JEE Main 2023 · April session

JEE Main 12 April 2023, Shift 1

89 questions (1 more dropped by NTA): 30 numerical-answer and 59 multiple choice. 21 were rated hard and 27 easy. Its hard-question count was the highest of the 12 2023 shifts Lumi analysed. The biggest chapter was Amines, with 3 questions.

Questions: 89; 1 dropped by NTA
Numerical answer: 30; 34% of the shift
Hard: 21; 24% of the shift
Chapters asked: 69; 10 questions with a figure

Key findings · 12 Apr 2023, Shift 1

1
21 hard questions (24%): the highest count of the 12 2023 shifts Lumi analysed. Across those shifts the hard share ran from 9% to 24%.
2
Maths was the hardest section, with 18 of 29 rated hard; Physics had the most easy questions (15 of 30).
3
20 questions tested a new idea, one no earlier year had asked: 29% of the 70 questions tagged to an idea.
4
40 came back from 2022: the same idea had been asked in the 2022 shifts Lumi analysed.
5
22 shared an idea with another 2023 shift (31% of tagged questions). Shifts in the same year can test the same idea in a new setting.
6
Biggest chapters: Current Electricity in Physics (2), Amines in Chemistry (3) and Three Dimensional Geometry in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 15Medium 14Hard 1

Top chapters

Chemistry

30 Q · 10 numerical

Easy 12Medium 16Hard 2

Top chapters

Maths

29 Q · 10 numerical

Easy 0Medium 11Hard 18

Top chapters

Question format

Single correct40 Q
Numerical value30 Q
Match the list5 Q
Two statements5 Q
Other4 Q
Assertion–reason4 Q
Diagram based1 Q

What each question asks you to do

Multi-step31 Q
Calculation28 Q
Conceptual16 Q
Recall8 Q
Application5 Q
Data or graph1 Q

Most common: Multi-step.

Against the other 2023 shifts

This shift next to the 11 other 2023 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
6 Apr, Shift 1	90	31%	11%	33%	30%	27%
6 Apr, Shift 2	89	33%	17%	34%	25%	20%
8 Apr, Shift 1	89	38%	9%	34%	29%	21%
8 Apr, Shift 2	89	42%	16%	34%	23%	30%
10 Apr, Shift 1	88	39%	9%	33%	12%	25%
10 Apr, Shift 2	90	38%	12%	33%	20%	21%
11 Apr, Shift 1	90	34%	16%	33%	25%	33%
11 Apr, Shift 2	88	24%	18%	34%	28%	39%
12 Apr, Shift 1	89	30%	24%	34%	29%	35%
13 Apr, Shift 1	89	24%	19%	34%	21%	37%
13 Apr, Shift 2	90	33%	13%	33%	35%	32%
15 Apr, Shift 1	90	43%	14%	33%	18%	30%

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
Open29 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 89 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

