JEE Main 2025 B.Planning January 30 (Paper 2B) Question Paper is available here with solutions PDF and detailed solutions for every question. NTA conducted the JEE Main 2025 B.Planning (Paper 2B) exam on January 30, 2025 in the afternoon session (Session 1). The question paper includes the following:
- 100 questions in a 3-hour paper: Part I Mathematics (25), Part II Aptitude Test (50) and Part III Planning (25)
- Mathematics: 20 multiple choice questions (MCQs) and 5 numerical value questions, 4 marks each (100 marks)
- Aptitude Test: 50 MCQs, 4 marks each (200 marks)
- Planning: 25 MCQs, 4 marks each (100 marks)
- Marking: +4 for a correct answer, -1 for an incorrect MCQ or numerical answer, 0 for an unattempted question; maximum marks 400
JEE Main 2025 B.Planning January 30 (Paper 2B) Question Paper with Solution PDF
| NTA Official PDF | CD PDF | CD PDF with Solutions |
|---|---|---|
| Download official PDF 6.57 MB | Download Collegedunia PDF 7.30 MB | Download solutions PDF 3.19 MB |
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JEE Main 2025 B.Planning January 30 (Paper 2B) Questions with Solutions
Mathematics (Q1 - Q25)
Let \(A=\{1,2,3,4,5,6,7,8,9,10,11,12\}\). Let \(R\) be a relation on \(A\) defined by \(xRy\) if and only if \(2x=3y\). Let \(l\) and \(m\) be the minimum number of elements required to be added in \(R\) to make it reflexive and symmetric relations, respectively. Then \(l+m\) is equal to :
If the domain of the function \(f(x)=\frac{1}{\log _{10}(1-2 x)}+\sqrt{2 x+1}\) is \([\alpha, \beta)-\{0\}\), then \(20\left(\alpha^{2}+\beta^{2}\right)\) equals :
If \(\sqrt{-24-10 i}=\alpha+i \beta\), \(i=\sqrt{-1}\), \(\alpha, \beta \in \mathbf{R}\), then \(\alpha^{2}+\beta^{2}\) is equal to :
The product of all real solutions of the equation \((3+2 \sqrt{2})^{x^{4}-15}+(3-2 \sqrt{2})^{x^{4}-15}=6\) is :
If the system of equations \(x+2 y+3 a z=4\), \(2 x+3 y+4 z=1\), \(3 x+7 y+2 z=b\) has infinitely many solutions, then \(b-40 a\) is equals to :
Let \(a, b, c\) be positive real numbers such that \(a, 7, c, b\) are in an arithmetic progression. If \(ab=3(a+b)\), then the largest value of \(b\) is :
If there are 19 and 16 points on two distinct parallel lines \(L_{1}\) and \(L_{2}\), respectively, then the total number of triangles that can be formed using these points as vertices, is :
| Variable (\(x_i\)) | 1 | 3 | 4 | 7 | 9 | Total |
| Frequency (\(f_i\)) | 1 | \(a\) | \(b\) | 3 | 1 | 10 |
is 5, then its variance is :
In a question paper containing 10 questions, A can solve 70% of the questions and B can solve 50% of the questions. The probability, that none of A and B will be able to solve the question, selected at random from the paper, is :
Let the line \( y = x + 3 \) intersect the parabola \( x^2 = 4y \) at the points \( A \) and \( B \). If \( F \) is the focus of the parabola, then the area of triangle \( AFB \) is :
Let \( A\left(3, 3\sqrt{3}\right) \), \( B(6, 0) \) and \( C(\alpha, \beta) \) be the vertices of an equilateral triangle. Let its incentre be \( D \), and \( P \) and \( Q \) be the feet of perpendiculars drawn from the point \( D \) on \( AC \) and \( BC \), respectively. Then the area of quadrilateral \( CPDQ \) is :
Let \( E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \), \( a > b \) be an ellipse of eccentricity \( \frac{1}{\sqrt{3}} \). If the distance between the foci of \( E \) is 4, then the length of its latus rectum is :
Let a circle of radius 3 pass through the origin \( O \) and meet the coordinate axes at the points \( A \) and \( B \). Then the locus of the centroid of the triangle \( AOB \) is :
