JEE Main 2024 B.Planning April 12 (Paper 2B) Question Paper is available here with solutions PDF and detailed solutions for every question. NTA conducted the JEE Main 2024 B.Planning (Paper 2B) exam on April 12, 2024, from 9:00 AM to 12:00 PM (Session 2). The question paper includes the following:
- 105 questions in a 3-hour paper (100 to be attempted): Part I Mathematics (30), Part II Aptitude Test (50) and Part III Planning (25)
- Mathematics: 20 multiple choice questions (MCQs) and 10 numerical value questions, of which any 5 are to be attempted; 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 2024 B.Planning April 12 (Paper 2B) Question Paper with Solution PDF
| NTA Official PDF | CD PDF | CD PDF with Solutions |
|---|---|---|
| Download official PDF 6.70 MB | Download Collegedunia PDF 6.86 MB | Download solutions PDF 2.74 MB |
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JEE Main 2024 B.Planning April 12 (Paper 2B) Questions with Solutions
Mathematics (Q1 - Q30)
| LIST I | LIST II | ||
| A. | ![]() | I. | Neither surjective nor injective |
| B. | ![]() | II. | Surjective but not injective |
| C. | ![]() | III. | Injective but not surjective |
| D. | ![]() | IV. | Injective and surjective |
Choose the correct answer from the options given below:
A college awarded 38 medals for cricket, 15 for tennis and 20 for football. If these medals were bagged by a total of 58 students and only 3 students got medals for all the three games, then how many students received medals for exactly two of the three games?
If \( \alpha \) and \( \beta \) are the roots of \( ax^{2}+bx+c=0 \), then the value of \( \frac{1}{(a\alpha+b)^{2}}+\frac{1}{(a\beta+b)^{2}} \) is
Let \( A=\left[\begin{array}{cccc}1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 9 & 9 & 9 \\ 8 & 8 & 8 & 8\end{array}\right] \), then determinant of \( A= \)
In how many ways can we select four cards from an ordinary pack of playing cards so that two of them are of the same denomination and the remaining two are of some other same denomination?
If the coefficient of \( x^{7} \) and \( x^{8} \) in the expansion of \( \left(2+\frac{x}{3}\right)^{n} \) are equal, then \( n \) is
The sum of all those terms of the arithmetic progression 2, 6, 10, 14, ....... , 598 which are not divisible by 3, is equal to
The first two terms of a G.P. are \( x^{-3} \) and \( x^{n} \), respectively. If \( x^{42} \) is the sixth term of the same progression, then \( n^{2} \) is equal to
Suppose L is the line joining the points \((0, 0)\) and \((1, 2)\). If a line parallel to L meets the curve \(y=2x^{2}+3x+1\) only at a single point P, then the point P is
A manufacturer can sell \(x\) items at a price of ₹ \(\left(5-\frac{x}{100}\right)\) each. The cost price of \(x\) items is ₹ \(\left(\frac{x}{5}+500\right)\). The number of items he should sell to reach maximum profit is
The value of \(\int_{0}^{1} \log _{e}\left(\frac{1}{x}-1\right) dx\) is
If \((1+\cos x) \frac{dy}{dx}-(y-3) \sin x=0\) and \(y(0)=0\), then the value of \(y\left(\frac{\pi}{2}\right)\) is
If a straight line passing through point P \((3, -5)\) is such that its intercepted portion between the co-ordinate axes is bisected at P, then the equation of the line is
The intercept on the line \(x=y\) by the circle \(x^{2}+y^{2}-2y=0\) is AB. The equation of the circle with AB as a diameter is
If the foot of the perpendicular from the point \((0, 0, 0)\) on the line \(\frac{x+2}{5}=\frac{y+2}{2}=\frac{z+8}{3}\) is \((a, b, c)\), then \(a^{2}+b^{2}+c^{2}\) is
If the vectors \(\overrightarrow{AB}=3 \hat{i}+8 \hat{k}\) and \(\overrightarrow{AC}=5 \hat{i}-2 \hat{j}+6 \hat{k}\) are the sides of a triangle \(ABC\), then the length of the median through \(A\) is
If \(\vec{a}=6 \hat{i}+2 \hat{j}-\lambda_{1} \hat{k}\), \(\vec{b}=3 \hat{i}+\left(3-\lambda_{2}\right) \hat{j}+2 \hat{k}\) and \(\vec{c}=2 \hat{i}+\left(1+\lambda_{3}\right) \hat{j}-3 \hat{k}\) are three vectors such that \(\vec{a}=3 \vec{c}\) and \(\vec{b}\) is perpendicular to \(\vec{c}\) then \(\left(\lambda_{1}, \lambda_{2}, \lambda_{3}\right)\) is
Let \(x_{1}, x_{2}, x_{3}, x_{4}, x_{5}\) be observations with mean \(m\) and standard deviation \(s\). Then, which of the following statements are correct:
