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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JEE Main 2025 January 28 Shift 1 Question Paper with Solutions ( Memory Based Questions)
JEE Mains Previous Years Question Papers
JEE Main Previous Year Analysis
JEE Main 2025 Question Paper Analysis as per the previous year
JEE Main 2025 January 28 Shift 1 Question Paper with Solutions - PDF Link
JEE Main 2025 January 28 Shift 1 Question Paper with Solutions ( Memory Based Questions)
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
$3 \quad x y z=\text { constant }$
$4 \quad x y+y z+z x=\text { constan }$
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.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 $E$.
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
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.
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.
JEE Main 2025 College Predictor
Know your college admission chances in NITs, IIITs and CFTIs, many States/ Institutes based on your JEE Main rank by using JEE Main 2025 College Predictor.
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.
JEE Main 2025 Question Paper Analysis as per the previous year
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.
Frequently Asked Questions (FAQs)
1.What is the eligibility criteria for JEE Main 2025?
Candidates must have passed 10+2 with Physics, Chemistry, and Mathematics, and meet the required percentage criteria.
2.What is the exam pattern for JEE Main 2025?
Paper 1 is for B.E./B.Tech, and Paper 2 is for B.Arch/B.Planning, with MCQs and numerical questions.
With a 67 percentile in JEE Main, your approximate rank would be around 3.5 to 4 lakh in the Common Rank List. Getting admission into top NITs, IIITs, or GFTIs through JoSAA may be difficult unless you have a strong category rank (SC/ST/OBC/EWS). However, you can still participate in the counselling rounds and look for seats in lesser-known GFTIs or North Eastern NITs in spot rounds, especially if you're open to any branch or location.
With 95.88 percentile in JEE Mains, your All India Rank is likely around 45,000–50,000, which gives you a decent chance to get CSE at CBIT (Chaitanya Bharathi Institute of Technology) under the B-Category (management quota).
Why you have a chance:
B-Category seats are not strictly based on JEE rank, but percentile and academic performance are considered.
95.88 percentile is considered strong for B-Category admissions, especially if you apply early and meet all requirements.
What to do:
Apply as soon as CBIT opens B-Category applications.
Yes it is possible to get admission in BTech in Gujarat even if you have not appeared for GUJCET or JEE and have not registered with ACPC but only through management quota or institute level admission Many private engineering colleges in Gujarat reserve some percentage of seats under management quota which are filled directly by the college based on class twelve marks usually in Physics Chemistry and Mathematics You need to visit the official website of the college or contact the admission office to know the eligibility fees and documents required It is important to note that government colleges and seats under the ACPC counseling process will not be available to you without GUJCET or JEE and ACPC registration Hence your chances are only in self financed private colleges through management quota
If you have got
5000 rank in JEE Main
and a
category rank of 36000
, here is what you can do:
Check Your Category and Home State Quota
Your chances depend on your category like OBC, SC, ST, EWS and home state. Category rank is useful for admission through reservation.
Use JoSAA Choice Filling
Participate in JoSAA counselling. Fill maximum choices including NITs, IIITs, GFTIs. Try branches like Metallurgy, Chemical, Civil, or newer branches in top institutes.
Target NITs and IIITs
With 5000 common rank, you have strong chances in
Top NITs
for core or less competitive branches
Good IIITs
for CSE or ECE if you belong to reserved category
Consider State Counselling Too
If you have a state quota like in Andhra Pradesh, Telangana, etc., apply in your state counselling where your chances might be higher.
Keep Backup Options
Include private colleges with good placement like VIT, SRM, or other state-level colleges if needed.
A flight attendant ensures passenger safety and comfort during flights. Key duties include conducting safety checks, assisting passengers, serving food and drinks, and managing emergencies. They must be well-trained in safety procedures and customer service. A high school diploma is typically required, followed by rigorous training to qualify for the role.
A Flight Engineer monitors and operates an aircraft’s complex systems like engines, fuel, and hydraulics during flight, ensuring optimal performance and safety. They assist pilots with technical issues, conduct inspections, and maintain records. This role requires strong technical knowledge, problem-solving, and communication skills. Training usually involves a degree in aviation or aerospace engineering and specialised certification.
An Aircrew Officer operates and navigates aircraft, ensuring safe flights and compliance with aviation regulations. Key duties include managing flight systems, conducting pre- and post-flight checks, and adhering to safety standards. The role typically requires working five days a week, with around 120 flight hours monthly. Employment may be contractual or permanent, depending on the airline.
An aerospace engineer designs, develops, tests, and maintains aircraft, spacecraft, and related systems. They apply physics and engineering principles to improve aerospace technologies, often working in aviation, defence, or space sectors. Key tasks include designing components, conducting tests, and performing research. A bachelor’s degree is essential, with higher roles requiring advanced study. The role demands analytical skills, technical knowledge, precision, and effective communication.
An air hostess, or flight attendant, ensures passenger safety and comfort during flights. Responsibilities include safety demonstrations, serving meals, managing the cabin, handling emergencies, and post-flight reporting. The role demands strong communication skills, a calm demeanour, and a service-oriented attitude. It offers opportunities to travel and work in the dynamic aviation and hospitality industry.