The length of the perpendicular from the point \( (1, 2, 3) \) on the line \( \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{-2} \) is :
Let \( L_1 \) be the line that passes through the point \( (1, 2, -4) \) and be perpendicular to the two lines \( \frac{x - 8}{3} = \frac{y + 19}{-16} = \frac{z - 10}{7} \) and \( \frac{x - 15}{3} = \frac{y - 29}{8} = \frac{z - 5}{-5} \). If \( L_2 \) is the line \( \vec{r} = 7\hat{i} - 6\hat{k} + \lambda(\hat{i} + 2\hat{j} + 2\hat{k}) \), \( \lambda \in \mathbf{R} \), then an angle between \( L_1 \) and \( L_2 \) is equal to :
Let \( f \) be a differentiable non-zero function and \( 3\int_0^x f(t)\,dt = 2(f(x))^3 \). Then \( \int_0^1 \frac{3(f(x))^4}{\sqrt{1 + (f(x))^{12}}}\,dx \) is equal to :
Let \( f(x)=\sum_{r=1}^{10} \cot^{-1}\left(1-(x+r)+(x+r)^{2}\right) \), \( x \geq 0 \). Then \( \lim_{x \rightarrow \infty}\left(\tan (f(x))+\sec^{2}(f(x))\right) \) is :
The area of the region, enclosed between the curves \( y=\cos x \) and \( y=|\cos x| \) for \( 0 \leq x \leq 3 \pi \), is :
If \( \int_{4}^{9} \dfrac{x-\sqrt{x}}{x(x-1)}\, \mathrm{d}x=\alpha \), then \( \mathrm{e}^{\alpha} \) is equal to :
If the function \( f(x) \) defined by \( f(x)=\begin{cases}\dfrac{\log_{e}(1+5x)-\log_{e}(1-2x)}{x}, & x \neq 0 \\ l, & x=0\end{cases} \) is continuous at \( x=0 \), then the value of \( l \) is :
Let \( A=\begin{bmatrix}1 & 2 & 3\\ 0 & 2 & 3\\ 0 & 0 & 1\end{bmatrix} \) and let \( P \) be a \( 3 \times 3 \) matrix. If \( AP=\begin{bmatrix}1 & 0 & 1\\ 1 & 1 & 0\\ 0 & 1 & 1\end{bmatrix} \) and \( \begin{bmatrix}1 & 0 & 2\end{bmatrix} P\begin{bmatrix}1\\ 0\\ 2\end{bmatrix}=[k]_{1 \times 1} \), then \( k \) is equal to ________.
If \( \left({ }^{10} C_{1}\right)^{2}+2\left({ }^{10} C_{2}\right)^{2}+\ldots+10\left({ }^{10} C_{10}\right)^{2}=m\left({ }^{n} C_{m}\right) \), then \( m+n \) equals ________.
If \( \sum_{x=1}^{n^{2}} \sqrt{\left(x \cos \left(\cot ^{-1} x\right)+\sin \left(\cot ^{-1} x\right)\right)^{2}-1}=A n^{4}+B n^{2} \), then \( 2(A+B) \) equals ________.
Let \( \vec{a}=2 \hat{i}+\hat{j}-\hat{k} \) and \( \vec{b}=3 \hat{i}+2 \hat{j}+4 \hat{k} \). Let for some \( \lambda, \mu \in \mathbf{R} \), a vector \( \vec{c}=\lambda \vec{a}+\mu \vec{b} \). If \( \vec{a} \cdot \vec{c}=16 \) and \( \vec{b} \times \vec{c}=-12 \hat{i}+22 \hat{j}-2 \hat{k} \), then \( |\vec{c}|^{2} \) equals ________.
If the differential equation for the family of circles passing through the points \((19, 0)\) and \((-19, 0)\) is \(2xy\,\mathrm{d}x + (\alpha x^{2} + \beta y^{2} + \gamma)\,\mathrm{d}y = 0\), then \(\alpha + \beta + \gamma\) is equal to ________.
Aptitude Test (Q26 - Q75)
A structure which is designed to look impressive and wonderful from a far distance has a :
The question fig. shows the 3D view of an object. Identify the correct number of visible surfaces.
The question figure shows the 3D view of an object. Identify the correct view looking in the direction of arrow.
The question figure shows the 3D view of an object. Identify the correct view looking in the direction of arrow.
The question figure shows the 3D view of an object. Identify the correct number of visible surfaces.
The question figure shows the 3D view of an object. Identify the correct number of visible surfaces.
The question figure shows the 3D view of an object. Looking in the direction of arrow identify the correct view.
The question figure shows the 3D view of an object. Identify the correct top view.
