JEE Main 2026 Jan 21 Shift 1 & 2 Question Paper with Solutions PDF

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Download JEE Main 2026 January 21 Shift 1 and Shift 2 Question Paper PDF with Solutions

The JEE Main 2026 January 21 Shift 1 and Shift 2 question paper with solutions is uploaded below. This memory-based paper will include detailed solutions for Physics, Chemistry, and Mathematics. Students can analyze the JEE Mains 2026 question paper to understand the overall difficulty level of the exam.

JEE Main 2026 January 21 Shift 1 Exam Analysis

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JEE Main 2026 January 21 Shift 2 Exam Analysis

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JEE Main 2026 January 21 Shift 1 and Shift 2 Question Paper with Solutions

Below are memory-based questions from the JEE Main 2026 January 21 Shift 1 and Shift 2 exams. The subject-wise analysis of Physics, Chemistry, and Mathematics will be shared to assist students in self-evaluating their performance and understanding the paper trend.

Jan 21 Shift 2 Questions

Chemistry

Question 1: 1 g of an organic compound produce 1.49 of $\mathrm{Mg}_2 \mathrm{P}_2 \mathrm{O}_7$ Determine % of P

Question 2: Given below are two statements
Statement-I : The correct order for radius is $\mathrm{Al}>\mathrm{Mg}>\mathrm{Mg}^{2+}>\mathrm{A}^{\beta+}$
Statement-II : Atomic size always, depends on electronegativity.
In the light of the above statements, choose the correct option.

1 Statement-I and II are correct

2 Both Statement-I and II are incorrect

3 Statement-I is correct but Statement-II incorrect

4 Statement-I is incorrect but Statement-II correct

Question 3: What will be significant figure of summation of $0.153,153.2$ and 153.2 ?

1) 3

2) 4

3) 5

4) 6

Question 4: When $8.74 \mathrm{~g} \mathrm{MnO}_2$ is treated with HCl , then what will be the weight of $\mathrm{Cl}_2(\mathrm{~g})$ obtained? Molar mass of $\mathrm{MnO}_2=87.4 \mathrm{~g} / \mathrm{mol}$
$1 \quad 7.1 \mathrm{~g}$
$2 \quad 17.1 \mathrm{~g}$
$3 \quad 14.2 \mathrm{~g}$
$4 \quad 3.55 \mathrm{~g}$

Question 5: The rms speed of oxygen molecules at $47^{\circ} \mathrm{C}$ is equal to that of hydrogen molecules kept at $\_\_\_\_$ ${ }^{\circ} \mathrm{C}\left(\frac{M(0)}{M(h)}=\frac{32}{2}\right)$
(A) -100
(B) -253
(C) -20
(D) -235

Question 6: Correct Nucleophilicity order, $\mathrm{CH}_3 \mathrm{COO}^{-}, \mathrm{Ph}-\mathrm{O}^{\ominus}, \mathrm{OH}^{\ominus}, \mathrm{ClO}_4^{-}$

Question 7: Some species are given $\mathrm{NI}^{2+}, \mathrm{Fe}^{2+}, \mathrm{Co}^{2+}, \mathrm{V}^{3+}$ and $\mathrm{Ti}^{2+}$
How many species has magnetic moment (spin only) less than 3 BM.

Question 8 :Match the following

Question 9: Following 4 molecules are given and among them, one is optically active. Find the percentage of carbon in that compound :-
a) n-propyl Chloride
b) iso-propyl Chloride
c) iso-butyl Chloride
d) secondary-butyl Chloride

Question 10: Find concentration of $\mathrm{X}^{2-}$ at equilibrium in $0.1 \mathrm{M} \mathrm{H}_2 \mathrm{X}$.
Given $\mathrm{K}_{\mathrm{a}_1}=2.5 \times 10^{-7}$

$K_{a_2}=1 \times 10^{-13}$

$1 \quad 2.5 \times 10^{-7}$
$2 \quad 1 \times 10^{-13}$
$3 \quad6 \times 10^{-12}$
$4 \quad 5 \times 10^{-10}$

Question 11: The energy of an electron an orbit of Bohr's atom is $-\varepsilon_0 / 4 \mathrm{eV}$ where $\varepsilon_0$ is (G - state) energy. If L is the angular momentum of e in this orbit and h is plank's constant then $\frac{2 \pi \mathrm{~L}}{\mathrm{~h}}$ is $\_\_\_\_$
(A) 2
(B) 4
(C) 5
(D) 6

Question 12: What will be the ratio of wavelength of $3^{\text {rd }}$ line at Paschen Series to $2^{\text {nd }}$ line of Balmer series of H -atom?
$1 \quad \frac{9}{4}$
$2 \quad \frac{3}{2}$
$3 \quad \frac{2}{3}$
$4 \quad \frac{16}{4}$

