JEE Main 2025 January 29 Shift 2 Question Paper with Solutions Available - Download PDF

JEE Main 2025 January 29 Shift 2 Exam Pattern and Structure

JEE Main 2025 January 29 Shift 2 Question Paper with Solutions(Memory Based)

The JEE Main 2025 January 29 Shift 1 Question Paper and Solutions will be available here post-exam. This will act as a useful resource for students taking further exams, providing a chance to examine the questions and answers thoroughly. It will ultimately help them to familiarize themselves fully with the types of questions and answers, to get an account of the format of the exam for this accurate result and realize the subject for further study on this topic and, finally, to perfect their exam-passing game.

29 Jan shift 2

Q.1 Which of the following form most stable carbocation ?
$1 \quad(\mathrm{Ph})_3 \mathrm{C}-\mathrm{Br}$
$2 \quad \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}$
$3 \quad \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}(\mathrm{Br}) \mathrm{CH}_3$
$4 \quad \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Br}$

Q.2 Number of $\sigma$ and $\pi$ bonds respectively in hex-1-en-4-yne are

$1 \quad13, 3$
$2 \quad14, 3$
$3 \quad 3,14$
$4 \quad 14,13$

Q.3. If the letters of the word "KANPUR" are arranged in dictionary, then the $440^{\text {th }}$ word is

1 PRKAUN
2 PRKUAN
3 PRKNAU
4 PRKUNA

Q.4 0.41 g of $\mathrm{BaSO}_4$ is obtained from 0.2 g of organic compound in Carius method. What is the percentage of sulphur present in organic compound?

Q.5 A solenoid of radius 10 cm carrying current 0.29 A and having total 200 turns. If the magnetic field inside the solenoid is $2.9 \times 10^{-4} \mathrm{~T}$. Find length of solenoid.
$1 \quad 6 \pi \mathrm{~cm}$
$2 \quad 8 \pi \mathrm{~cm}$
$3 \quad 4.5 \mathrm{~cm}$
$4 \quad 16 \mathrm{~cm}$

Q.6 An equiconvex lens is cut in two ways as shown. If the focal length of the parts are as mentioned in the diagram. Find $\frac{L_1}{L_i}$

$1 \quad 2$

$2 \quad 4$
$3 \quad \frac{1}{2}$
$4 \quad \frac{1}{4}$

Q.7 If $3^{107}$ is divided by 23 , then remainder is

Q.8 Which element in group $\mathbf{1 5}$ has lowest Ionisation Energy
$1 \quad \mathrm{Bi}$

$2 \quad P$

$3 \quad As$
$4 \quad \mathrm{Sb}$

Q.9 Three identical particles, each of mass $m$ move under the influence of mutual attraction forces. Initially, the are on the vertices of an equipotential triangle of side ' $a$ ' and have equal speed $v$ directed towards the adjacent particles as shown. The net angular momentum about the centre just before collision is
$1 \quad \frac{3 m v a}{2}$
$2 \quad \frac{2}{3} m v a$
$3 \quad \frac{\sqrt{3}}{2} m v a$
$4 \quad \frac{2}{\sqrt{3}} m v a$

Q.10 Which of the following formsthe most stable carbocation?
(A) $(\mathrm{Ph})_3 \mathrm{C}-\mathrm{Br}$
B) $\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}$
(C) $\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}(\mathrm{Br}) \mathrm{CH}_3$
b) $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Br}$

Q.11 $\mathrm{XeF}_3^{\ominus}$ shape ?

Q.12 Let $a_{i j}=(\sqrt{2})^{i+j}, A=\left[a_{i j}\right]_{3 \times 0}$. If sum of third row of $A^2$ is $\alpha+\beta \sqrt{2}$, then $\alpha+\beta$ is

Q.13 A solenoid of radius 10 cm carrying current 0.29 A and having a total of 200 turns. If the magnetic field inside the solenoid is $2.9 \times 10^{-4} \mathrm{~T}$. Find the length of the solenoid.
(a) $8 \pi \mathrm{~cm}$
(b) $6 \pi \mathrm{~cm}$
(c) 16 cm
(d) 4.5 cm

Q.14 $$
\begin{aligned}
&\text { Match the physical quantities with their corresponding dimensions }\\
&\begin{array}{|l|l|l|l|}
\hline & \text { Column-I } & & \text { Column-II } \\
\hline \text { (A) } & \text { Young's modulus } & \text { (i) } & {\left[\mathrm{AL}^2\right]} \\
\hline \text { (B) } & \text { Magnetic moment } & \text { (ii) } & {\left[\mathrm{ML}^2 T^{-2} \mathrm{~A}^{-1}\right]} \\
\hline \text { (C) } & \text { Magnetic flux } & \text { (iii) } & {\left[\mathrm{AL}^{-1}\right]} \\
\hline \text { (D) } & \text { Magnetic Intensity } & \text { (iv) } & {\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]} \\
\hline
\end{array}
\end{aligned}
$$

$\begin{array}{ll}1 & \text { A-(iii), B-(i), C-(ii), D-(iii) } \\ 2 & \text { A-(iv), B-(ii), C-(i), D-(iii) } \\ 3 & \text { A-(iii), B-(i), C-(ii), D-(iv) } \\ 4 & \text { A-(iii), B-(ii), C-(i), D-(iv) }\end{array}$

Q.15 River is flowing with velocity $9 \mathrm{~km} / \mathrm{hr}$. velocity of boat with respect to river is $27 \mathrm{~km} / \mathrm{hr}$ in the direction of flow of river. Person standing over this boat throw a ball vertically upward with respect to himself with velocity $10 \mathrm{~m} / \mathrm{s}$. Determine the horizontal displacement or range (in cm ) till ball come to same horizontal level from where it was projected.