89 of 89 questions

Physics30 questions

15 easy14 medium1 hard

Q31
Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be
Gravitation Orbital Mechanics Orbital Velocity
EasySingle correctIdea asked in 5 yearsAsked the year before
Q32
Match List I with List II LIST I | LIST II A. Spring constant | I. $[T^{-1}]$ B. Angular speed | II. $[MT^{-2}]$ C. Angular momentum | III. $[ML^2]$ D. Moment of Inertia | IV. $[ML^2T^{-1}]$ Choose the correct answer from the options given below:
Units and Measurements
EasyMatch the list
Q33
Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance. Statement II : A car moving towards east takes a…
Work, Energy and Power Work and Kinetic Energy Stopping Distance of a Vehicle
MediumTwo statementsNew idea
Q34
The amplitude of 15 sin (1000 $\pi$ t) is modulated by 10 sin (4 $\pi$ t) signal. The amplitude modulated signal contains frequencies of A. 500 Hz B. 2 Hz C. 250 Hz D. 498 Hz E. 502 Hz Choose the correct answer from the options given below:
Communication Systems
MediumOther
Q35
Given below are two statements: Statement I : When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement II : In a series LCR circuit, the value of…
Alternating Current LCR Resonance Power Factor at Resonance
EasyTwo statementsIdea asked in 3 yearsAsked the year before
Q36
The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.
Gravitation Orbital Mechanics Escape Velocity
EasySingle correctIdea asked in 5 yearsAsked the year before
Q37
A body cools from $80^\circ$ C to $60^\circ$ C in 5 minutes. The temperature of the surrounding is $20^\circ$ C. The time it takes to cool from $60^\circ$ C to $40^\circ$ C is:
Thermal Properties of Matter Thermal Radiation Average Temperature Method for Newton's Law of Cooling
MediumSingle correctIdea asked in 2 years
Q38
An engine operating between the boiling and freezing points of water will have A. efficiency more than 27%. B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures. C. efficiency equal to 27% D. efficiency less…
Thermodynamics Heat Engines and Refrigerators Carnot Efficiency Limit
MediumOtherIdea asked in 3 yearsAsked the year before
Q39
If the r. m. s speed of chlorine molecule is 490 m/s at $27^\circ$ C, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon = 39.9 u, molecular mass of chlorine = 70.9 u)
Kinetic Theory Kinetic Theory of Gases Molecular Speed Types
EasySingle correctIdea asked in 3 yearsAsked the year before
Q40
A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
Oscillations Energy in SHM Fractional Energy Displacements
EasySingle correctIdea asked in 2 years
Q41
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : If an electric dipole of dipole moment $30\times10^{-5}$ C m is enclosed by a closed surface, the net flux coming out of the surface will be…
Electric Charges and Fields Electric Dipoles Electric Flux of an Enclosed Dipole
EasyAssertion–reasonNew idea
Q42
A wire of resistance 160 $\Omega$ is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will be
Current Electricity Ohm's Law and Resistance Resistance of Stretched Wires
EasySingle correctIdea asked in 4 yearsAsked the year before
Q43
Given below are two statements: Statement I : The diamagnetic property depends on temperature. Statement II : The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field. In the light of given statements, choose the…
Magnetism and Matter
EasyTwo statements
Q44
A ball is thrown vertically upward with an initial velocity of 150 m/s. The ratio of velocity after 3 s and 5 s is $\frac{x+1}{x}$ . The value of $x$ is ______. {take, g = 10 m/s $^2$ }
Motion in a Straight Line Kinematics in 1D Free Fall Sign Conventions
EasySingle correctIdea asked in 5 yearsAsked the year before
Q45
Three forces $F_1$ =10 N, $F_2$ =8 N, $F_3$ =6 N are acting on a particle of mass 5 kg. The forces $F_2$ and $F_3$ are applied perpendicularly so that particle remains at rest. If the force $F_1$ is removed, then the acceleration of the particle is:
Laws of Motion Newton's Laws of Motion Static Equilibrium
EasySingle correctIdea asked in 4 yearsAsked the year before
Q46
An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. When viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index…
