JEE Main 2024 · January session

JEE Main 1 February 2024, Shift 1

90 questions: 30 numerical-answer and 60 multiple choice. 10 were rated hard and 32 easy. Its hard-question count was the joint 8th highest of the 18 2024 shifts Lumi analysed. The biggest chapter was Conic Sections, with 4 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 10; 11% of the shift
Chapters asked: 61; 7 questions with a figure

Key findings · 1 Feb 2024, Shift 1

1
10 hard questions (11%): the joint 8th highest count of the 18 2024 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 20%.
2
Maths was the hardest section, with 9 of 30 rated hard; Chemistry had the most easy questions (18 of 30).
3
16 questions tested a new idea, one no earlier year had asked: 21% of the 77 questions tagged to an idea.
4
28 came back from 2023: the same idea had been asked in the 2023 shifts Lumi analysed.
5
47 shared an idea with another 2024 shift (61% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Units and Measurements in Physics (3), Haloalkanes and Haloarenes in Chemistry (4) and Conic Sections in Maths (4).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 13Medium 16Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 18Medium 12Hard 0

Top chapters

Maths

30 Q · 10 numerical

Easy 1Medium 20Hard 9

Top chapters

Conic Sections4 Q
Complex Numbers and Quadratic Equations3 Q
Determinants2 Q
Differential Equations2 Q
Integrals2 Q
Permutations and Combinations2 Q

Question format

Single correct48 Q
Numerical value30 Q
Two statements4 Q
Diagram based3 Q
Assertion–reason2 Q
Other2 Q
Match the list1 Q

What each question asks you to do

Calculation39 Q
Multi-step17 Q
Conceptual11 Q
Recall11 Q
Application10 Q
Diagram reading1 Q
Data or graph1 Q

Most common: Calculation.

Against the other 2024 shifts

This shift next to the 17 other 2024 shifts Lumi analysed

Shares are of each shift’s scored questions. The highlighted row is this shift.

Shift	Questions	Easy	Hard	Numerical	New ideas	Multi-step
27 Jan, Shift 1	90	50%	9%	33%	29%	29%
29 Jan, Shift 1	89	38%	10%	34%	28%	34%
30 Jan, Shift 1	90	37%	11%	33%	22%	17%
30 Jan, Shift 2	89	42%	10%	34%	32%	29%
31 Jan, Shift 1	90	39%	12%	33%	31%	34%
31 Jan, Shift 2	89	28%	13%	34%	23%	30%
1 Feb, Shift 1	90	36%	11%	33%	21%	19%
1 Feb, Shift 2	88	40%	8%	34%	19%	21%
4 Apr, Shift 1	89	26%	20%	33%	26%	36%
4 Apr, Shift 2	90	33%	18%	33%	13%	26%
5 Apr, Shift 1	90	40%	8%	33%	22%	27%
5 Apr, Shift 2	90	37%	10%	33%	23%	32%
6 Apr, Shift 1	88	43%	11%	34%	18%	22%
6 Apr, Shift 2	89	35%	15%	33%	28%	33%
8 Apr, Shift 1	90	31%	9%	33%	19%	37%
8 Apr, Shift 2	90	33%	12%	33%	19%	28%
9 Apr, Shift 1	90	31%	11%	33%	20%	50%
9 Apr, Shift 2	90	31%	16%	33%	27%	39%

New ideas: share of a shift’s questions testing an idea no earlier year had asked. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.

Drill down

What this shift asked, and its history

Every chapter this shift asked, with all its topics and ideas. Counts and squares cover every analysed shift from 2017 to 2026; rows this shift did not ask are faded, and each row lists this shift’s questions with the most recent from other shifts.

subjectAskedShareYears’17’20’21’22’23’24’25’26

Open30 this shift3092 · 33%33%8/830299720720358540200225
Open30 this shift3084 · 33%33%8/830298716720359538199224
Open30 this shift3065 · 33%33%8/829299715710354533200225

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Every question

All 90 questions of this shift

The opening words of each question, with its chapter, topic, idea and how hard it was. Open one for the full text, options and the official answer. “New idea” means no earlier year had tested it.

