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JEE Main 2025 January 28 Shift 1 Question Paper with Solutions - PDF Link
Edited By Shivani Poonia | Updated on Feb 04, 2025 06:11 PM IST | #JEE Main
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.
This Story also Contains
- 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 ( 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
$1 \quad x^2+y^2+z^2=$ 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
Also Check:
- JEE Main 2025 January 22 Shift 1 Question Paper with Solutions
- JEE Main 2025 January 22 Shift 2 Question Paper with Solutions
- JEE Main 2025 January 23 Shift 1 Question Paper with Solutions
- JEE Main 2025 January 23 Shift 2 Question Paper with Solutions
- JEE Main 2025 January 24 Shift 1 Question Paper with Solutions
- JEE Main 2025 January 24 Shift 2 Question Paper with Solutions
JEE Mains Previous Years Question Papers
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.
JEE Main Previous Year Analysis
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.
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.
Use NowMathematics:
-
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.
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.
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Questions related to JEE Main
Have a question related to JEE Main ?
With 64 percentile and a CRL rank around 5.4 lakh in JEE Mains 2025, getting admission in any NIT or IIIT is very unlikely, especially in the general category. Most NITs close their admissions below a rank of 1.5 lakh, and even the newer NITs usually fill seats by around 3 to 3.5 lakh rank. IIITs generally have closing ranks below 3 lakh.
Instead, you can try for state government engineering colleges through your state counselling or look for private engineering colleges that have lower cutoff ranks. Another option is to explore management quota or direct admission routes if available.
harsh singh 05 June,2025
HEY THERE!!!
- Given a JEE B.Arch rank of approximately 30,000 in the general category, gaining admission to DCRUST for B.Arch is, frankly ,not feasible .
- The university’s recent cutoffs are far more competitive; for instance, the round 1 cutoff for the general category in 2024 was only 36.
- Your rank is significantly above this threshold, so admission to DCRUST with your current standing is highly improbable.
- It would be advisable to explore alternative institutions or consider other academic pathways.
Tanisha chaudhary 05 June,2025
Hello Aspirant,
If your B.Arch rank is approximately 30,000 in JEE in general category, it might not be easy to get admission into DR-CUET (Delhi Regional Centre of the Central University of Technology) or comparable or significantly better institutions, and therefore, the cut-off is much earlier for general candidates in good reputation colleges at about a range of 5000-15,000 rank. That said, you may still have a chance at newer or even less reputed NITs, SPAs, or GFTIs as an option at JOSAA or CSAB; you are recommended to apply in all rounds of counselling, keep open state-level architecture colleges too, and explore private universities that are accepting NATA or JEE B.Arch scores.
gopi 05 June,2025
With a JEE B.Arch rank of 30,000, getting admission in DCRUST is not possible because their cutoff ranks are much lower and they mainly consider NATA scores, not JEE Paper 2.
You can try these options instead:
Apply to other colleges accepting NATA scores.
Consider management quota seats in private colleges.
Prepare and appear for NATA exam for better chances.
harsh singh 05 June,2025
With a JEE Advanced rank of 20,340, your son can likely get admission in newer IITs like IIT Bhubaneswar, Gandhinagar, Ropar, Mandi, Indore, Patna, or Jodhpur, mostly in less competitive branches.
Top IITs and popular branches like CS or ECE are unlikely.
harsh singh 05 June,2025
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