Ray Optics and Optical Instruments Refraction and Snell's Law Apparent Depth and Shift
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q47
A proton and an $\alpha$ -particle are accelerated from rest by 2 V and 4 V potentials, respectively. The ratio of their de-Broglie wavelength is :
Dual Nature of Radiation and Matter Matter Waves Wavelength from Accelerating Potential
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q48
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:
Atoms Bohr's Atomic Model Number of Spectral Lines
MediumSingle correctIdea asked in 3 years
Q49
In an n-p-n common emitter (CE) transistor the collector current changes from 5 mA to 16 mA for the change in base current from 100 $\mu$ A and 200 $\mu$ A, respectively. The current gain of transistor is ________.
Semiconductor Electronics: Materials, Devices and Simple Circuits Transistors Current Gains Alpha and Beta
EasySingle correctIdea asked in 2 years
Q50
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason R : Infrared EM…
Electromagnetic Waves
EasyAssertion–reason
Q51
A compass needle oscillates 20 times per minute at a place where the dip is $30^\circ$ and 30 times per minute where the dip is $60^\circ$ . The ratio of total magnetic field due to the earth at two places respectively is $\frac{4}{\sqrt{x}}$ . The value of…
Magnetism and Matter Earth's Magnetism Magnetic Inclination (Dip)
HardNumerical valueIdea asked in 2 yearsAsked the year before
Q52
To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ________ KJ. [The coefficient of friction between tyre of bus and road is 0.04.]
Work, Energy and Power Work and Kinetic Energy Work Done by Friction
EasyNumerical valueNew ideaIdea asked in 3 years
Q53
For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$ . The value of $x$ is ______
System of Particles and Rotational Motion Moment of Inertia MOI of Standard Shapes
MediumNumerical valueIdea asked in 5 yearsAsked the year before
Q54
Glycerin of density $1.25\times10^3$ kg m $^{-3}$ is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends are 10 cm $^2$ and 5 cm $^2$ and pressure drop across its length is 3 Nm $^{-2}$ . The rate of flow of glycerin…
Mechanical Properties of Fluids Fluid Dynamics Venturi Meter Principles
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q55
For a certain organ pipe, the first three resonance frequencies are in the ratio of 1:3:5 respectively. If the frequency of fifth harmonic is 405 Hz and the speed of sound in air is 324 ms $^{-1}$ the length of the organ pipe is ______ m
Waves Resonance in Air Columns Closed Organ Pipe Harmonics
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q56
64 identical drops each charged upto potential of 10 mV are combined to form a bigger drop. The potential of the bigger drop will be _______ mV.
Electrostatic Potential and Capacitance Electric Potential Potential of a Spherical Shell
MediumNumerical valueIdea asked in 3 years
Q57
The current flowing through a conductor connected across a source is 2 A and 1.2 A at $0^\circ$ C and $100^\circ$ C respectively. The current flowing through the conductor at $50^\circ$ C will be __________ $\times10^2$ mA.
Current Electricity Ohm's Law and Resistance Temperature Coefficient of Resistance
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q58
A conducting circular loop is placed in a uniform magnetic field of 0.4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 mm/s. The magnitude of induced emf in the loop at an instant when…
Electromagnetic Induction Faraday's Law Faraday's Law Magnitude
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q59
Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at _______ cm from the first lens.
Ray Optics and Optical Instruments Lens Maker's Formula Lenses Separated by a Distance
MediumNumerical valueIdea asked in 6 years
Q60
A common example of alpha decay is $^{238}_{92}\mathrm{U} \longrightarrow\, ^{234}_{90}\mathrm{Th} + {}_{2}\mathrm{He}^{4} + Q$ Given : $^{238}_{92}\mathrm{U} = 238.05060\,\mathrm{u}$ , $^{234}_{90}\mathrm{Th} = 234.04360\,\mathrm{u}$ ,…
Nuclei Nuclear Binding Energy Q-Value Calculation
EasyNumerical valueIdea asked in 2 yearsAsked the year before