Question 13: $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ is heated with KCl in pressure of $\mathrm{H}_2 \mathrm{SO}_4$. Find the correct match of product with their oxidation state.
$1 \quad \mathrm{CrO}_2 \mathrm{Cl}_2,+6$
$2 \quad \mathrm{Cr}_2 \mathrm{O}_2 \mathrm{Cl}_2,+6$
$3 \quad \mathrm{Cr}_2 \mathrm{O}_2 \mathrm{Cl}_2,+5$
$4 \quad \mathrm{CrO}_2 \mathrm{Cl}_2,+5$

Maths

Question 1: If three vectors are given as shown.
If angle between vector $\vec{p}$ and $\vec{q}$ is $q$ where $\cos \theta=\frac{1}{\sqrt{3}}$ and $|\vec{p}|=2 \sqrt{3},|\vec{q}|=2$. Then the value of $|\vec{p} \times(\vec{q}-3 \vec{r})|^2-3|\vec{p}|^2$ is

Question 2: The locus of point of intersection of tangents drawn from a point to the circle $(x-2)^2+(y-3)^2=16$, which substends an angle of $120^{\circ}$ is
(A) $3 x^2+3 y^2-12 x-18 y-25=0$
(B) $x^2+y^2-12 x-18 y-25=0$
(C) $3 x^2+3 y^2+12 x+18 y-25=0$
(D) $x^2+y^2-12 x+18 y-25=0$

Question 3: Let $f(x)=x^3+x^2 f(1)+2 x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in R$. Then the value of $f^{\prime}(5)$ is

A) $\frac{117}{5}$
B) $\frac{62}{5}$
C) $\frac{657}{5}$
D) $\frac{2}{5}$

Question 4: Let one end of a focal chord of the parabola $y^2=16 x$ be $(16,16)$. If $P(\alpha, \beta)$ divides this focal chord internally in the ratio 5: 2; then the minimum value of $\alpha+\beta$ is equal to:

A) 7
B) 22
C) 5
D) 16

Question 5: The largest $n \in N$, for which $7^n$ divides $101!$ is

A) 16
B) 18
C) 19
D) 15

Question 6: Let one end of a focal chord of the parabola $y^2=16 x$ be $(16,16)$. If $P(\alpha, \beta)$ divides this focal chord internally in the ratio $5: 2$; then the minimum value of $\alpha+\beta$ is equal to:
(A) 7
(B) 22
(C) 5
(D) 16

Question 7: Let $Z$ be the compelx number satisfing $|z-5|<3$ and having maximum positive arguement, then $34\left[\frac{5 z=12}{5 i z+16}\right]^2$ is equal to
A) 16

B) 26
C) 12
D) 20

Question 8: Let $a_1, \frac{a_2}{2}, \frac{a_3}{2^2}, \ldots \frac{a_{10}}{2^2}$ be a G.P of common ratio $\frac{1}{\sqrt{2}}$. If $a_1+a_2+\cdots+a_{10}=62$, then $a_1$ is equal to
A) $\sqrt{2}-1$
B) $2(2-\sqrt{2})$
C) $2(\sqrt{2}-1)$
D) $2-\sqrt{2}$

Physics

Question 1: Refractive index of prism is $\sqrt{2}$. What should be angle of incidence for a light ray such that the emerging ray grazes out the surface.

1) $90^{\circ}$

2) $60^{\circ}$

3) $30^{\circ}$

4) $45^{\circ}$

Question 2: Keeping the significantigures in view the sum of the physical quantilies $5.01 \mathrm{~m}, 153.2 \mathrm{~m}$ and 0.123 m is
a. 205.3 m
b. 205 m
c. 205.333 m
d. 205.33 m

Question 3: A block of mass $m$ is at rest w.r.t. hollow cylinder which is rotating with angular speed $\omega$. Radius of cylinder is R. Find minimum coefficient of friction between block and cylinder.

