JEE Main 2025 January 29 Shift 1 Question Paper with Solutions Available - Download PDF

JEE Main 2025 January 29 shift 1 Examination Pattern and Structure

JEE Main 2025 January 29 Shift 1 Question Paper with Solutions (Memory Based)

Once the JEE Main 2025 Shift 1 exam is completed, the question paper and solutions is published on this page. These materials will be essential for candidates taking later shifts, offering them a comprehensive overview of the exam format and difficulty level. By reviewing the questions and solutions, they can identify important concepts, practice problem-solving techniques, and better prepare for the upcoming exams.

We are providing the live sessions for JEE main January 29 shift 1 overall exam analysis memory-based.

29 Jan shift 1

Q.1 Which of the following is animal starch?

1 Glycogen
2 Lactose

3 Amylopectin

4 Amylose

Q.2 Assertion: At the peak of the mountain, time period of the pendulum increases. Reason: Time period of the pendulum increases with a decrease in $g$.

1 Assertion is correct, Reason is incorrect
2 Assertion is incorrect, Reason is correct

3 Assertion is incorrect, Reason is incorrect
4 Assertion is correct, Reason is correct

Q.3 Q. The velocity of a particle moving on a straight line varies with time as $v=A t^2+\frac{B t}{C+t^{\prime}}$, where $A, B$, $C$, are constants. Find the dimension of $A B C$.
$1 \quad \mathbf{L}^2 \mathrm{~T}^{-2}$
$2 \quad \mathrm{~L}^2 \mathrm{~T}^{-1}$
$3 \quad \mathrm{~L}^2 \mathrm{~T}^{-3}$
$4 \quad \mathrm{LT}^{-3}$

Q.4 $80 \int_0^{\frac{\pi}{2}} \frac{\sin x+\cos x}{9+16 \sin 2 x} d x$

Q.5 Statement-1 : Correct order of ionic radius for $\mathrm{Mg}^{2+}, \mathrm{Na}^{+}, \mathrm{O}^{2-} \& \mathrm{~F}^{-}$is $\mathrm{F}^{-}>\mathrm{O}^{2-}>\mathrm{Na}^{+}>\mathrm{Mg}^{2+}$

Statement-2 : Correct order of magnitude of gain Enthalpy for $17^{\text {th }}$ group follows order $\mathrm{Cl}>\mathrm{F}>\mathrm{Br}>\mathrm{I}$ (Magnitude only)

1 Both Statement-1 \& Statement-2 are correct
2 Statement-1 is correct \& Statement-2 is incorrect
3 Both Statement-1 \& Statement-2 are incorrect
4 Statement-1 is incorrect \& Statement-2 is correct

Q.6 $\bar{a}=2 i-j+3 k, \bar{b}=3 i-5 j+k$, if $\bar{a} \times \bar{c}=\bar{c} \times \bar{b}$ and $(\bar{a}+\bar{c}) \cdot(\bar{b}+\bar{c})=168$ then $|c|^2=$ $\qquad$

Q.7 $\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{k^3+6 k^2+11 k+5}{(k+3)!}$ is equal to

$1 \quad\frac{5}{3}$
$2 \quad \frac{8}{3}$

$3 \quad$ 3
$4 \quad \frac{7}{3}$

Q.8 $
\mathrm{L}_1=\frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-1}{2}, L_2: \frac{x+1}{-1}=\frac{y-2}{2}=\frac{z}{1}=\mu
$
Let the line $L_3$ passes through the point $(\alpha, \beta, \gamma)$ perpendicular to $L_1 \& L_2$ and $L_3$ intersect line $L_1$ then $|5 \alpha-11 \beta-8 \gamma|$.

a) 25
b) 18
c) 16
d) 20

Q.9 Q. A pendulum of mass $\frac{m}{2}$ is released from given situation. Find speed of another pendulum after collision. $(e=1$ )
$1 \quad\sqrt{\frac{3}{2} g l}$
$2 \quad\frac{2}{3} \sqrt{g l}$
$3 \quad \sqrt{\frac{q l}{3}}$
$4 \quad \frac{1}{3} \sqrt{g l}$

Q.10 The velocity of a particle moving on a straight line varies with time as $\mathbf{v}=\mathrm{At}^{\mathbf{2}}+\frac{\mathrm{Bt}}{\mathrm{c}+\mathrm{t}^{\prime}}$ where $\mathrm{A}, \mathrm{B}, \mathrm{C}$, are constants. Find the dimension of $A B C$.
(A) $\mathrm{L}^2 \mathrm{~T}^2$
(B) $\mathrm{L}^2 \mathrm{~T}^1$
(C) $\mathrm{L}^2 \mathrm{~T}^{\mathbf{3}}$
(D) $\mathrm{LT}^{\mathbf{3}}$

Q.11 The minimum value of $\mathbf{n}$ for which the number of integer terms in the binomial expansion of $\left(7^{1 / 3}+11^{1 / 2}\right)^n$ is 183 , is

Q.12 The graph between wavelengths $(\lambda)$ of incident light and kinetic energy (K.E.) of photoelectrons in the photoelectric effect is