The question figure shows the 3D view of an object. Identify the correct view looking in the direction of arrow.
The question figure shows the 3D view of an object. Identify the correct view of the object looking in the direction of arrow.
In a question figure a 3D object is given. Identify the correct top view of the object amongst the answer figures.
How many edges does a cube have ?
How many squares are there in the given figure ?
Which of the given shapes would complete the sequence ?
Identify the figure which is odd from rest :
Identify the mirror image of the given word along X-X' axis :
What is the total number of triangles in the given diagram ?
Choose the appropriate option which most closely resembles the water image of the given word "FROG" :
Identify the mirror image of the given word along X-X' axis :
Identify the correct mirror image of the given figure along X-X' axis :
Which among the following is an excellent hardwood (timber) for furniture ?
Which colour scheme is typically considered to be calming and is often used in bedrooms and bathrooms ?
Bharat Mandapam is designed by which architecture firm ?
Gable : Roof : : Pier : ________.
In which architectural style are you most likely to find "chhatris" as decorative elements ?
Which of these is a well known proportion that is aesthetically pleasing and used in architecture ?
The primary function of a "roof truss" is ________.
Choose the appropriate answer from the following :
Hawa Mahal located at Jaipur was built by :
The textural appearance of "exposed aggregate" concrete is created by :
The term "International style" is used to describe architecture that :
Which of the following finishing materials is known for its textured surface and is commonly used in facades ?
Central Vista Redevelopment Project was designed by which architect ?
Guggenheim Museum located in Manhattan, New York city was designed by :
Which organisation maintains the registration of Architects in India ?
“Fenestration” in architecture refers to :
National Gallery of Art was designed by whom ?
What does “ISI” stands for ?
The famous “Parthenon” is located in which city ?
“PRASAD” scheme stands for :
| List - I | List - II | ||
| (A) | B.V. Doshi, India | (I) | Pritzker Award in 2004 |
| (B) | Philip Johnson, United States | (II) | Pritzker Award in 1995 |
| (C) | Tadao Ando, Japan | (III) | Pritzker Award in 2018 |
| (D) | Zaha Hadid, Iraq | (IV) | Pritzker Award in 1979 |
| List - I | List - II | ||
| (A) | Colosseum | (I) | Temple dedicated to the Goddess Athena |
| (B) | Parthenon | (II) | Church, Italy |
| (C) | Milan Cathedral | (III) | Roman goddess of freedom |
| (D) | Statue of Liberty | (IV) | Roman Amphitheatre |
| List - I | List - II | ||
| (A) | Abacus | (I) | Vertical member of railing |
| (B) | Bollard | (II) | Top part of column |
| (C) | Baluster | (III) | Tapered upright structure rising from roof |
| (D) | Pinnacle | (IV) | Short free standing column |
| List - I | List - II | ||
| (A) | Matt | (I) | Silk like gloss |
| (B) | Satin | (II) | Highest level of gloss |
| (C) | Semi-gloss | (III) | More gloss than a satin finish |
| (D) | Glossy | (IV) | Lowest level of gloss |
Given below are two statements :
Statement (I) : Human scale in architecture refers to the design dimensions that are comfortable for human interaction.
Statement (II) : Monumental scale is most suitable for intimate and cozy spaces.
In the light of the above statements, choose the most appropriate answer from the options given below :
Given below are two statements :
Statement (I) : A colour triangle is basically an arrangement of colors within a triangle, based on the additive combination of three primary colours at its corners. Where primary colours are yellow, red and blue.
Statement (II) : Secondary colours on the other hand are created when equal amounts of any two primary colours are mixed together.
In the light of the above statements, choose the most appropriate answer from the options given below :
Given below are two statements :
Statement (I) : Due to sun, we have day and night, seasons, rains, winds, plants and human life.
Statement (II) : The lattitude of a place is an angle of the place with reference to the plane passing through the equator on earth.
In the light of the above statements, choose the most appropriate answer from the options given below :
Given below are two statements :
Statement (I) : Precipitation is the collective term that indicates the prevailing humidity conditions.
Statement (II) : Precipitation is measured by rain gauges and expressed in millimetres per time unit.
In the light of the above statements, choose the most appropriate answer from the options given below :
Identify the temple style of India represented in the given figure :
Identify the famous building in the given picture :
Identify the correct mirror image of the given figure along X-X' axis :
Planning (Q76 - Q100)
The main focus/goal of 'Sustainable Urban Planning' is :
'________' is used to visualize and plan land use patterns in the city.