Subject

Difficulty

Idea

Find

90 of 90 questions

Physics30 questions

13 easy16 medium1 hard

Chemistry30 questions

18 easy12 medium0 hard

Q61
According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron( $\lambda$ ) and momentum of electron (p) ?
Structure of Atom Matter Waves Graphical Variation of Wavelength vs Momentum
EasyDiagram based · figureNew idea
Q62
Arrange the bonds in order of increasing ionic character in the molecules. LiF, $\mathrm{K_2O}$ , $\mathrm{N_2}$ , $\mathrm{SO_2}$ and $\mathrm{ClF_3}$ :
Chemical Bonding and Molecular Structure
MediumSingle correct
Q63
Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following :
Thermodynamics (Chemistry)Thermodynamic Processes Free Expansion of Ideal Gas
EasySingle correctIdea asked in 2 years
Q64
We have three aqueous solutions of NaCl labelled as 'A', 'B' and 'C' with concentration 0.1 M, 0.01 M and 0.001 M, respectively. The value of van't Hoff factor(i) for these solutions will be in the order :
Solutions Colligative Properties Van't Hoff Factor (i)
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q65
In case of isoelectronic species the size of $\mathrm{F^-}$ , Ne and $\mathrm{Na^+}$ is affected by :
Classification of Elements and Periodicity in Properties Periodic Trends Isoelectronic Species Radii Comparison
EasySingle correctIdea asked in 5 yearsAsked the year before
Q66
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : $\mathrm{PH_3}$ has lower boiling point than $\mathrm{NH_3}$ . Reason (R) : In liquid state $\mathrm{NH_3}$ molecules are associated…
Chemical Bonding and Molecular Structure Periodic Trends Boiling Point Anomalies of p-Block Hydrides
EasyAssertion–reasonIdea asked in 2 years
Q67
In acidic medium, $\mathrm{K_2Cr_2O_7}$ shows oxidising action as represented in the half reaction : $\mathrm{Cr_2O_7^{2-} + XH^+ + Ye^{\ominus} \rightarrow 2A + ZH_2O}$ X, Y, Z and A are respectively are :
Redox Reactions Ion-Electron Acidic
EasySingle correctIdea asked in 2 yearsAsked the year before
Q68
Which of the following reactions are disproportionation reactions ? (A) $\mathrm{Cu^+ \rightarrow Cu^{2+} + Cu}$ (B) $\mathrm{3MnO_4^{2-} + 4H^+ \longrightarrow 2MnO_4^- + MnO_2 + 2H_2O}$ (C) $\mathrm{2KMnO_4 \longrightarrow K_2MnO_4 + MnO_2 + O_2}$ (D)…
Redox Reactions Disproportionation Balancing
MediumOtherIdea asked in 3 years
Q69
Given below are two statements : Statement (I) : A solution of $\mathrm{[Ni(H_2O)_6]^{2+}}$ is green in colour. Statement (II) : A solution of $\mathrm{[Ni(CN)_4]^{2-}}$ is colourless. In the light of the above statements, choose the most appropriate answer…
Coordination Compounds Crystal Field Theory Color and d-d Transitions
MediumTwo statementsIdea asked in 5 yearsAsked the year before
Q70
Which of the following complex is homoleptic ?
Coordination Compounds
EasySingle correct
Q71
In Kjeldahl's method for estimation of nitrogen, $\mathrm{CuSO_4}$ acts as :
