(D)
$4~sin^{-1}(\frac{3}{5})-\frac{6}{5}$
HARD

NUMERICAL

1 APPLY NUMERICAL 4 Mark(s) 2026
#1151
The sum of roots of the equation $|x-1|^{2}-5|x-1|+6=0$ is:
MEDIUM
2 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1167
If $x^{2}+x+1=0$ then evaluate $(x+\frac{1}{x})^{4}+(x^{2}+\frac{1}{x^{2}})^{4}+...+(x^{25}+\frac{1}{x^{25}})^{4}$
HARD
3 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1174
If $A=\{1,2,3,4,5,6\}$ and $B=\{1,2,3,...,9\}$, then the number of strictly increasing functions $f:A\rightarrow B$ such that $f(i)\ne i$ for all $i$ is:
HARD
4 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1192
If $a_{1}=1$ and for all $n\ge1$, $a_{n+1}=\frac{1}{2}a_{n}+\frac{n^{2}-2n-1}{n^{2}(n+1)^{2}}$, then the value of $\sum_{n=1}^{\infty}(a_{n}-\frac{2}{n^{2}})$ is equal to:
HARD

Chemistry

Multiple Choice Questions

1 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1146
Correct order of acidic strength: (I) Phenol, (II) p-Cresol, (III) m-Nitrophenol, (IV) p-Nitrophenol
(A)
$III>IV>II$
(B)
$IV>III>II$
(C)
$IV>I>III>II$
(D)
$III>IV>II$
MEDIUM
2 COMPETENCY UNDERSTAND MCQ_SINGLE 4 Mark(s) 2026
#1149
An organic compound (A) undergoes the following reactions (see figure). Which of the following is compound (A)?
(A)
Structure 1
(B)
Structure 2
(C)
Structure 3
(D)
Structure 4
HARD
3 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1152
Which of the following is the correct order with respect to the property indicated?
(A)
$Cl>F$ (Ionisation energy)
(B)
$K_{2}O>Na_{2}O>Al_{2}O_{3}$ (Basic nature)
(C)
$K>Na>Al>Mg$ (Metallic character)
(D)
None of these
MEDIUM
4 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1155
Given below are two statements: Statement I: Arginine and Tryptophan are essential amino acids. Statement II: Glycine does not have any chiral carbon.
(A)
Both statement-I and statement-II are correct
(B)
Both statement-I and statement-II are incorrect
(C)
Statement-I is correct and statement-II is incorrect
(D)
Statement-I is incorrect and statement-II is correct
MEDIUM
5 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1165
Observe the following reaction sequence: $(P)\xrightarrow{NH_{3}, \Delta}(Q)\xrightarrow{Br_{2}/KOH}(R)$. Which of the following is the correct structure for P, Q and R? (Refer to image)
(A)
Option 1
(B)
Option 2
(C)
Option 3
(D)
Option 4
MEDIUM
6 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1166
In the following reaction, $MnO4^{2-} \xrightarrow{H^{+}}$ ?. Manganate ion undergoes disproportionation to form:
(A)
$MnO_2, MnO_4^-$
(B)
$MnO_4^-, MnO_2$
(C)
$MnO_2, MnO$
(D)
$MnO_4^-, MnO$
MEDIUM
7 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1170
80 mL of an organic compound is mixed with 264 mL of $O_{2}$ and ignited. It gives 224 mL of gaseous mixture at NTP. After passing through KOH, 64 mL of gas remains. The organic compound is:
(A)
$C_{2}H_{4}$
(B)
$C_{2}H_{2}$
(C)
$C_{4}H_{10}$
(D)
$C_{3}H_{6}$
HARD
8 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1171
Consider the following reaction: $Ca+2HCl \rightarrow CaCl_2+H_2$. If 14g of calcium reacts with excess HCl, choose the incorrect option.
(A)
Mass of $CaCl_2$ produced is 38.85 g
(B)
Moles of $H_2$ produced is 0.35 mol
(C)
Volume of $H_2$ produced at STP is 7.84 L
(D)
Mass of $CaCl_2$ produced is 3.885 g
MEDIUM
9 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1177
Given below are two statements. Statement I: All the pairs of molecules $(PbO,PbO_{2})$; $(SnO,SnO_{2})$ and $(GeO,GeO_{2})$ contain amphoteric oxides. Statement II: $AlCl_{3}$, $BH_{3}$, $BeH_{2}$ and $NO_{2}$ all have incomplete octet.
(A)
Both Statement I and Statement II are correct
(B)
Both Statement I and Statement II are incorrect
(C)
Statement I is correct but Statement II is incorrect
(D)
Statement I is incorrect but Statement II is correct
MEDIUM
10 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1178
Which of the following resonating structures is the most stable?
(A)
Structure 1
(B)
Structure 2
(C)
Structure 3
(D)
Structure 4
MEDIUM
11 COMPETENCY APPLY MCQ_SINGLE 4 Mark(s) 2026
#1188
Find the change in internal energy of a gas if its temperature changes by 10K. Moles=10, $C_{p}=7 cal K^{-1}mol^{-1}$, $R=2~cal~K^{-1}mol^{-1}$.
(A)
$500 cal$
(B)
$1000 cal$
(C)
$250 cal$
(D)
$100 cal$
MEDIUM
12 REMEMBER MCQ_SINGLE 4 Mark(s) 2026
#1190
$C_{6}H_{12}O_{3}$ gives positive iodoform test. On hydrolysis with dilute acid, the product formed gives both Tollens' test and iodoform test. Find the correct structure.
(A)
Structure 1
(B)
Structure 2
(C)
Structure 3
(D)
Structure 4
EASY
13 APPLY MCQ_SINGLE 4 Mark(s) 2026
#1191
Consider the following statements: (A) Propanal and propanone are functional isomers; (B) Ethoxyethane and methoxypropane are metamers; (C) But-2-ene shows optical isomerism; (D) But-1-ene and but-2-ene are functional isomers; (E) Pentane and 2,2-dimethylpropane are chain isomers. The correct statements are:
(A)
A, B, D only
(B)
B, C, D only
(C)
A, B, E only
(D)
A, B, D, E only
MEDIUM

NUMERICAL

1 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1158
Benzene undergoes the following sequence of reactions (see figure). Find the percentage of nitrogen in compound (E).
HARD
2 COMPETENCY APPLY NUMERICAL 4 Mark(s) 2026
#1184
1 g of $AB_{2}$ is dissolved in 50 g of a solvent such that $\Delta T_{f}=0.689~K.$ When 1 g of AB is dissolved in 50 g of the same solvent, $\Delta T_{f}=1.176~K$. Find the molar mass of $AB_{2}$. (Report to nearest integer).
HARD
3 APPLY NUMERICAL 4 Mark(s) 2026
#1185
Out of the following, how many compounds have tetrahedral geometry? $NH4^{+}$, $XeF4$, $[NiCl4]^{2-}$, $[PtCl4]^{2-}$, $[Cu(NH3)4]^{2+}$, $BF3$, $[Ni(CO)4]$
MEDIUM