'H.I.G' stands for :
Following are the population density of 03-different sectors of a city :
Sector-A = 150 persons/Ha.
Sector-B = 230 persons/Ha.
Sector-C = 400 persons/Ha.
Find out the 'Avg. population density' of the city.
Document published by government for the development of a 'city' for next 20 years is called :
Given below are two statements :
Statement (I) : Agora was a part of the towns of 'Indus Valley Civilisation'.
Statement (II) : Towns of 'Indus Valley Civilisation' are laid with road network and sewer lines.
In the light of the above statements, choose the most appropriate answer from the options given below :
Given below are two statements :
Statement (I) : Without control over development and use of land and building, no planning will be successful.
Statement (II) : Development controls are statutory in nature and the planning/development authority has the power to punish the defaulters.
In the light of the above statements, choose the correct answer from the options given below :
Given below are two statements :
Statement (I) : The urban climate will have deviations from the regional macro climate.
Statement (II) : The manmade environment impacts the micro climate of a particular area which deviates from the macro climate of the region.
In the light of the above statements, choose the most appropriate answer from the options given below :
Name the "Administrative Capital" of Punjab and Haryana :
The "green belt" in urban planning is ________.
Name the person responsible for "Green Revolution" in India :
Who stated "Man needs his difficulties because they are necessary to enjoy success."
Match the correct term for "Sthapati" :
Identify the full form of "WHO" :
A person starts moving from point ‘A’ towards ‘East’ direction for 100 meters. Then he moves in ‘South’ direction for 50 meters. Again he changes the direction and moves 100 meters towards ‘West’ direction. At last he moves 50 meters further in ‘North’ direction. Identify the 2D shape he has formed after finishing this journey :
| List - I | List - II | ||
| (A) | Radial City | (I) | Chandigarh |
| (B) | Linear City | (II) | Kolkata |
| (C) | Organic City | (III) | New Delhi |
| (D) | Grid Iron Pattern City | (IV) | Varanasi |
Choose the correct answer from the options given below :
| List - I (States) | List - II (Reserve forest) | ||
| (A) | Kerala | (I) | Kaziranga |
| (B) | Assam | (II) | Pench |
| (C) | Rajasthan | (III) | Periyar |
| (D) | Madhya Pradesh | (IV) | RanthamBor |
Choose the correct answer from the options given below :
| List - I | List - II | ||
| (A) | Jordan | (I) | Burj-Al-Arab |
| (B) | Cairo | (II) | Hanging Gardens |
| (C) | Babylon | (III) | Pyramids |
| (D) | UAE | (IV) | Dead Sea |
Choose the correct answer from the options given below :
| List - I | List - II | ||
| (A) | Housing area | (I) | Ecological zone |
| (B) | Shopping mall/area | (II) | Industrial zone |
| (C) | Urban forest | (III) | Residential zone |
| (D) | Factory/workshop | (IV) | Commercial zone |
Choose the correct answer from the options given below :
In the given diagram the ‘Δx’ is located in a ________.
What is the percentage area covered by water bodies in the given plan ?
What is the full form of ‘D.R.D.O.’ ?
Which of the following cities started as a port during the colonial period and is presently the financial capital of India?
In the given diagram hospital was planned to be built on the contour level 65 and the ground was proposed at the contour level 45, houses were planned on the eastern part of the river on the contour level 40, where the existing ground is located. If a person plans to travel from ground to temple and return to the house, what is the level of the existing park?
In the given diagram if a person has to travel from hospital to ground crossing the bridge how many contour intervals have to be crossed?
JEE Main 2025 B.Planning (Paper 2B) Exam Pattern and Marking Scheme
| Particulars | Details |
|---|---|
| Exam Mode | Online (Computer-Based Test) |
| Paper | B.Planning (Paper 2B) |
| Duration | 3 hours (180 minutes) |
| Type of Questions | Multiple Choice Questions (MCQs), numerical value questions |
| Subjects | Mathematics, Aptitude Test, Planning |
| Total Questions | 100 questions |
| Total Marks | 400 marks |
| Marking Scheme | +4 for correct answer & -1 for incorrect answer; 0 for unattempted |
































































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