An aeronautical engineer designs, develops, tests, and maintains aircraft and related systems. They work on components like engines and wings, ensuring performance, safety, and efficiency. The role involves simulations, flight testing, research, and technological innovation to improve fuel efficiency and reduce noise. Aeronautical engineers collaborate with teams in aerospace companies, government agencies, or research institutions, requiring strong skills in physics, mathematics, and engineering principles.
A Safety Manager ensures workplace safety by developing policies, conducting training, assessing risks, and ensuring regulatory compliance. They investigate incidents, manage workers’ compensation, and handle emergency responses. Working across industries like construction and healthcare, they combine leadership, communication, and problem-solving skills to protect employees and maintain safe environments.
An airline pilot operates aircraft to transport passengers and cargo safely. Responsibilities include pre-flight planning, in-flight operations, team collaboration, and post-flight duties. Pilots work in varying schedules and environments, often with overnight layovers. The demand for airline pilots is expected to grow, driven by retirements and industry expansion. The role requires specialized training and adaptability.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.
An architect plans and designs buildings, ensuring they are safe, functional, and aesthetically pleasing. They collaborate with clients, engineers, and contractors throughout the construction process. Key skills include creativity, design software proficiency, and knowledge of building codes. In India, a 5-year B.Arch degree and registration with the Council of Architecture are required to practise professionally.
Having a landscape architecture career, you are involved in site analysis, site inventory, land planning, planting design, grading, stormwater management, suitable design, and construction specification. Frederick Law Olmsted, the designer of Central Park in New York introduced the title “landscape architect”. The Australian Institute of Landscape Architects (AILA) proclaims that "Landscape Architects research, plan, design and advise on the stewardship, conservation and sustainability of development of the environment and spaces, both within and beyond the built environment". Therefore, individuals who opt for a career as a landscape architect are those who are educated and experienced in landscape architecture. Students need to pursue various landscape architecture degrees, such as M.Des, M.Plan to become landscape architects. If you have more questions regarding a career as a landscape architect or how to become a landscape architect then you can read the article to get your doubts cleared.
Urban Planning careers revolve around the idea of developing a plan to use the land optimally, without affecting the environment. Urban planning jobs are offered to those candidates who are skilled in making the right use of land to distribute the growing population, to create various communities.
Urban planning careers come with the opportunity to make changes to the existing cities and towns. They identify various community needs and make short and long-term plans accordingly.
A plumber installs, maintains, and repairs water, gas, and waste systems in homes and buildings. Their duties include fixing leaks, installing fixtures, testing systems, ensuring safety compliance, and working with other professionals on projects. They also document repairs and may supervise apprentices. Plumbers play a key role in ensuring public health and the smooth functioning of essential utilities.
Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.
Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.
Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.
Energy efficiency engineering is a broad field of engineering which deals with energy efficiency, energy services, facility management, plant engineering, and sustainable energy resources. Energy efficiency engineering is one of the most recent engineering disciplines to emerge. The field combines the knowledge and understanding of physics, chemistry, and mathematics, with economic and environmental engineering practices. The main job of individuals who opt for a career as an energy performance engineer is to find the most efficient and sustainable path to operate buildings and manufacturing processes.
Individuals who opt for a career as energy performance engineers apply their understanding and knowledge to increase efficiency and further develop renewable sources of energy. The energy efficiency engineers also examine the use of energy in those procedures and suggest the ways in which systems can be improved.
A geologist attempts to comprehend the historical backdrop of the planet we live on, all the more likely to anticipate the future and clarify current events. He or she analyses the components, deployments, results, physical characteristics, and past of the planet. A geologist examines the landforms and landscapes of the earth in relation to the geology, climatic, and human processes that have shaped them.
A geologist studies earth procedures, for example, seismic tremors, avalanches, floods, and volcanic eruptions to review land and draw up safe structure plans. When he or she researches earth materials, explores metals and minerals, yet in addition search for oil, petroleum gas, water, and strategies to extricate these.
A career as a Petroleum engineer is concerned with activities related to producing petroleum. These products can be in the form of either crude oil or natural gas. Petroleum engineering also requires the exploration and refinement of petroleum resources. Therefore, a career as a petroleum engineer comes up with oil and gas onshore jobs. There are also desk jobs in the petroleum industry. In layman’s terms, a petroleum engineer is a person who finds the best way to drill and extract oil from oil wells. Individuals who opt for a career as petroleum engineer also tries to find new ways to extract oil in an efficient manner.
A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.
A career as a civil engineer is of great importance for the infrastructural growth of the country. It is one of the most popular professions and there is great professional as well as personal growth in this civil engineering career path. There is job satisfaction in this civil engineering career path, but it also comes with a lot of stress, as there are multiple projects that need to be handled and have to be completed on time. Students should pursue physics, chemistry and mathematics in their 10+2 to become civil engineers.
A career as a Transportation Engineer is someone who takes care of people's safety. He or she is responsible for designing, planning and constructing a safe and secure transportation system. The transportation sector has seen a huge transformation and is growing day by day and improving every day.
As a Transport Engineer, he or she needs to solve complex problems such as accidents, costs, traffic flow, and statistics. A Transport Engineer also collaborates for projects with some other companies.
A Loco Pilot operates trains, ensuring safe and timely transport of passengers or goods. Starting as an Assistant Loco Pilot, one can progress to senior roles with experience. The job demands technical knowledge, focus, and adherence to safety protocols. It involves coordination with train staff and may require working long hours under pressure.