A. Mean of the observations \(x_{1}+k, x_{2}+k, x_{3}+k, x_{4}+k, x_{5}+k\) is \(m+5k\)
B. Mean of the observations \(kx_{1}, kx_{2}, kx_{3}, kx_{4}, kx_{5}\) is \(km\).
C. The standard deviation of the observations \(x_{1}+k, x_{2}+k, x_{3}+k, x_{4}+k, x_{5}+k\) is \(s\).
D. The standard deviation of the observations \(kx_{1}, kx_{2}, kx_{3}, kx_{4}, kx_{5}\) is \(k^{5}s\).
Choose the correct answer from the options given below :
Let the area of the region enclosed between the two circles \(x^{2}+y^{2}=a^{2}\) and \((x-a)^{2}+y^{2}=a^{2}\) be \(\frac{m}{3}(4\pi-3\sqrt{3})\) sq. units for some \(a \geq 2\). If \(a\) is a root of \(x^{3}-3x^{2}-6x+8=0\), then
Suppose \(\left|\begin{array}{cc}f'(x) & f(x) \\ f''(x) & f'(x)\end{array}\right|=0\), where \(f(x)\) is continuously differentiable function with \(f'(x) \neq 0\ \forall x \in \mathbb{R}\) and satisfies \(f(0)=1\) and \(f'(0)=4\). If \(f(x)=e^{\lambda x}+\mu\), where \(\lambda, \mu \in \mathbb{R}\) then the value of \(\lambda^{2}+\mu^{2}\) is
The equations \(ax^{2}+bx+a=0\), \((a, b \in \mathbb{R})\) and \(x^{3}-2x^{2}+2x-1=0\) have two common roots. Then the value of \(a+b\) is ________.
Let \(A\) be a matrix satisfying \(A^{3}=3A+2I\) where \(A \neq nI\), \(n \in \mathbb{Z}\). If \(A^{2}+\alpha A+\beta I=O\), then maximum value of \(|\alpha+\beta|\) is ________.
An equilateral triangle is inscribed in the ellipse \(\frac{x^{2}}{3}+y^{2}=1\) such that one of the vertex of the triangle is \((0, 1)\) and one of the altitude of the triangle is along the \(y\)-axis. If A is the area of the equilateral triangle. Then \(625A^{2}\) is equal to ________.
The volume of the greatest cylinder that can be inscribed in a cone of height \(\frac{3}{\sqrt[3]{\pi}}\) and semi-vertical angle \(45^{\circ}\) is ________.
If the function \( f(x) \) is defined as \( f(x)=\begin{vmatrix}\frac{1}{1+e^{\sin x}} & \sin x \\ \sqrt{1-x^{2}} & 2\end{vmatrix} \). Then the value of \( \frac{1}{\pi}\int_{-\pi/2}^{\pi/2} f(x)\,dx \) is equal to ________.
A line touches the curve \( y=y(x) \) at a point \( (x, y) \) having slope \( \frac{1+y^{2}}{1+x^{2}} \), where \( x>0 \). If \( y(2)=1 \), \( y(3)=\frac{\alpha}{\beta} \) and \( \gcd\{\alpha, \beta\}=1 \), then the value of \( \alpha+\beta \) is ________.
The equation of the base of an equilateral triangle is \( x+y=1 \) and the opposite vertex has co-ordinates \( (-3, 2) \). The area of the triangle (in square units) is represented by \( A \), then the value of \( \sqrt{3}A \) is ________.
Let R be the point \( (13, -8, 10) \) and P\( (\alpha, \beta, \lambda) \) be the image of the point Q \( (5, 2, 1) \) in the line \( x-2=3-y=z+1 \). Then the square of the area of the triangle PQR is ________.