Organic Chemistry: Some Basic Principles and Techniques Stoichiometry Stoichiometry of Kjeldahl Method
EasySingle correctIdea asked in 4 years
Q72
Given below are two statements : Statement (I) : Aminobenzene and aniline are same organic compounds. Statement (II) : Aminobenzene and aniline are different organic compounds. In the light of the above statements, choose the most appropriate answer from the…
Amines IUPAC Nomenclature Retained Common Names for Aromatic Compounds
EasyTwo statementsNew idea
Q73
Ionic reactions with organic compounds proceed through : (A) homolytic bond cleavage (B) heterolytic bond cleavage (C) free radical formation (D) primary free radical (E) secondary free radical Choose the correct answer from the options given below :
Organic Chemistry: Some Basic Principles and Techniques
EasyOther
Q74
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Haloalkanes react with KCN to form alkyl cyanides as a main product while with AgCN form isocyanide as the main product. Reason (R) :…
Haloalkanes and Haloarenes SN1 and SN2 Mechanisms Ambident Nucleophiles (Cyanide vs Isocyanide)
MediumAssertion–reasonIdea asked in 2 years
Q75
Identify A and B in the following sequence of reaction [toluene: benzene ring with $\mathrm{CH_3}$ ] $\xrightarrow{\mathrm{Cl_2/h\nu}}$ A $\xrightarrow[373\ \mathrm{K}]{\mathrm{H_2O}}$ B
Haloalkanes and Haloarenes
MediumDiagram based · figure
Q76
Match List - I with List - II. List - I (Reactions) (A) $\mathrm{CH_3(CH_2)_5-C(=O)-OC_2H_5 \longrightarrow CH_3(CH_2)_5CHO}$ (B) $\mathrm{C_6H_5COC_6H_5 \rightarrow C_6H_5CH_2C_6H_5}$ (C) $\mathrm{C_6H_5CHO \rightarrow C_6H_5CH(OH)CH_3}$ (D)…
Aldehydes, Ketones and Carboxylic Acids Carboxylic Acids and Derivatives Reduction of Acids
MediumMatch the listIdea asked in 5 yearsAsked the year before
Q77
Given below are two statements : Statement (I) : The $\mathrm{NH_2}$ group in Aniline is ortho and para directing and a powerful activating group. Statement (II) : Aniline does not undergo Friedel-Craft's reaction (alkylation and acylation). In the light of…
Amines Aromatic Hydrocarbons Friedel-Crafts Failure with Aniline
EasyTwo statementsIdea asked in 2 years
Q78
Which of the following compound will most easily be attacked by an electrophile ?
Haloalkanes and Haloarenes Aromatic Hydrocarbons Ranking Activating Groups
EasyDiagram based · figureIdea asked in 3 yearsAsked the year before
Q79
If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary strand is :
Biomolecules
EasySingle correct
Q80
Given below are two statements : Statement (I) : Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution. Statement (II) : In this titration phenolphthalein can be used as indicator. In the light of the above…
Some Basic Concepts of Chemistry pH and Buffers Indicator Selection for Titrations
EasyTwo statementsIdea asked in 2 years
Q81
Consider the following reaction : $\mathrm{3PbCl_2 + 2(NH_4)_3PO_4 \rightarrow Pb_3(PO_4)_2 + 6NH_4Cl}$ If 72 mmol of $\mathrm{PbCl_2}$ is mixed with 50 mmol of $\mathrm{(NH_4)_3PO_4}$ , then the amount of $\mathrm{Pb_3(PO_4)_2}$ formed is ________ mmol…