1) $\frac{3 g}{2 \omega^2 R}$

2) $\frac{g}{\omega^2 R}$

3) $\frac{g}{4 \omega^2 R}$

4) $ \frac{2 g}{\omega^2 R}$

Question 4: The total length of potentiometer wire $A B$ is som in the arrangement so in the in fig. If ' $P$ ' is the point where the galvanometer shows zero reading Then the length Ap is cm.
(A) 15
(B) 20
(C) 30
(D) 25

Question 5: The Kinetic energy of a simple hormonic oscillating with angular frequency of $176 \mathrm{rad} / \mathrm{s}$. The frequency of the simple harmonic oscillator is $-\mathrm{Hz}\left(\pi=\frac{22}{7}\right)$
(A) 176
(B) 14
(C) 28
(d) 88

Question 6: Two spheres having equal mass $m$, charge $q$ and radlus $R$, are moving towards each other. Both have speed $u$ at an instant when distance between their centers Is $4 R$. Minimum value of $u$ so that they touch each other is

1 $\sqrt{\frac{g^2}{4 K P_y m R}}$
$2 \sqrt{\frac{q^2}{16 \pi \varepsilon_0 m R}}$
$3 \sqrt{\frac{-q^2}{\pi E_0 \mathrm{mRR}}}$
$4 \sqrt{\frac{9^2}{\sqrt{2 \pi 4^2 \min }}}$

Question 7: A block of mass $m$ is at rest w.r.t. hollow cylinder which is rotating with angular speed $\omega$. Radius of cylinder is R. Find minimum coefficient of friction between block and cylinder.
(A) $\frac{3 \mathrm{~g}}{2 \omega^2 \mathrm{R}}$
(B) $\frac{\mathrm{g}}{\omega^2 \mathrm{R}}$
(C) $\frac{g}{4 \omega^2 R}$
(D) $\frac{2 \mathrm{~g}}{\omega^2 \mathrm{R}}$

Jan 21 Shift 1 Questions

Question 1:

Solution: Option (1) is correct

Question 2: For two chemical reactions A and B, if the difference between their activation energy is 20 kJ at 300 K(R=8.3 J K−1 mol−1). Determine ln⁡k2k1.

Question 3: In Carius method, 0.75 g of an organic compound gave 1.2 g of barium sulphate,
Find % of sulphur (molar mass 32 g mol−1.)
Molar mass of barium sulphate is 233 mol−1
(A) 16.48%
B) 4.55%
C) 21.97%
D) 10.30%

Question 4: In 'S' estimation 0.7 g of an organic compound gives 1 g BaSO. in Carius method. What is the % of ' S ' in compound?
1) 19.61
2) 23.85
3) 27.93
4) 14.57

Question 5: 14.0 g of calcium metal is allowed to react with excess HCl at 1.0 atm pressure &273 K. Which of the following statement is incorrect?
(Molar Mass in g mol−1Ca=40,Cl=35.5 )
(a) 0.35 mol of H2 gas is evolved.
(b) The limiting reagent is calcium metal.
(c) 33.3 g of CaCl2 is produced.
(d) 7.84 L of H2 gas is evolved.

Question 6: Which of the following is the correct order with respect to the property indicated?

1 Cl>F (lonisation energy)
2 K2O>Na2O>Al2O3 (Basic nature)
3 K>Na>Al>Mg (Metallic character)
4 None of these

Question 7: Given below are two statements.
Statement 1 : Arginine and Tryptophan are essential amino acids.
Statement 1 : Glycine does not have any chiral carbon.
In the light of the above statements, which is the correct option.

Both statement-I and statement-II are correct

2 Both statement-I and statement-II are incorrect
3 Statement-I is correct and statement-II is incorrect
4 Statement-I is incorrect and statement-II is correct

Question 8:

Solution :

A is nitrobenzene and then nitrobenzene reduced to Aniline

So, B is Aniline and C is then D is the final product E is para-nitroaniline.

C6H4NH2NO2=2×14138×100=20.28 so the nearest integer is 20

Hence, 20 is the answer.

Question 9: In the following reaction,

MnO42−→H+
Manganate ion undergoes ion undergoes disproportionation to form
1) MnO2,MnO4−
2) MnO,MnO2
3) MnO2,MnO
4) MnO4−,MnO

Question 10: Observe the following reaction sequence:
(P)→ΔNH3(Q)→Br2,KOH(R)
Which of he following is the correct structure for P, Q and R?

Question 11: 80 mL of organic compound is mixed with 264 mLO2 and ignited. It gives 224 mL of gaseous mixture at NTP. After passing KOH 64 mL of gas - remains. The organic compound is
1C2H4
2C2H2
3C4H10
4C3H6

Question 12: Statement A: But-ene show Optical Isomer.
Statement B: Propanal & Propanone are Functional Group Isomer
Statement C: Pentane & 2, 2-Dimethyl propane are Chain Isomer
Identify the correct statement
(A) Only A & B

(B)Only A &C
(C) Only B & C

(D) All

Question 13: Given below are two statements :
Statement 1 : All the pairs of molecules (PbO,PbO2);(SnO,SnO2) and (GeO,GeO2) contain amphoteric oxides.
Statement II: AlCl3,BH3,BeH2 and NO2 all have incomplete octet.
In the light of the above statements, choose the correct option.