Q.16 Two particles of same mass are performing SHM vertically with two different springs of spring constants $K_1$ and $K_2$. If the amplitude of both is the same. Find the ratio of the maximum speed of two particles.

Q.17 Q. A physical quantity $Q$ is given as $Q=\frac{a b^4}{c d}$, if the percentage error $\{0, b, c$ and $d$ are $2 \%, 1 \%, 2 \%$ and $1 \%$, the $\%$ error in $Q$ will be
$ 1\quad 5 \%$
$2 \quad15 \%$
$3 \quad9 \%$
$4 \quad2 \%$

Q.18 Q. Let $f(x)=\int_0^x t\left(t^2-3 t+20\right) d t, x \in(1,3)$ and range of $f(x)$ is $(\alpha, \beta)$, then $\alpha+\beta$ is equal to
$1 \quad \frac{185}{4}$
$2 \quad \frac{185}{2}$
$3 \quad \frac{185}{3}$
$4 \quad \frac{37}{4}$

Q.19 The value of the limit

$$
\lim _{x \rightarrow 0}(\operatorname{cosec} x)\left(\sqrt{2 \cos ^2 x+3 \cos x}-\sqrt{\cos ^2 x+\sin x+4}\right) \text { is }
$$

$1 \quad 0$
$2 \quad 1$
$3 \quad \frac{1}{2 \sqrt{5}}$
$4 \quad-\frac{1}{2 \sqrt{5}}$

JEE Main 2025 Question Paper with Solutions (Last 3 Days)

Students can download the JEE main Question paper with solutions of 22, 23, and 24 January 2025.

• JEE Main 2025 22 January Shift 1 Question Paper
• JEE Main 2025 22 January Shift 2 Question Paper
• JEE Main 2025 23 January Shift 1 Question Paper
• JEE Main 2025 23 January Shift 2 Question Paper
• JEE Main 2025 24 January Shift 1 Question Paper
• JEE Main 2025 24 January Shift 2 Question Paper

JEE Main 2025 January 29 Shift Question Paper -Difficulty Level

As per the observation of the previous days' analysis, the difficulty level of the JEE Main question paper is overall moderate level. In Chemistry, students would do better with NCERT-only, for all chemistry questions are right out of the NCERT. For Physics, they must practice formula questions, and Mathematics is quite lengthy and time-consuming.

You can check the JEE Main 2025 question paper analysis according to the feedback we got for the last few days’ shifts. Here you can check it:

1. Mathematics:

• The paper was manageable for those who had prepared well. The topics covered were a mix of easy questions and moderate-level problems.

• Difficult questions were fewer, but those who prepared thoroughly could still tackle them effectively.

• Topics like Quadratic Equations, Sequences and Series, and Matrices were frequently asked.

• Complex numbers and the Binomial Theorem also had a few questions.

• Differentiation and Integration were prominent, with several questions on the Application of Derivatives and Definite Integrals.

• Questions on Straight Lines and Conic Sections (especially Circles and Parabolas) were commons

• Trigonometric identities and equations were included, though not extensively.

2. Physics:

• Most questions were easy to moderate, with only a small portion being tough.

• Physics was manageable for most students, especially if they had a solid grasp of basic concepts. Moderate-level questions were expected, and easier questions made the section more approachable.

• Topics like Newton's Laws of Motion, Work, Energy & Power, and Rotational Motion appeared frequently.

• Gravitation and Kinetic Theory of Gases were also important areas.

• Coulomb’s Law, Capacitance, Current Electricity, and Magnetic Effects of Current were commonly tested.

• Electromagnetic Induction had a couple of questions as well.

• Photoelectric Effect, Atomic Structure, and Radioactivity were recurring topics in the exam.

3. Chemistry:

• Chemistry was slightly more challenging compared to Physics and Mathematics.

• The difficult portion was notable, requiring thorough preparation, especially in areas like Physical Chemistry and Inorganic Chemistry. Students should focus more on Chemistry in future shifts as it poses a challenge for many candidates.

• Topics like Chemical Kinetics, Thermodynamics, and Mole Concepts were highly featured.

• Equilibrium and Electrochemistry appeared in moderate questions.

• Reaction Mechanisms, especially Aromatic Substitution and Functional Groups, were frequently tested.

• Hydrocarbons and Polymers appeared as well.