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JEE Main 2025 January 28 Shift 1 Question Paper with Solutions - JEE Main plays a significant role in shaping the future of aspiring engineers in India. The January 28 Shift 1 paper for JEE Main 2025 will offer valuable feedback on the types of questions, the level of difficulty, and how to approach various subjects effectively. As the JEE Mains exam continues to adapt, candidates can anticipate a test that not only evaluates their knowledge but also their critical thinking and problem-solving abilities. JEE Main 2025 Jan 28 shift question paper will be an important reference for those aiming to excel in future shifts and for understanding the exam's evolving nature. JEE Main answer is released.
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The JEE Main 2025 Jan 28 Shift 1 Question Paper and Solutions is accessible now. These documents will serve as a valuable tool for students appearing in future shifts, providing an opportunity to explore the questions and solutions in detail. This will help them familiarize themselves with the exam format, identify key topics, and fine-tune their approach for better results in the upcoming shifts.
28 Jan Shift 1
Q.1 If $\int_{-\pi / 2}^{\pi / 2} \frac{96\left(x^2+\cos x\right)}{1+e^x} d x=\alpha \pi^3+\beta$ (where $\alpha, \beta$ are positive integers), then $\alpha+\beta$ equal to
1) 144
2) 100
3) 64
4) 196
Q.2 The product $A$ and $B$ in the following reactions, respectively
(A) $\stackrel{\mathrm{AgNO}_2}{\longleftrightarrow} \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Br}_2 \xrightarrow{\mathrm{AgCN}} \mathrm{B}$
(A) $\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{ONO}, \mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{CN}$
(B) $\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{NO}_2, \mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{NC}$
(C) $\mathrm{CH}_3-\mathrm{CH}_2 \rightarrow+\mathrm{CH}_2-\mathrm{NO}_2, \mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2 \mathrm{CN}$
(D) $\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{ONO}, \mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2-\mathrm{NC}$
Q.3 The molecules having square pyramidal geometry are
(A) $\mathrm{SbF}_5 \& \mathrm{PCl}_5$
(B) $\mathrm{BrF}_5 \& \mathrm{XeOF}_4$
(C) $\mathrm{BrF}_5 \& \mathrm{PCl}_5$
(D) $\mathrm{SbF}_5 \& \mathrm{XeF}_4$
Q.4 The incorrect decreasing order of atomic radii is
(A) $\mathrm{Si}>\mathrm{P}>\mathrm{Cl}>\mathrm{F}$
(B) $\mathrm{Mg}>\mathrm{Al}>\mathrm{C}>0$
(C) $A l>B>N>F$
(D) $\mathrm{Be}>\mathrm{Mg}>\mathrm{Al}>\mathrm{Si}$
Q.5 A uniform wire of linear charge density $\lambda$ is placed along $y$-axis. The locus of equipotential surface is
$1 \quad x^2+y^2+z^2=$ constant
$2 \quad x^2+z^2=$ constant
$3 \quad x y z=\text { constant }$
$4 \quad x y+y z+z x=\text { constan }$
Q.6 Q. Number of ways to form 5 digit numbers greater than 50000 with the use of digits $0,1,2,3$, 5, 6,7 such that sum of first and last digit is not more than 8 , is equal to
$1 \quad 5119$
2 5120
3 4067
4 4068
Q.7 Consider the following element in In $\mathrm{TI}, \mathrm{Al}$, and Pb The most stable oxidation states of elements with highest and lowest first Ionisation enthalpies, respectively are
(A) +4 and +1
(B) +2 and +3
(C) +4 and +3
(D) +1 end +4
Q.8 $\frac{x-1}{2}=\frac{y-2}{5}=\frac{z-3}{6}$. Image of point $(2,3,4)$
Q.9 Q. Which of following reaction is correct? (Where symbols have their usual meanings)
$1 \quad n \rightarrow p+e^{-}+\mathrm{v}$
$2 \quad n \rightarrow p+e^{+}+v$
$3 \quad n \rightarrow p+c^{+}+\bar{v}$
$4 \quad n \rightarrow p+e^{-}+\bar{v}$
Q.10 $\int_0^x t f(t) d t=x^2 f(x), f(2)=3, f(6)=?$
Q.11 If $f(x)=\frac{2^x}{2^x+\sqrt{2}}, x \in R$, then $\sum_{k=1}^{81} f\left(\frac{k}{82}\right)$ is equal to
a) $81 \sqrt{2}$
b) 82
c) $\frac{81}{2}$
d) 41
Q.12 Two disc of radius $R$ and $2 R$ having moment of inertia $I_1$ and $I_2$ respectively. Find $I_1 / I_2$.