A hospital conducts a free eye check-up drive at 3 different locations A, B and C of a city. The number of people that came for test at A is thrice as much as that at B, and number of people that came at B is same as that at C. The results show that 4% population at A, 2% at B and 3% at C have poor eye-sight. If a person from the city goes for an army job and is found to have poor eye-sight, and the probability that he is not from location C is \( \frac{p}{q} \), where \( \frac{p}{q} \) is in simplest form, then value of \( (p+q) \) is ________.
The number of pairs \( (x, y) \) satisfying the equations \( \sin x+\sin y=\sin (x+y) \) and \( |x|+|y|=1 \) is ________.
Aptitude Test (Q31 - Q80)
In a certain word code, EXHAUST is written as CZFCSUR. How is NETWORK written in that code ?
In a code language, if "BRICK" is written as "CQJBL", then "CEMENT" is ________
When the paper is folded in a given pattern and is cut at the end. Identify which pattern is formed when the paper is unfold?
| LIST I (Components/Material) | LIST II (Functions) |
| A. Cement | I. Load Bearing |
| B. Window | II. Tensile strength |
| C. Foundation | III. Setting time |
| D. Steel | IV. Glazing |
Choose the correct answer from the options given below:
| LIST I (structure) | LIST II (places) |
| A. Humayun's Tomb | I. Gujarat |
| B. Bibi Ka Maqbara | II. New Delhi |
| C. Hussain Doshi Gufa | III. Maharashtra |
| D. Group of monuments, Mahabalipuram | IV. Tamilnadu |
Choose the correct answer from the options given below:
| LIST I | LIST II |
| A. Stairs | I. Key stone |
| B. Door | II. Toothing |
| C. Arch | III. Jamb |
| D. Brick work | IV. Tread |
Choose the correct answer from the options given below:
Give below are two statements :
Statement I : A partition wall is defined as an internal wall whose function is to divide the space within the building.
Statement II : Partition wall could be load bearing or non-load bearing.
In the light of the above statements, choose the most appropriate answer from the options given below:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : Social integration at work place is necessary.
Reason R : There are many backward classes in society.
In the light of the above statements, choose the correct answer from the options given below :
Primary colours are ________.
The stairs kept in motion by a revolving drum is known as a ________.
Which of the following structure does not have a dome?
Given below is the famous temple in India. Identify the style of temple architecture adopted in the temple.
| LIST I (Plan) | LIST II (Building Name) | ||
| A. | ![]() | I. | Taj Mahal |
| B. | ![]() | II. | Qutub Minar, New Delhi |
| C. | ![]() | III. | Matri Mandir, Auroville |
| D. | ![]() | IV. | Sanchi Stupa |
The botanical name of "MANGO" tree is
Scientific study of human body measurements :
FAR stands for
On an engineer scale, 1 cm = 10 m. Identify the representative fraction (R.F.)
Identify the iconic Landmark :
Identify the name of the Landmark :
Identify the famous Monument in the given picture.
A man is facing towards East and turns through \(45^{\circ}\) anti clockwise, again \(180^{\circ}\) anticlockwise and then turns through \(270^{\circ}\) clockwise. In which direction is he facing now?
The 'lightness or darkness' of a colour is defined as :
Select a figure amongst the answer figures which will continue the same series or pattern as established by the problem figures.
Identify the true mirror image of the figure amongst the answer figures with respect to X-X.
Identify the mirror image of given word :
Identify the correct mirror image of the given figure along x-y axis :
The question figure shows the 3D view of an object. Identify the correct view of the object looking in the direction of arrow.
Identify the true mirror image of the figure amongst the answer figures with respect to X-X :
'Kuchipudi' is a unique dance from which state ?
Which of the below given material is not a plaster type ?
Who initiated the construction of Qutub-Minar, Delhi?
When is the world Environment Day celebrated?
Visual weight is associated with :
Lines those branch off of a central point are referred to as :
V7 concept of Chandigarh city is associated with which architect?
Who is known as "Father of contemporary architecture"?
Who designed 'India Gate'?
Who among the following architects has not won the Pritzker prize till 2019?
Terra cotta is a type of earthen work which is processed by:
Which building material is primarily used as a building material for the Great Wall of China?
Identify the architectural symbol represented in the given figure.
Percentage of lime content in ordinary Portland cement is
Sill Level is associated with
What is the terminology for the vertical portion between each tread of the stairs?
The question figure shows the 3D view of an object. Identify the correct view of the object looking in the direction of arrow :
Complete the number sequence :
18, 27, 38, 51, ........., 83
In the question figure a-3-D object is given, Identify the correct top view of the object amongst the answer figures.