1 Both Statement I and Statement II are correct

2 Both Statement I and Statement II are incorrect

3 Statement I is correct but Statement II is incorrect

4 Statement I is incorrect but Statement II is correct

Question 14:

Maths

Question 1: The value of cosec10∘−3sec⁡10∘:
1. 1
2. 2
3. 4
4. None of these

Question 2: If the roots of x2+x+1=0 are α and β, find
(α+β)4+(α2+β2)4+⋯+(α25+β25)4.

Question 3: If A=[α212], B=[11 β1] and A2−4A+2I=0, B2−2B+I=0, then find |adj(A3−B3)|.

1. 11
2. 7
3. -11
4. 121

Question 4:
∫0π|Sinx+Sin3x+Sin4x|dx

Question 5:
The value of ∫0π/2|sin⁡x+sin⁡2x+sin⁡3x|dx is:

1. 83
2. 73
3. 23
4. 3

Question 6:
If y=y(x) and (1+x2)dy+(1−tan−1⁡x)dx=0 and y(0)=1 then y(1) is

1.π232+π4+12.π232−π4+1
3.π232−π2−1
4.π232−π2+1

Question 7:

The sum of roots of the equation |x−1|2−5|x−1|+6=0 is:

Question 8:
Find all the points on the curve y=x3−3x+1 where the tangent passes through (1,2)

Question 9:
If L1 and L2 are two parallel lines and △ABC is an equilateral triangle then area of triangle ABC is

1.73
2.43
3.213
4. 84

Question 10:

If α & β are roots of Quadratic eqn x2+x+1=0 then the value of (α+β)4+(α2+β2)4+(α3+β3)4…(α25+β25)4 is
(1) 145
(2) 140
(3) 415
(4) 541

Question 11:

Ellipse E:x236+y216=1, A hyperbola confocal with the ellipse and eccentricity of the hyperbola is equal to 5. The length of the latus rectum of a hyperbola is, if principle axis of the hyperbola is x-axis?

1. 965
2. 245
3.185
4.125

Question 12:

Consider a set S={a,b,c,d}. Then, number of reflexive as well as symmetric relations from S→S are:

1. 1024

2. 256

3. 16

4. 64

Question 13:

If x2+x+1=0, then (x+1x)4+(x2+1x2)4+(x3+1x3)4+…+(x25+1x25)4 is

Question 14:

The locus of the point of intersection of the tangent drawn to the circle (x−2)2+(y−3)2=16, which subtends an angle of 120∘, is:
1. 3x2+3y2−12x−18y−25=0
2. x2+y2−12x−18y−25=0
3. 3x2+3y2+12x+18y−25=0
4. x2+y2+12x+18y−25=0

Question 15:
If a1,a2,a3,… are in increasing geometric progression such that

a1+a3+a5=21a1a3a5=64

then a1+a2+a3 is:

1. 5

2. 7

3. 10

4. 15

Question 16:

Find the sum of rational terms in (2+3)8

Question 17:
Let center of circle C is 0(2,3)& radius of 4. Let A & B are point of contact of tangents, then the locus of points of intersection of tangents if ∠AOB=90∘

Question 18:

In the expansion (ax2+bx+c)(1−2x)26, if coefficient of x,x2 & x3 are −56,0,0 respectively, then find the value of a+b+c.

Question 19:

Find the value of the integral ∫π6π62π+4x111−sin⁡(|x|+π6)dx

Question 20:

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

1. 18

2. 20

3. 22

4. 24

Question 21:

If A={1,2,3,4,5,6},B={1,2,3,…8,9}. Then the number of strictly increasing functions from A→B such that f(0)≠i ∀ i=1,2,3,4,5,6 are:

Physics

Question 1:

Question 2: Find dimensions of AB if (P+At2B)+12ρV2= constant, where P→ pressure, ρ→ density, V→ speed.
1ML1 T−4
2ML−1 T−4
3ML2 T−4
4ML−1 T−2

Question 3: Find the heat produced in external circuit ( AB ) in one second.

1 1181.25 J
2 1311.25 J

3 1207.50 J
4 1410.50 J

Question 4: A conducting circular loop of area is placed Perpendicular to a magnetic field which varies as, tesla. If the resistance of the they average thermal energy dissipated in the loop in one period is -

Question 5: An α-particle having kinetic energy 7.7 MeV is approaching fixed gold nucleus (atomic number is 79). Find distance of closest approach.

1 1.72 nm
2 6.2 nm
316.8 nm
40.2 nm

Question 6: An air filled capacitor of capacitance C filled with dielectric (k=3) of width d/3, where d is separation between plates. The new capacitance is

195C
254C
343C
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