Chemistry30 questions

12 easy16 medium2 hard

Q61
A metal chloride contains 55.0% of chlorine by weight . 100 mL vapours of the metal chloride at STP weigh 0.57 g. The molecular formula of the metal chloride is (Given: Atomic mass of chlorine is 35.5u)
Some Basic Concepts of Chemistry Mole Concept Molecular Formula Determination
MediumSingle correctNew ideaIdea asked in 2 years
Q62
The bond order and magnetic property of acetylide ion are same as that of
Chemical Bonding and Molecular Structure Molecular Orbital Theory Isoelectronic Species Principle in MOT
MediumSingle correctNew idea
Q63
For lead storage battery pick the correct statements A. During charging of battery, $\mathrm{PbSO_4}$ on anode is converted into $\mathrm{PbO_2}$ B. During charging of battery, $\mathrm{PbSO_4}$ on cathode is converted into $\mathrm{PbO_2}$ C. Lead storage…
Electrochemistry
MediumOther
Q64
Four gases A, B, C and D have critical temperatures 5.3, 33.2, 126.0 and 154.3K respectively. For their adsorption on a fixed amount of charcoal, the correct order is:
Surface Chemistry Adsorption Critical Temperature and Extent of Adsorption
EasySingle correctIdea asked in 2 yearsAsked the year before
Q65
The density of alkali metals is in the order
The s-Block Elements Periodic Trends Density Anomaly in Alkali Metals (K vs Na)
EasySingle correctNew idea
Q66
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : In the Ellingham diagram, a sharp change in slope of the line is observed for $\mathrm{Mg \rightarrow MgO}$ at $\sim 1120\,^{\circ}\mathrm{C}$ …
General Principles and Processes of Isolation of Elements Metallurgical Extraction Ellingham Diagram Phase Transitions
MediumAssertion–reasonIdea asked in 2 yearsAsked the year before
Q67
Match List I with List II LIST I (Type of Hydride) / LIST II (Example) A. Electron deficient hydride - I. $\mathrm{MgH_2}$ B. Electron rich hydride - II. $\mathrm{HF}$ C. Electron precise hydride - III. $\mathrm{B_2H_6}$ D. Saline hydride - IV.…
Hydrogen Hydrogen and Hydrides Covalent Hydride Types
EasyMatch the listIdea asked in 2 yearsAsked the year before
Q68
In the given reaction cycle $\mathrm{CaCl_2 + Na_2CO_3 \longrightarrow \underline{X} + \underline{Y}}$ with an arrow from the underlined X back up to $\mathrm{CaCl_2}$ via a path labelled Z X, Y and Z respectively are
The s-Block Elements
EasyDiagram based · figure
Q69
Given below are two statements: Statement I : Boron is extremely hard indicating its high lattice energy Statement II : Boron has highest melting and boiling point compared to its other group members. In the light of the above statements, choose the most…
The p-Block Elements
EasyTwo statements
Q70
Given below are two statements: Statement I : $\mathrm{SbCl_5}$ is more covalent than $\mathrm{SbCl_3}$ Statement II: The higher oxides of halogens also tend to be more stable than the lower ones. In the light of the above statements, choose the most…
The p-Block Elements Periodic Trends Inert Pair Effect and Oxidation State Stability
MediumTwo statementsNew ideaIdea asked in 2 years
Q71
Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: 5f electrons can participate in bonding to a far greater extent than 4f electrons Reason R: 5f orbitals are not as buried as 4f orbitals In the…
The d- and f-Block Elements d-Block Elements Actinoid vs Lanthanoid Contraction
MediumAssertion–reasonNew idea
Q72
Match List I with List II LIST I (Complex) / LIST II (CFSE ( $\Delta_o$ )) A. $\mathrm{[Cu(NH_3)_6]^{2+}}$ - I. $-0.6$ B. $\mathrm{[Ti(H_2O)_6]^{3+}}$ - II. $-2.0$ C. $\mathrm{[Fe(CN)_6]^{3-}}$ - III. $-1.2$ D. $\mathrm{[NiF_6]^{4-}}$ - IV. $-0.4$ Choose the…
Coordination Compounds Crystal Field Theory CFSE Calculation
MediumMatch the listIdea asked in 6 yearsAsked the year before
Q73
Match List I with List II LIST I / LIST II A. Nitrogen oxides in air - I. Eutrophication B. Methane in air - II. pH of rain water becomes 5.6 C. Carbon dioxide - III. Global warming D. Phosphate fertilisers in water - IV. Acid rain Choose the correct answer…
Environmental Chemistry Acid Rain Mechanism
EasyMatch the listIdea asked in 4 yearsAsked the year before
Q74
Correct statements for the given reaction are : [figure: 'A' -> 'B' with OH $^-$ (2eq)] A. Compound 'B' is aromatic B. The completion of above reaction is very slow C. 'A' shows tautomerism D. The bond lengths of C-C in compound B are found to be same Choose…
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Huckel's Rule
MediumOther · figureIdea asked in 5 yearsAsked the year before
Q75
[figure: 2-hexene --(i) $\mathrm{O_3}$ , (ii) $\mathrm{H_2O}$ --> Products] The two products formed in above reaction are -
Hydrocarbons Alkenes and Alkynes Oxidative Ozonolysis
EasySingle correct · figureNew idea
Q76
In the following reaction [figure: CH3-C(=O)-CH2-CH(CH3)-Br, (i) Mg (ii) $\mathrm{H_2O}$ -> 'A' (Major Product)] A is
Haloalkanes and Haloarenes Nucleophilic Addition Grignard Reagent Addition
HardSingle correct · figureIdea asked in 4 yearsAsked the year before
Q77
[figure: $\mathrm{Me-C(=O)}$ -(zig-zag chain)- $\mathrm{C(=O)-CH_3}$ -- $\mathrm{OEt^-}$ , $\Delta$ --> 'A' major Product] A in the above reaction is:
Aldehydes, Ketones and Carboxylic Acids Aldol and Cannizzaro Intramolecular Aldol
MediumSingle correct · figureIdea asked in 5 yearsAsked the year before
Q78
The major product 'P' formed in the following sequence of reactions is [figure: $\mathrm{Ph-CH=CH-CH_2-C(=O)OH}$ --(i) $\mathrm{SOCl_2}$ , (ii) $\mathrm{R-NH_2}$ , (iii) $\mathrm{LiAlH_4}$ , (iv) $\mathrm{H_3O^+}$ --> 'P' (Major Product)]
Amines Carboxylic Acids and Derivatives Nucleophilic Acyl Substitution
MediumSingle correct · figureIdea asked in 4 yearsAsked the year before
Q79
The incorrect statement regarding the reaction given below is [figure: 'A' = N,N-dimethylaniline (benzene ring bearing $\mathrm{N(Me)Me}$ ) $+ \mathrm{NaNO_2 + HX} \longrightarrow$ 'B']
Amines Diazonium Salts Reaction of Tertiary Aryl Amines with HNO2
MediumSingle correct · figureNew idea
Q80
Match List I with List II LIST I (Examples) / LIST II (Type) A. 2-chloro-1,3- butadiene - I. Biodegradable polymer B. Nylon 2-nylon 6 - II. Synthetic Rubber C. Polyacrylonitrile - III. Polyester D. Dacron - IV. Addition Polymer Choose the correct answer from…
