JEE Mains 2025 January 22 Shift 2 Question Paper with Solutions Available

JEE Main 2025 January 22 Shift 2 Exam Pattern and Structure

JEE Main January 22 Shift 2 Memory-based questions

Q. if $2 x^2+(\cos \theta) x-1=0 \quad \theta \in[0,2 \pi]$ has roots $\alpha+\beta$. Then the sum of maximum and minimum value of $\alpha^4+\beta^4$ is

4) $25 / 16$
b) $9 / 16$
c) $41 / 16$
d) $8 / 17$

Q. Which of the following doesn't show disproportionation reaction

(1) $\mathrm{ClO}^{-}$

(2) $\mathrm{ClO}_2^{-}$

(3) $\mathrm{ClO}_3^{-}$

(4) $\mathrm{ClO}_4^{-}$

Q. Density of 3M NaOH is 1.25 g/mol. Molarity of the solution is _____.

Q. A ball of mass 100 grams throw $m$ at speed $20 \mathrm{~m} / \mathrm{s}$ with angle 60 percent degree with horizontal. Now tell the decrease in kinetic energy from point of throwing to the ball when it reaches to Max height basically a projectile question

Q. Which of the following has "two secondary hydrogens"

(1) 2,2,3,3-Dimethyl Pentane
(2) 2,2,4,4-Dimethyl Heptane
(3) 4- Ethyl-2,2 Di methyl hexane
(4) None of these

Q. If $\theta \in(0,2 \pi]$ satisfying the system of equations $2 \sin ^2 \theta=\cos 2 \theta$ and $2 \cos ^2 \theta=3 \sin \theta$. Then the sum of all real values of $\theta$ is

$\begin{array}{cc}1 & \frac{3 \pi}{2} \\ 2 & \pi \\ 3 & \frac{\pi}{2} \\ 4 & \frac{5 \pi}{6}\end{array}$

Q. Arrange according to CFSE.
(i) $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4\right]^{2+}$
(ii) $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$
(iii) $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{2+}$
(iv) $\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+}$

1) (iv) $>$ (ii) $>$ (iii) $)>($ (i)

2) (iv) $>$ (iii) $>$ (ii) $>$ (i)

3) (i) $>$ (iii) $)>$ (ii) $>$ (iv)

4) (i) $>$ (ii) $>$ (iii) $>$ (iv)

Q. Find the correct dimensional formula for the capacitance in terms of M, L, T and C where they stand for unit of mass, length, time and charge.

Q. The maximum percentage error in the measurement of density of a wire is

$
\begin{aligned}
& m=(0.60 \pm 0.003) \mathrm{g} \\
& r=(0.50 \pm 0.01) \mathrm{cm} \\
& l=(10.00 \pm 0.05) \mathrm{cm}
\end{aligned}
$

Q. If the mean deviation about median for the number $3,5,7,2 \mathrm{k}, 12,16,21,24$ arranged in ascending order is 6 then the median is

Q. Assertion:- simple pendulum is taken on a planet of mass 4 times of earth and radius 2 time of earth then the time period is remains constant
Reason:- Time period of simple pendulum is constant on earth and on any other planet

Q. Let $A=\{1,2,3,4\}$ and $B=\{1,4,9,16\}$.
If $f: A \rightarrow B$, then number of many-one functions from $A$ to $B$ are

Q. 4 boys and 3 girls are to be seated in a row that all girl seat together and two particular boys $B_1$ and $S_2$ are not adjecent to each other. Then the number of ways in which this aseagerpent can be done
4) 432
b) 430
c) 516
d) 1002

Q. $\sum_{r=1}^{30} \frac{r^2\left({ }^{30} C_r\right)^2}{{ }^{30} C_{r-1}}=\alpha \times 2^{29}$, then $\alpha=$

Q. which of the following anion will not undergoes disproportionation?

a) $\mathrm{ClO}_4^{-}$

b) $\mathrm{ClO}_3^{-}$

c) $\mathrm{ClO}_2^{-}$

d) $\mathrm{ClO}^{-}$

Previous Years Question Paper

Below are the past years question paper that can help you prepare better for JEE Main 2025 January 22 Shift 2 Exam.

JEE Main 2025 January 22 Shift 2 Analysis

Mathematics Section

The Mathematics section for Shift 2 focused on problem-solving and concept mastery approaches. Key topics that was include:

• Calculus: 30-35% weightage was given to these topics and includes topics such as complex integration, differential equations continuity, and differentiability.
• Algebra: About 30%, it is recommended to the students to pay attention to matrices, determinants, and quadratic equations for next shift.
• Coordinate Geometry: 20%,
• Vectors and 3D Geometry: 15%

In general, this section was Moderate, and it contained a good number of theoretical and practical questions.

Physics Section

In Physics, there is a stronger bias towards mechanics and electromagnetism in the section as well. The major topic distribution included:

• Mechanics: 35 %
• Electromagnetism: 30% detailing on electric fields, electricity circuits, and magnetic effects of current.
• Modern Physics: radioactivity and the atomic models being 20%.
• Thermodynamics: 15%, with questions related to application in such areas as heat transfer and the law of thermodynamics being tested in an application-based question.

It is considered moderately challenging. The JEE Main 2025 22 Jan shift 2 paper and the JEE Mains 2025 question paper pdf shift 2 will help students practice time-bound questions effectively.

Chemistry Section

The Chemistry section was easy, with the following distribution:

• Organic Chemistry: 40%
• Physical Chemistry: 35%, specifically chemical kinetics, thermodynamics, and chemical equilibria.
• Inorganic Chemistry 25%.

Trends and Overall Analysis

The overall difficulty level of the paper is moderate, with Mathematics and Physics being relatively more challenging than Chemistry. Questions across all sections adhered to the NCERT syllabus, combining theoretical knowledge with practical application. For optimal preparation, students should utilize both the JEE Mains 22 January shift 2 question paper analysis and the JEE Mains 2024 question paper pdf.