Q.13 $\int_{-\pi / 2}^{\pi / 2} \frac{96 x^2 \cos x^2}{1+e^x} d x$
Q.14 Area of region $\left\{(x, y): 0 \leq y \leq 2|x|+1,0 \leq y \leq x^2+1,|x| \leq 3\right.$
a) $\frac{17}{3}$
b) $\frac{32}{3}$
c) $\frac{64}{3}$
d) $\frac{80}{3}$
Q.15 The relation $R=\{(x, y) \mid x, y \in z, x+y=e v e n\}$ then $R$ is
(a) Equivalence
(b) Reflexive \& Transitive but-not Symmetric
(c) Symmetric \& Transitive but not reflexive
(d) Reflexive \& symmetric but not transitive
Q.16 $\left[\frac{\text { Modulus of rigidity }}{\text { Torque }}\right]=\mathrm{M}^{\prime} \mathrm{L}^{-3} \mathrm{~T}^c$. Find the value of C .
Q.17 $\begin{gathered}\int_0^x t f(t) d t=x^2 f(x) \\ f(2)=3, f(6)=?\end{gathered}$
Q.18 A coin is placed at the bottom of a hemispherical container filled with a liquid of refractive index $\mu$. Find the least refractive index if the coin is visible to an observer at $E$.
$\begin{array}{ll}1 & \sqrt{3}\end{array}$
$2 \quad\sqrt{2}$
$3 \quad \frac{8}{2}$
$4 \quad3 \sqrt{2}$
Q.19 Find co-ordinate of center of mass of given rectangular plate, given surface mass density $\sigma=\sigma_0 \frac{x}{a}$.
Q.20 If $\int_0^x t f(t) d t=x^2 f(x)$ and $f(2)=3$, then $f(6)$ equals to
$1 \quad 1$
2 6
$3 \quad 3$
4 2
Q.21 In the given figure, the square and the triangle have same resistance per unit length. Find the ratio of their resistances about adjacent corners.
1 32/27
2 27/32
$3 \quad 8 / 9$
$4 \quad 9 / 8$
Q. 22. Assertion : Work done by central force is independent of path. Reason : Potential energy is associated with every force.
1 Both Assertion and Reason are correct
2 Assertion is correct, Reason is incorrect
3 Assertion is incorrect, Reason is correct
4 Both Assertion and Reason are incorrect
Q.23 There is a smooth ring of radius $R$ in the vertical plane. A spring of natural length $R$ and elastic constant $K$ is vertical across along a diameter. The free end is connected to a bead of mass $m$ and when slightly disturbed it reaches point $C$ with speed where $V$ is
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Previous year question papers are an essential resource for JEE Main aspirants as they provide a clear understanding of the exam's pattern, frequently asked topics, and the level of difficulty. By solving these papers, candidates can familiarize themselves with the type of questions that commonly appear, which helps in effective time management and enhances problem-solving skills.
Let’s take a look at the previous year analysis:
Physics:
Topics like Mechanics, Thermodynamics, Modern Physics, and Electrostatics are featured prominently.
The difficulty level ranged from moderate to tough, with some lengthy calculations and tricky conceptual questions.