Polymers Polymer Classification
EasyMatch the listIdea asked in 3 yearsAsked the year before
Q81
At 600K, the root mean square (rms) speed of gas X (molar mass = 40) is equal to the most probable speed of gas Y at 90K. The molar mass of the gas Y is ______ g mol $^{-1}$ .(Nearest integer)
States of Matter Ideal Gas Laws Gas Molecular Velocity Ratios
EasyNumerical valueNew idea
Q82
Values of work function ( $W_0$ ) for a few metals are given below Metal: Li, Na, K, Mg, Cu, Ag $W_0$ /eV: 2.42, 2.3, 2.25, 3.7, 4.8, 4.3 The number of metals which will show photoelectric effect when light of wavelength 400nm falls on it is _______ Given: h =…
Structure of Atom Bohr's Atomic Theory Photoelectric Effect Coupling
EasyNumerical value · figureIdea asked in 3 years
Q83
One mole of an ideal gas at 350K is in a 2.0 L vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from 2.0L to 3.0L against a constant pressure of 4 atm. The change in entropy of the…
Thermodynamics (Chemistry)Entropy Entropy of Surroundings and Universe
MediumNumerical valueNew idea
Q84
80 mole percent of $\mathrm{MgCl_2}$ is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of $\mathrm{MgCl_2}$ at 38°C is ________ mm Hg. (Nearest integer) Given : Vapour pressure of water at 38°C is 50 mm Hg
Solutions Colligative Properties Van't Hoff Factor (i)
MediumNumerical valueIdea asked in 4 yearsAsked the year before
Q85
An analyst wants to convert 1L HCl of pH =1 to a solution of HCl of pH 2. The volume of water needed to do this dilution is _________ mL. (Nearest integer)
Equilibrium pH and Buffers pH of Strong Acids and Bases
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q86
The reaction $\mathrm{2NO + Br_2 \rightarrow 2NOBr}$ takes places through the mechanism given below: $\mathrm{NO + Br_2 \rightleftharpoons NOBr_2}$ (fast) $\mathrm{NOBr_2 + NO \rightarrow 2NOBr}$ (slow) The overall order of the reaction is _______.
Chemical Kinetics Rate Laws Rate Law from Rate-Determining Step
MediumNumerical valueNew idea
Q87
Three organic compounds A, B and C were allowed to run in thin layer chromatography using hexane and gave the following result (see figure). The $R_f$ value of the most polar compound is _______ $\times 10^{-2}$
Organic Chemistry: Some Basic Principles and Techniques
EasyNumerical value · figure
Q88
[figure: $\mathrm{H_5C_2O-C_6H_4-CH_2CHO}$ (para-substituted benzene) --(i) $\mathrm{NH_4Cl/KCN}$ , (ii) $\mathrm{H_2SO_4/H^+}$ --> 'A' --Conc. $\mathrm{HNO_3-H_2SO_4}$ (2eq)--> 'B' --(i) $\mathrm{(CH_3CO)_2O}$ , (ii) EtOH, $\Delta$ , (iii) $\mathrm{H_2}$ , Pd/C,…
Amines
HardNumerical value · figure
Q89
In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of sp $^2$ hybridised carbons is ________.
Biomolecules
MediumNumerical value
Q90
The mass of $\mathrm{NH_3}$ produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is _________kg. (Nearest Integer) Molar Mass of C = 12g/mol N = 14g/mol O = 16g/mol
Aldehydes, Ketones and Carboxylic Acids
MediumNumerical value