Some Basic Concepts of Chemistry Mole Concept Limiting Reagent and Reaction Yield
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q82
The number of molecules/ion/s having trigonal bipyramidal shape is ________. $\mathrm{PF_5}$ , $\mathrm{BrF_5}$ , $\mathrm{PCl_5}$ , $\mathrm{[PtCl_4]^{2-}}$ , $\mathrm{BF_3}$ , $\mathrm{Fe(CO)_5}$
Chemical Bonding and Molecular Structure VSEPR Theory Trigonal Bipyramidal Positions
MediumNumerical valueIdea asked in 5 years
Q83
$\mathrm{K_a}$ for $\mathrm{CH_3COOH}$ is $1.8\times10^{-5}$ and $\mathrm{K_b}$ for $\mathrm{NH_4OH}$ is $1.8\times10^{-5}$ . The pH of ammonium acetate solution will be ________.
Equilibrium pH and Buffers pH of Weak Acid-Weak Base Salts
EasyNumerical valueIdea asked in 3 years
Q84
The lowest oxidation number of an atom in a compound $\mathrm{A_2B}$ is $-2$ . The number of electrons in its valence shell is ________.
Redox Reactions
EasyNumerical value
Q85
The potential for the given half cell at 298 K is $(-)$ ________ $\times 10^{-2}\,\mathrm{V}$ . $\mathrm{2H^+_{(aq)} + 2e^- \longrightarrow H_2(g)}$ $\mathrm{[H^+] = 1M,\ P_{H_2} = 2\ atm}$ (Given : $2.303RT/F = 0.06\ \mathrm{V}$ , $\log 2 = 0.3$ )
Electrochemistry Nernst Equation Nernst Equation for Gas Electrodes
MediumNumerical valueNew idea
Q86
The ratio of $\frac{^{14}\mathrm{C}}{^{12}\mathrm{C}}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of $^{14}\mathrm{C}$ is 5730 years, the age of wood sample is ________ years.
Chemical Kinetics Integrated Rate Equations First Order Half-Life
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q87
Among the following oxides of p-block elements, number of oxides having amphoteric nature is ________. $\mathrm{Cl_2O_7}$ , CO, $\mathrm{PbO_2}$ , $\mathrm{N_2O}$ , NO, $\mathrm{Al_2O_3}$ , $\mathrm{SiO_2}$ , $\mathrm{N_2O_5}$ , $\mathrm{SnO_2}$
The p-Block Elements Periodic Trends Acidic and Basic Character of Oxides
MediumNumerical valueIdea asked in 4 years
Q88
Total number of deactivating groups in aromatic electrophilic substitution reaction among the following is ________. $\mathrm{-C(=O)OCH_3}$ , $\mathrm{-NH-C(=O)-CH_3}$ , $\mathrm{-NH-CH_3}$ , $\mathrm{-C{\equiv}N}$ , $\mathrm{-OCH_3}$
Haloalkanes and Haloarenes Aromatic Hydrocarbons Ortho-Para vs Meta Directing
MediumNumerical value · figureIdea asked in 5 years
Q89
Number of optical isomers possible for 2-chlorobutane ________.
Organic Chemistry: Some Basic Principles and Techniques Stereoisomerism Chiral Centers
EasyNumerical valueIdea asked in 5 yearsAsked the year before
Q90
The number of white coloured salts, among the following is ________. (a) $\mathrm{SrSO_4}$ (b) $\mathrm{Mg(NH_4)PO_4}$ (c) $\mathrm{BaCrO_4}$ (d) $\mathrm{Mn(OH)_2}$ (e) $\mathrm{PbSO_4}$ (f) $\mathrm{PbCrO_4}$ (g) AgBr (h) $\mathrm{PbI_2}$ (i)…
The d- and f-Block Elements
MediumNumerical value