Mathematics:
Algebra, Calculus, and Coordinate Geometry were the key areas covered, with Calculus presenting some of the most difficult problems.
A few questions in the paper required students to apply multiple concepts, increasing the level of complexity.
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Chemistry:
Physical Chemistry focuses on concepts such as Chemical Kinetics, Thermodynamics, and Mole Concepts.
Organic Chemistry had straightforward questions, especially regarding reaction mechanisms and functional groups.
Inorganic Chemistry was mostly conceptual, with questions centered around periodic properties and coordination compounds.
Based on the analysis of previous years, the JEE Main 2025 January 28 Shift 1 exam is anticipated to have a moderate overall difficulty level. Mathematics is likely to be the toughest section, with a significant focus on Calculus and Algebra, which may present more complex challenges. Physics is expected to be challenging as well, with topics like Mechanics and Electromagnetism leaning towards moderate difficulty. While all sections will require thorough preparation, Mathematics is likely to stand out as the most demanding. A solid understanding of Organic Chemistry concepts and reactions is also crucial for performing well in the Chemistry section.
Candidates must have passed 10+2 with Physics, Chemistry, and Mathematics, and meet the required percentage criteria.
Paper 1 is for B.E./B.Tech, and Paper 2 is for B.Arch/B.Planning, with MCQs and numerical questions.
With an 87 percentile and a rank of 188681 in JEE Main, your chances of getting into ECE or Mechanical Engineering (ME) in top NITs or IIITs are limited, especially within the general category. However, you may have a chance in some lower-ranked NITs or GFTIs (Government Funded Technical Institutes).
Check college predictor here -:
Thanks for sharing your JEE Main details:
At a CRL Rank of -188,000,it might be challenging to get ECE or ME in top-tier NITs,IITs or GFTIs under the general category.However,you still have a good chances in :
1.Lower-Ranked NITs or IITs ( especially in north-eastern or newer ones)
If you have any reservation or home state quota.You might get ECE/ME in:
-NIT Mizoram -NIT Nagaland - NIT Meghalaya - IIT Una,IIT Nagpur( for ECE)
2.State level government engineering colleges ( through your state quota)
- if you are in a state like Maharasthra,MP,UP,Rajasthan,etc your state quote may help you get ECE/ME in government colleges through JEE Main.
3.Private collages accepting JEE Main scores.Collages like:
- Shiv Nadar University
-UPES Dehradun
-Amity University
These accept JEE Main scores for admission and offer good ECE/ME programs.
First of all congratulations on getting 87 percentile.
With an 87 percentile in the JEE Main and rank 188681, securing ECE or ME in the top NITs or IIITs will be difficult, particularly in the general category. But there is a possibility of making it in:
You can also seek possibilities in the CSAB special rounds or investigate colleges where the cut-off rank exceeds 180,000 in past years.
No need to worry , but you need to be sincere .
If you have entered the wrong school name or board details in your JEE application, do not worry as this can usually be resolved with the right steps. First, you should immediately contact the National Testing Agency (NTA) by doing a mail to them and covering all your doubts and all correct details. They may not allow corrections now, but having it officially noted could help during counselling. When the JOSAA counselling process begins, document verification will play a crucial role. Make sure you carry your original Class 12 marksheet and school documents to prove the correct information. As long as your academic records are genuine and match the eligibility criteria, small application errors like this typically do not lead to disqualification or blacklisting. Just stay updated on the official JOSAA website and follow their instructions carefully to ensure a smooth counselling process.
Hello,
Satakshi Gupta with CRL 289509 and NCL 101585 in JEE 2025 may get a Delhi-based engineering college through home state quota, especially in private or lower-ranked g9overnment colleges. top-tier institutions like DTU, NSUT, or IIIT-D may be through at this rank unless tehre's a category relxation. exact admission depends on cutoff trends, so check official JoSAA or state counselling portals for accurate options.
https://engineering.careers360.com/jee-main-college-predictor
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