Maths29 questions

0 easy11 medium18 hard

Q2
Let $\alpha, \beta$ be the roots of the quadratic equation $x^2+\sqrt{6}x+3=0$ . Then $\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}$ is equal to
Complex Numbers and Quadratic Equations Quadratic Roots Newton's Sums
HardSingle correctIdea asked in 7 yearsAsked the year before
Q3
Let $A=\begin{bmatrix}1&\frac{1}{51}\\0&1\end{bmatrix}$ . If $B=\begin{bmatrix}1&2\\-1&-1\end{bmatrix}A\begin{bmatrix}-1&-2\\1&1\end{bmatrix}$ , then the sum of all the elements of the matrix $\sum_{n=1}^{50}B^n$ is equal to
Matrices Matrix Multiplication Powers of Square Matrices
HardSingle correctIdea asked in 6 yearsAsked the year before
Q4
The number of five digit numbers, greater than $40000$ and divisible by $5$ , which can be formed using the digits $0, 1, 3, 5, 7$ and $9$ without repetition, is equal to
Permutations and Combinations
MediumSingle correct
Q5
The sum, of the coefficients of the first $50$ terms in the binomial expansion of $(1-x)^{100}$ , is equal to
Binomial Theorem Binomial Coefficients Alternating Binomial Series
MediumSingle correctIdea asked in 2 years
Q6
If $\frac{1}{n+1}{}^{n}\mathrm{C}_{n}+\frac{1}{n}{}^{n}\mathrm{C}_{n-1}+\ldots+\frac{1}{2}{}^{n}\mathrm{C}_{1}+{}^{n}\mathrm{C}_{0}=\frac{1023}{10}$ then $n$ is equal to
Binomial Theorem Binomial Coefficients Integration Method for Sums
MediumSingle correctNew ideaIdea asked in 3 years
Q7
Let C be the circle in the complex plane with centre $z_0=\frac{1}{2}(1+3i)$ and radius $r=1$ . Let $z_1=1+i$ and the complex number $z_2$ be outside the circle C such that $|z_1-z_0||z_2-z_0|=1$ . If $z_0$ , $z_1$ and $z_2$ are collinear, then the smaller…
Complex Numbers and Quadratic Equations
HardSingle correct
Q8
Let $\langle a_n\rangle$ be a sequence such that $a_1+a_2+\ldots+a_n=\frac{n^2+3n}{(n+1)(n+2)}$ . If $28\sum_{k=1}^{10}\frac{1}{a_k}=p_1p_2p_3\cdots p_m$ , where $p_1, p_2,\ldots, p_m$ are the first m prime numbers, then m is equal to
Sequences and Series AP and GP Method of Differences for Telescoping Series
HardSingle correctIdea asked in 6 yearsAsked the year before
Q9
If the local maximum value of the function $f(x)=\left(\frac{\sqrt{3e}}{2\sin x}\right)^{\sin^2 x}$ , $x\in\left(0,\frac{\pi}{2}\right)$ , is $\frac{k}{e}$ , then $\left(\frac{k}{e}\right)^8+\frac{k^8}{e^5}+k^8$ is equal to
Application of Derivatives Maxima and Minima Extrema of Variable-Base Exponentials
HardSingle correctIdea asked in 2 years
Q10
The area of the region enclosed by the curve $y=x^3$ and its tangent at the point $(-1,-1)$ is
Application of Integrals Area Under Curves Area Between Cubic Curve and Tangent
MediumSingle correctNew idea
Q11
Let $y=y(x)$ , $y>0$ , be a solution curve of the differential equation $(1+x^2)\,dy=y(x-y)\,dx$ . If $y(0)=1$ and $y(2\sqrt{2})=\beta$ , then
Differential Equations Linear Differential Equations Integrating Factor Calculation
HardSingle correctIdea asked in 7 yearsAsked the year before
Q12
Let $P\left(\frac{2\sqrt{3}}{\sqrt{7}},\frac{6}{\sqrt{7}}\right)$ , Q, R and S be four points on the ellipse $9x^2+4y^2=36$ . Let PQ and RS be mutually perpendicular and pass through the origin. If $\frac{1}{(PQ)^2}+\frac{1}{(RS)^2}=\frac{p}{q}$ , where $p$ and…
Conic Sections
HardSingle correct
Q13
If the point $\left(\alpha,\frac{7\sqrt{3}}{3}\right)$ lies on the curve traced by the mid-points of the line segments of the lines $x\cos\theta+y\sin\theta=7$ , $\theta\in\left(0,\frac{\pi}{2}\right)$ between the co-ordinates axes, then $\alpha$ is equal to
Straight Lines Straight Line Distance Origin Distance to Intercept Form
MediumSingle correctNew ideaIdea asked in 2 years
Q14
Let the plane P: $4x-y+z=10$ be rotated by an angle $\frac{\pi}{2}$ about its line of intersection with the plane $x+y-z=4$ . If $\alpha$ is the distance of the point $(2,3,-4)$ from the new position of the plane P, then $35\alpha$ is equal to
Three Dimensional Geometry Planes in 3D Family of Planes Perpendicular to a Third Plane
HardSingle correctIdea asked in 3 yearsAsked the year before
Q15
Let the lines $l_1: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}$ and $l_2: 3x+2y+z-2=0=x-3y+2z-13$ be coplanar. If the point $P(a,b,c)$ on $l_1$ is nearest to the point $Q(-4,-3,2)$ , then $|a|+|b|+|c|$ is equal to
Three Dimensional Geometry Skew Lines Coplanarity Determinant Test