Maths30 questions

1 easy20 medium9 hard

Q1
Let $S=\{z\in\mathbb{C}:|z-1|=1$ and $(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2\sqrt{2}\}$ . Let $z_1, z_2\in S$ be such that $|z_1|=\max_{z\in S}|z|$ and $|z_2|=\min_{z\in S}|z|$ . Then $\left|\sqrt{2}z_1-z_2\right|^2$ equals :
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Modulus and Argument
HardSingle correctIdea asked in 5 yearsAsked the year before
Q2
Let $S=\{x\in\mathbb{R}:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\}$ . Then the number of elements in S is :
Complex Numbers and Quadratic Equations Quadratic Roots Exponential Reducible to Quadratic
MediumSingle correctIdea asked in 4 years
Q3
If $A=\begin{bmatrix}\sqrt{2}&1\\-1&\sqrt{2}\end{bmatrix}$ , $B=\begin{bmatrix}1&0\\1&1\end{bmatrix}$ , $C=ABA^T$ and $X=A^TC^2A$ , then $\det X$ is equal to :
Determinants Matrix Multiplication Determinant of Product
EasySingle correctIdea asked in 4 years
Q4
If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to :
Permutations and Combinations Distribution into Identical Groups (Stirling Numbers)
MediumSingle correctNew idea
Q5
If the system of equations $2x+3y-z=5$ $x+\alpha y+3z=-4$ $3x-y+\beta z=7$ has infinitely many solutions, then $13\alpha\beta$ is equal to __________.
Determinants Cramer's Rule Condition for Infinite Solutions
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q6
Let 3, a, b, c be in A.P. and 3, a $-$ 1, b+1, c+9 be in G.P. Then, the arithmetic mean of a, b and c is :
Sequences and Series AP and GP Conditions for Three Terms in AP or GP
MediumSingle correctIdea asked in 5 years
Q7
If $5f(x)+4f\left(\frac{1}{x}\right)=x^2-2,\ \forall\ x\neq0$ and $y=9x^2f(x)$ , then $y$ is strictly increasing in :
Application of Derivatives Monotonicity Finding Intervals
HardSingle correctIdea asked in 5 years
Q8
Let $f:\mathbb{R}\to\mathbb{R}$ be defined as : $f(x)=\begin{cases}\frac{a-b\cos 2x}{x^2} & ; x<0\\ x^2+cx+2 & ; 0\leq x\leq 1\\ 2x+1 & ; x>1\end{cases}$ If $f$ is continuous everywhere in $\mathbb{R}$ and m is the number of points where $f$ is NOT…
Continuity and Differentiability Finding Unknown Constants for Continuity
MediumSingle correctIdea asked in 3 years
Q9
The area enclosed by the curves $xy+4y=16$ and $x+y=6$ is equal to :
Application of Integrals Area Under Curves Area Between Curves
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q10
The value of the intergral $\int_0^{\pi/4}\frac{x\,dx}{\sin^4(2x)+\cos^4(2x)}$ equals :
Integrals Definite Integral Properties King's Property
HardSingle correctIdea asked in 6 yearsAsked the year before
Q11
Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx}=2x(x+y)^3-x(x+y)-1$ , $y(0)=1$ . Then, $\left(\frac{1}{\sqrt{2}}+y\left(\frac{1}{\sqrt{2}}\right)\right)^2$ equals :
Differential Equations Variable Separable Form Reducible to Separable
HardSingle correctIdea asked in 3 years
Q12
For $0<\theta<\pi/2$ , if the eccentricity of the hyperbola $x^2-y^2\mathrm{cosec}^2\theta=5$ is $\sqrt{7}$ times eccentricity of the ellipse $x^2\mathrm{cosec}^2\theta+y^2=5$ , then the value of $\theta$ is :
Conic Sections Ellipse Eccentricity Eccentricity calculation
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q13
Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a>b$ be an ellipse, whose eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latusrectum is $\sqrt{14}$ . Then the square of the eccentricity of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is :
Conic Sections Ellipse Eccentricity Length of Latus Rectum
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q14
Let $f:\mathbb{R}\to\mathbb{R}$ and $g:\mathbb{R}\to\mathbb{R}$ be defined as $f(x)=\begin{cases}\log_e x, & x>0\\ e^{-x}, & x\leq 0\end{cases}$ and $g(x)=\begin{cases}x, & x\geq 0\\ e^{x}, & x<0\end{cases}$ . Then, $gof:\mathbb{R}\to\mathbb{R}$ is :
Relations and Functions
MediumSingle correct
Q15
Let $C: x^2+y^2=4$ and $C': x^2+y^2-4\lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles C and C' intersect at two distinct points, is $\mathbb{R}-[a,b]$ , then the point $(8a+12, 16b-20)$ lies on the curve :
Conic Sections Circle Tangents Number of Common Tangents
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q16
If the shortest distance between the lines $\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and $\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1}$ is 1, then the sum of all possible values of $\lambda$ is :