Q.13 A ball falling in a sea of depth 2.5 km shows $x$ \% decrease in its volume at the bottom. The bulk modulus of the material of the ball is $2 \times 10^9 \mathrm{~N} / \mathrm{m}^2$ value of $x$ is:

Q.14 Chromite ore $+\mathrm{Na}_2 \mathrm{CO}_3+\mathrm{O}_2 \longrightarrow$ insoluble product containing Fe
Calculate the molar mass of insoluble product formed. (Given : Molar mass of $\mathrm{Cr}=52 \mathrm{~g} / \mathrm{mol}, \mathrm{Na}$ $=23 \mathrm{~g} / \mathrm{mol}, \mathrm{Fe}=56 \mathrm{~g} / \mathrm{mol}, 0=16 \mathrm{~g} / \mathrm{mol})$

Q.15 Area enclosed by $y \geq|x-1|, y+|x| \leq 3, x^2 \leq 2 y-3$ is $A$, then $6 A$ is (in sq. units)

Q.16 River is flowing with velocity $9 \mathrm{~km} / \mathrm{hr}$. velocity of boat with respect to river is $\mathbf{2 7} \mathbf{~ k m} / \mathrm{hr}$ in the direction of flow of river. Person standing over this boat throw a ball vertically upward with respect to himself with velocity $\mathbf{1 0 ~ m} / \mathrm{s}$. Determine the horizontal displacement or range (in cm) till ball come to the same horizontal level from where it was proiected.

Q.17 Statement-1: Electromagnetic wave have both energy and momentum.

Statement-2: Rest mass of photon is zero.

1 Statement- 1 is correct, statement- 2 is correct
2 Statement- 1 is correct, statement- 2 is incorrect

3 Statement-1 is incorrect, statement-2 is correct
4 Statement-1 is incorrect, statement-2 is incorrect

Q.18 $\left|z_1-8-2 i\right| \leq 1$ and $\left|z_2-6+8 i\right| \leq 2$ then minimum value of $\left|z_1-z_2\right|$ is equal to

Q.19 Q. Two projectiles were launched from same position simultaneously only same speed on of the projectile was launched at angle $(45-\alpha)^{\circ}$ and the other at an angle of $(45+\alpha)^{\circ}$. Find the ratio of maximum height of the projectile.
$1 \quad\frac{1-\sin \alpha}{1+\sin \alpha}$
$2 \quad\frac{1-\sin 2 \alpha}{1+\sin 2 \alpha}$
$3 \quad\frac{1-\tan \alpha}{1+\tan \alpha}$
$4 \quad \frac{1-\cos \alpha}{1+\cos \alpha}$

Q.20 The minimum value of $n$ for which the number of integer terms in the binomial expansion of $\left(7^{1 / 3}+11^{1 / 2}\right)^n$ is 183, is

Q.21

Consider the following complexes

$$
\begin{aligned}
& {\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{4-}\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}\left[\mathrm{Co}(\mathrm{CN})_6\right]^{3-}} \\
& \begin{array}{lll}
\text { (1) } & \text { (2) } & \text { (3) } \text { (4) }
\end{array}
\end{aligned}
$$

Q.22 Correct order of CFSE ( $\Delta_0$ ) will be

$1 \quad 3>4>2>1$
$2 \quad 4>3>2>1$
$3 \quad 4>3>1>2$
$4 \quad 3>4>1>2$

Q.23 Q. What is the value of van't Hoff Factor for $A_2 B$ is $30 \%$ of $A_2 B$ is dissociated?
$1 \quad 1.60$
$2 \quad 1.30$
$3 \quad 1.50$
$4 \quad 1.20$

Q.24 Find the order of the reaction

$$
A+B \rightarrow F
$$

if the mechanism of the reaction is given below:
Step 1: A + B $\rightarrow$ D (slow)
Step 2: $\mathrm{D} \rightarrow \mathrm{C}+\mathrm{E}$ (fast)
Step 3: C + E $\rightarrow$ F (fast)
$1 \quad 1$
$2 \quad 3$
$3 \quad 2$
$4 \quad 4$

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

For those students who prefer digital utility, they can download the JEE Main 2025 Question Paper PDF.

JEE Main 2025 January 29 Shift 1 Question Paper -Difficulty Level

Based on the previous 3 days' analysis the JEE Main question paper is overall moderate level.

Students should read NCERT for chemistry because chemistry questions are directly asked from NCERT. For Physics formula questions should be practiced, Maths is lengthy and time-consuming.

JEE Main 2025 Question Paper Analysis as per the previous year

The JEE Main 2025 January 29 Shift 1 exam may possibly have a moderate level to difficulty. Physics is anticipated to be moderately difficult as per the previous year's analysis with key areas such as Mechanics and Electromagnetism posing a higher level of complexity. While Physics will require a strong conceptual understanding, Mathematics will likely demand more time and problem-solving skills. Chemistry, particularly Organic Chemistry, is expected to be relatively easier, but a solid grasp of key reactions and mechanisms will be essential for securing good marks in this section.