In question figure - 3D object is given, Identify the correct view of the object looking in the direction of the arrow, amongst the answer figures.
In question figure a 3-D object is given. Identify the correct view of the object looking in the direction of arrow, amongst the answer figures.
In the question figure a 3-D object is given. Identify the correct top view of the object amongst the answer figures.
Planning (Q81 - Q105)
Urban heat island is ____________ its surrounding rural areas.
| LIST I (Cities) | LIST II (Planner) | ||
| A. | Jaipur | I. | O. Konigsberger |
| B. | Gandhi Nagar | II. | Doxiadis |
| C. | Islamabad | III. | H.K.Mewada |
| D. | Bhubneswar | IV. | Vidyadhar |
Given below are two statement:
Statement I : On November 8, 2016, demonetization was declared in India.
Statement II : On that day, Prime Minister of India announced the demonetization of Rs. 500 & Rs. 1000 notes.
In the light of the above statements, choose the correct answer from the options given below:
The given diagram shows the demand & supply of food items amongst users. Identify which food item was least supply among all.
In which five year plan period was the slogan 'Garibi hatao' given?
Which of the following is considered to be the first planned city of independent India?
The full form of "NITI" in NITI Aayog is
Who was the President of Indian National Congress at the time of independence of India?
| LIST I (Vehicle) | LIST II (Manufacture) |
| A. THAR | I. Volkswagen |
| B. Yaris | II. Mahindra & Mahindra |
| C. I 20 | III. Toyota Motor |
| D. Vento | IV. Hyundai |
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The full form of NCR is the National Capital Region.
Reason R : 'NCR' in India is the designation for the conurbation which includes New Delhi with surrounding urban areas of neighbouring states of Haryana, Uttar Pradesh and Rajasthan.
In the light of the above statements, choose the most appropriate answer from the options given below:
Most of the energy used on Earth today originally come from which of these sources?
The 74th amendment of the constitution is related to __________.
Dandaka form of settlement layout is basically a __________.
A. Radial pattern
B. Grid Iron pattern
C. Star pattern
D. Octagonal pattern
Choose the most appropriate answer from the options given below:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Between 1921-1922, the production of tea and coffee grew up.
Reason R : As the non-cooperation moved into economic sphere and foreign goods were boycotted and burnt.
In the light of the above statements, choose the most appropriate answer from the options given below:
Who was the first Vice-chairman of NITI Aayog?
Name the Entrepreneur of India who set factories during colonical period
A. Dwarakanath Tagore
B. Dinshoo Petit
C. Dhirubhai Ambani
D. Jamset Ji Nusserwanji Tata
E. Seth Hukumchand
Choose the correct answer from the options given below:
What are the three R's those are used to save the environment which includes forest?
The 'National Development Council' was constituted on
Following pie chart gives a percentage distribution of time spent by a student on various activities in a day. How much time she spent in playing every day?

The given diagram shows the sales of a company with respect to years. Which of the following is correct?
A. Company made minimum profit in 2010-2020.
B. Company made more than 500 crore profit in 2000-2010.
C. In 1990-2000, company has reached highest sale.
D. In, 2010-2020, company made highest profit.
Choose the correct answer from the options given below:

In which year the sales of company is minimum ?
A. 2000-2010
B. 1990-2000
C. 1980-1990
D. 2010-2020
Choose the most appropriate answer from the options given below:

Given below are two statements:
Statement I : In 2010-2020 company made maximum profit and minimum sale.
Statement II : In 1980-1990 company made 50% profit of its total sale.
In the light of the above statements, choose the most appropriate answer from the options given below

In 1990-2000 company profit percentage is
Given below are two statements:
Statement I : The last five year plan executed is 12th plan. It was launched in 2012.
Statement II : 12th five year plan was for faster, sustainable and more inclusive growth.
In the light of the above statements, choose the correct answer from the options given below :
From the given diagram find out that mandir is located at which direction to forest?
JEE Main 2024 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 | 105 questions (100 to be attempted) |
| Total Marks | 400 marks |
| Marking Scheme | +4 for correct answer & -1 for incorrect answer; 0 for unattempted |
































































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