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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.
Last year, NTA removed the optional questions from section B of the JEE Main papers, which were introduced during Covid. Instead of getting choices in 10 questions, candidates will now have to attempt all 5 questions.
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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.
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.
Frequently Asked Questions (FAQs)
Paper 1 is for B.E./B.Tech, and Paper 2 is for B.Arch/B.Planning, with MCQs and numerical questions.
Candidates must have passed 10+2 with Physics, Chemistry, and Mathematics, and meet the required percentage criteria.
On Question asked by student community
Hello,
Generally an income certificate isn't required for the JEE Main registration, but if you want to claim the EWS quota, then you need this. You must provide the certificate, issued by a government authority, as proof of your family's income being below the specified limit for the reservation category you wish to apply under.
I hope it will clear your query!!
Yes, as JEE does accepts improvement examination scores, so you must go for it but most of the state boards have already conducted or are conducting their 2025 improvement exams. If you have already given your improvement that's fine. If you have not given improvement this year then you can take your improvement next year.
Thank You.
Hello,
Yes, you can prepare for and take the JEE Main exam after completing your intermediate (12th year) exams. This is a common path for students who want to dedicate a year to intensive preparation without the pressure of simultaneous board exams.
I hope it will clear your query!!
Hello,
You can get the JEE 2025 Syllabus from this link : JEE Main Class 12th Syllabus 2026
Hope it helps !
You said you belong to the BC category, converted Christian from a Scheduled Caste background under 16A, and your community certificate is BC. You are giving the JEE exam and want to know which category you should choose and what benefits are there.
If you have a BC certificate, it means you are not eligible for the Scheduled Caste category now because after conversion to Christianity, SC reservation does not apply. So, in JEE or any central exam, you cannot use SC.
JEE and other central exams use the Central Government category list, not the state one. The Central categories are General, General-EWS, OBC-NCL, SC, and ST.
The BC category used by your state is not always the same as OBC-NCL. You need to check if your BC community name appears in the Central OBC list. If it appears there, you can select OBC-NCL. If it is not in the Central OBC list, you must select either General or General-EWS, depending on your family income.
If your family income is below 8 lakh per year, and you do not belong to any reserved category, you can choose General-EWS. If your income is above that, you must select General.
The difference between OBC-NCL and General-EWS is that OBC-NCL students get 27 percent reservation in IITs, NITs, and IIITs, and they also get government scholarships. General-EWS students get 10 percent reservation and can apply for EWS scholarships. General students do not get reservation or category-based scholarships.
So, the steps are simple. Check if your community is listed in the Central OBC list. If it is there, choose OBC-NCL in your JEE form. If it is not there, see if you are eligible for EWS. Otherwise, choose General.
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