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
$$
\lim _{x \rightarrow 0}(\operatorname{cosec} x)\left(\sqrt{2 \cos ^2 x+3 \cos x}-\sqrt{\cos ^2 x+\sin x+4}\right) \text { is }
$$
$1 \quad 0$
$2 \quad 1$
$3 \quad \frac{1}{2 \sqrt{5}}$
$4 \quad-\frac{1}{2 \sqrt{5}}$