HardSingle correctIdea asked in 3 yearsAsked the year before
Q16
Let $a, b, c$ be three distinct real numbers, none equal to one. If the vectors $a\hat{i}+\hat{j}+\hat{k}$ , $\hat{i}+b\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}+c\hat{k}$ are coplanar, then $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is equal to
Vector Algebra Triple Products Solving for Unknown in Coplanarity
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q17
Let $\lambda\in\mathbb{Z}$ , $\vec{a}=\lambda\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=3\hat{i}-\hat{j}+2\hat{k}$ . Let $\vec{c}$ be a vector such that $(\vec{a}+\vec{b}+\vec{c})\times\vec{c}=\vec{0}$ , $\vec{a}\cdot\vec{c}=-17$ and $\vec{b}\cdot\vec{c}=-20$ . Then…
Vector Algebra Cross Product Condition for Parallel Vectors
HardSingle correctNew ideaIdea asked in 2 years
Q18
Two dice A and B are rolled. Let the numbers obtained on A and B be $\alpha$ and $\beta$ respectively. If the variance of $\alpha-\beta$ is $\frac{p}{q}$ , where $p$ and $q$ are co-prime, then the sum of the positive divisors of $p$ is equal to
Statistics
MediumSingle correct
Q19
In a triangle ABC, if $\cos A+2\cos B+\cos C=2$ and the lengths of the sides opposite to the angles A and C are $3$ and $7$ respectively, then $\cos A-\cos C$ is equal to
Trigonometric Functions Properties of Triangles Projection Rule
HardSingle correctNew idea
Q20
Among the two statements (S1) : $(p\Rightarrow q)\wedge(p\wedge(\sim q))$ is a contradiction and (S2) : $(p\wedge q)\vee((\sim p)\wedge q)\vee(p\wedge(\sim q))\vee((\sim p)\wedge(\sim q))$ is a tautology
Mathematical Reasoning
MediumSingle correct
Q21
The number of relations, on the set $\{1,2,3\}$ containing $(1,2)$ and $(2,3)$ , which are reflexive and transitive but not symmetric, is ____________.
Relations and Functions Sets and Relations Counting Relations
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q22
Let $D_k=\begin{vmatrix}1&2k&2k-1\\ n&n^2+n+2&n^2\\ n&n^2+n&n^2+n+2\end{vmatrix}$ . If $\sum_{k=1}^{n}D_k=96$ , then $n$ is equal to __________.
Determinants
HardNumerical value
Q23
Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?
Permutations and Combinations Principle of Inclusion-Exclusion in Counting
HardNumerical valueIdea asked in 3 yearsAsked the year before
Q24
Let the positive numbers $a_1, a_2, a_3, a_4$ and $a_5$ be in a G.P. Let their mean and variance be $\frac{31}{10}$ and $\frac{m}{n}$ respectively, where $m$ and $n$ are co-prime. If the mean of their reciprocals is $\frac{31}{40}$ and $a_3+a_4+a_5=14$ , then…
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
HardNumerical valueIdea asked in 7 yearsAsked the year before
Q25
Let $[x]$ be the greatest integer $\le x$ . Then the number of points in the interval $(-2,1)$ , where the function $f(x)=|[x]|+\sqrt{x-[x]}$ is discontinuous, is ________.
Continuity and Differentiability Continuity involving GIF and Fractional Part
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q26
If $\int_{-0.15}^{0.15}\left|100x^2-1\right|dx=\frac{k}{3000}$ , then $k$ is equal to _________.
Integrals Definite Integral Properties Interval Splitting
MediumNumerical valueNew ideaIdea asked in 2 years
Q27
Let $I(x)=\int\sqrt{\frac{x+7}{x}}\,dx$ and $I(9)=12+7\log_e 7$ . If $I(1)=\alpha+7\log_e(1+2\sqrt{2})$ , then $\alpha^4$ is equal to _________.
Integrals Integration by Substitution Fractional Powers LCM Substitution
HardNumerical valueIdea asked in 4 years
Q28
Two circles in the first quadrant of radii $r_1$ and $r_2$ touch the coordinate axes. Each of them cuts off an intercept of $2$ units with the line $x+y=2$ . Then $r_1^2+r_2^2-r_1r_2$ is equal to__________.
Conic Sections
HardNumerical value
Q29
Let the plane $x+3y-2z+6=0$ meet the co-ordinate axes at the points A, B, C. If the orthocenter of the triangle ABC is $\left(\alpha,\beta,\frac{6}{7}\right)$ , then $98(\alpha+\beta)^2$ is equal to _______.
Three Dimensional Geometry
HardNumerical value
Q30
A fair $n$ $(n>1)$ faces die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$ , then $n$ is equal to _______.
Probability Conditional Probability Conditional Probability in Infinite Games
MediumNumerical valueNew ideaIdea asked in 2 years

Dropped from the final key and left out of every count: Q1.

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 2023 shifts.