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q17
A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls…
Probability Bayes' Theorem Implicit Equally Likely Priors
MediumSingle correctIdea asked in 2 years
Q18
Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is :
Statistics
MediumSingle correct
Q19
Let $\vec{a}=-5\hat{i}+\hat{j}-3\hat{k}$ , $\vec{b}=\hat{i}+2\hat{j}-4\hat{k}$ and $\vec{c}=\left(\left(\left(\vec{a}\times\vec{b}\right)\times\hat{i}\right)\times\hat{i}\right)\times\hat{i}$ . Then $\vec{c}\cdot\left(-\hat{i}+\hat{j}+\hat{k}\right)$ is equal…
Vector Algebra Triple Products VTP with Repeated Vectors
MediumSingle correctIdea asked in 2 years
Q20
If $\tan A=\frac{1}{\sqrt{x(x^2+x+1)}}$ , $\tan B=\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$ and $\tan C=\left(x^{-3}+x^{-2}+x^{-1}\right)^{1/2}$ , $0<A,B,C<\frac{\pi}{2}$ , then $A+B$ is equal to :
Inverse Trigonometric Functions Inverse Trig Identities Tan-1 Sum and Difference
MediumSingle correctIdea asked in 3 years
Q21
Let $A=\{1,2,3,\ldots,20\}$ . Let $R_1$ and $R_2$ two relation on A such that $R_1=\{(a,b): b$ is divisible by $a\}$ $R_2=\{(a,b): a$ is an integral multiple of $b\}$ . Then, number of elements in $R_1-R_2$ is equal to __________.
Relations and Functions Sets and Relations Counting Relations
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q22
Let $P=\{z\in\mathbb{C}:|z+2-3i|\leq1\}$ and $Q=\{z\in\mathbb{C}:z(1+i)+\bar{z}(1-i)\leq-8\}$ . Let in $P\cap Q$ , $|z-3+2i|$ be maximum and minimum at $z_1$ and $z_2$ respectively. If $|z_1|^2+2|z_2|^2=\alpha+\beta\sqrt{2}$ , where $\alpha,\beta$ are integers,…
Complex Numbers and Quadratic Equations Complex Numbers - Polar Form Polar Triangle Inequality Extrema
HardNumerical valueIdea asked in 5 years
Q23
If the Coefficient of $x^{30}$ in the expansion of $\left(1+\frac{1}{x}\right)^6(1+x^2)^7(1-x^3)^8$ ; $x\neq0$ is $\alpha$ , then $|\alpha|$ equals __________.
Binomial Theorem Binomial Coefficients Coefficient Extraction from Products
HardNumerical valueIdea asked in 2 years
Q24
The number of elements in the set $S=\{(x,y,z): x,y,z\in\mathbb{Z}, x+2y+3z=42, x,y,z\geq0\}$ equals __________.
Permutations and Combinations Distribution of Identical Objects
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q25
Let 3, 7, 11, 15, $\ldots$ , 403 and 2, 5, 8, 11, $\ldots$ , 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to __________.
Sequences and Series AP and GP Common Terms of Two APs
MediumNumerical valueIdea asked in 2 years
Q26
Let $\{x\}$ denote the fractional part of $x$ and $f(x)=\frac{\cos^{-1}(1-\{x\}^2)\sin^{-1}(1-\{x\})}{\{x\}-\{x\}^3}$ , $x\neq0$ . If L and R respectively denotes the left hand limit and the right hand limit of $f(x)$ at $x=0$ , then $\frac{32}{\pi^2}(L^2+R^2)$ …
Limits and Derivatives L'Hopital's Rule L'Hopital with Inverse Trigonometric Functions
HardNumerical valueIdea asked in 2 years
Q27
If $\int_{-\pi/2}^{\pi/2}\frac{8\sqrt{2}\cos x\,dx}{(1+e^{\sin x})(1+\sin^4 x)}=\alpha\pi+\beta\log_e(3+2\sqrt{2})$ , where $\alpha,\beta$ are integers, then $\alpha^2+\beta^2$ equals __________.
Integrals Definite Integral Properties Symmetric Limits with Exponential Denominator Trick
HardNumerical valueIdea asked in 5 years
Q28
If $x=x(t)$ is the solution of the differential equation $(t+1)dx=(2x+(t+1)^4)dt$ , $x(0)=2$ , then, $x(1)$ equals __________.
Differential Equations Linear Differential Equations Integrating Factor Calculation
MediumNumerical valueIdea asked in 7 yearsAsked the year before
Q29
Let the line $L:\sqrt{2}x+y=\alpha$ pass through the point of the intersection P (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola $x^2=2y$ . Let the line L touch two circles $C_1$ and $C_2$ of equal radius $2\sqrt{3}$ . If the centres $Q_1$ …
Conic Sections Circle Tangents Condition of tangency
HardNumerical valueIdea asked in 4 years
Q30
Let the line of the shortest distance between the lines $L_1:\vec{r}=(\hat{i}+2\hat{j}+3\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})$ and $L_2:\vec{r}=(4\hat{i}+5\hat{j}+6\hat{k})+\mu(\hat{i}+\hat{j}-\hat{k})$ intersect $L_1$ and $L_2$ at P and Q respectively.…
Three Dimensional Geometry Skew Lines Equation of Shortest Distance Line
MediumNumerical valueNew idea

Questions from the official paper published by NTA, answers from the final key. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026; see the other 2024 shifts.