JEE Main 2022 · June session

JEE Main 27 June 2022, Shift 2

90 questions: 30 numerical-answer and 60 multiple choice. 15 were rated hard and 29 easy. Its hard-question count was the joint 2nd highest of the 24 2022 shifts Lumi analysed. The biggest chapter was Determinants, with 3 questions.

Questions: 90; none dropped
Numerical answer: 30; 33% of the shift
Hard: 15; 17% of the shift
Chapters asked: 69; 16 questions with a figure

Key findings · 27 Jun 2022, Shift 2

1
15 hard questions (17%): the joint 2nd highest count of the 24 2022 shifts Lumi analysed. Across those shifts the hard share ran from 8% to 22%.
2
Maths was the hardest section, with 11 of 30 rated hard; Physics had the most easy questions (14 of 30).
3
25 questions tested a new idea, one no earlier year had asked: 34% of the 74 questions tagged to an idea.
4
39 came back from 2021: the same idea had been asked in the 2021 shifts Lumi analysed.
5
43 shared an idea with another 2022 shift (58% 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), Chemical Bonding and Molecular Structure in Chemistry (2) and Determinants in Maths (3).

The shift at a glance

Subjects, difficulty and chapters

Physics

30 Q · 10 numerical

Easy 14Medium 13Hard 3

Top chapters

Chemistry

30 Q · 10 numerical

Easy 14Medium 15Hard 1

Top chapters

Maths

30 Q · 10 numerical

Easy 1Medium 18Hard 11

Top chapters

Determinants3 Q
Complex Numbers and Quadratic Equations2 Q
Conic Sections2 Q
Differential Equations2 Q
Integrals2 Q
Probability2 Q

Question format

Single correct44 Q
Numerical value30 Q
Diagram based5 Q
Two statements4 Q
Other3 Q
Match the list3 Q
Assertion–reason1 Q

What each question asks you to do

Multi-step41 Q
Calculation15 Q
Recall12 Q
Conceptual12 Q
Application7 Q
Data or graph3 Q

Most common: Multi-step.

Against the other 2022 shifts

This shift next to the 23 other 2022 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
24 Jun, Shift 1	89	29%	17%	34%	31%	37%
24 Jun, Shift 2	90	40%	14%	33%	39%	36%
25 Jun, Shift 1	90	44%	13%	33%	33%	30%
25 Jun, Shift 2	90	30%	13%	33%	34%	22%
26 Jun, Shift 1	89	34%	16%	34%	37%	32%
26 Jun, Shift 2	90	30%	13%	33%	36%	27%
27 Jun, Shift 1	90	34%	8%	33%	38%	31%
27 Jun, Shift 2	90	32%	17%	33%	34%	46%
28 Jun, Shift 1	90	32%	12%	33%	38%	27%
28 Jun, Shift 2	90	30%	17%	33%	33%	31%
29 Jun, Shift 1	90	41%	11%	33%	36%	30%
29 Jun, Shift 2	88	35%	9%	33%	41%	30%
30 Jun, Shift 1	90	36%	13%	33%	27%	27%
25 Jul, Shift 1	88	28%	15%	33%	38%	38%
25 Jul, Shift 2	90	37%	12%	33%	33%	33%
26 Jul, Shift 1	90	27%	13%	33%	34%	31%
26 Jul, Shift 2	89	37%	16%	34%	41%	38%
27 Jul, Shift 1	89	29%	15%	34%	30%	32%
27 Jul, Shift 2	88	19%	15%	33%	40%	35%
28 Jul, Shift 1	90	36%	17%	33%	36%	30%
28 Jul, Shift 2	90	28%	14%	33%	40%	28%
29 Jul, Shift 1	90	31%	22%	33%	41%	37%
29 Jul, Shift 2	90	39%	12%	33%	48%	32%
30 Jul, Shift 2	90	30%	17%	33%	36%	33%

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

14 easy13 medium3 hard

Q31
The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :
Units and Measurements Viscosity Units and Dimensions of Viscosity
EasySingle correctIdea asked in 2 yearsAsked the year before
Q32
The distance of the Sun from earth is $1.5 \times 10^{11}$ m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :
Units and Measurements
EasySingle correct
Q33
When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity $v$ and then sinks to the bottom with the constant velocity $v$ . It reaches the bottom of the lake 4.0 s after it is dropped. The approximate…
Motion in a Straight Line Kinematics in 1D Free Fall Sign Conventions
EasySingle correctIdea asked in 5 years
Q34
One end of a massless spring of spring constant $k$ and natural length $l_0$ is fixed while the other end is connected to a small object of mass $m$ lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at…
Laws of Motion Circular Motion Spring-Mass in Circular Motion
EasySingle correctIdea asked in 3 years
Q35
A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$ . The magnitude of change in its velocity, as it reaches…
Work, Energy and Power Circular Motion Vertical Circular Motion
MediumSingle correctIdea asked in 2 yearsAsked the year before
Q36
Four spheres each of mass $m$ form $a$ square of side $d$ (as shown in figure). A fifth sphere of mass $M$ is situated at the centre of square. The total gravitational potential energy of the system is :
Gravitation Gravitational Potential Potential Energy of Systems
MediumSingle correct · figureIdea asked in 2 yearsAsked the year before
Q37
For a perfect gas, two pressures P $_1$ and P $_2$ are shown in figure. The graph shows :
Kinetic Theory Thermodynamic Processes Isobaric Process Analysis
EasyDiagram based · figureNew ideaIdea asked in 3 years
Q38
According to kinetic theory of gases, A. The motion of the gas molecules freezes at 0°C. B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased…
Kinetic Theory Kinetic Theory of Gases Mean Free Path
MediumOtherIdea asked in 4 yearsAsked the year before
Q39
A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is : (Given, initial temperature of the bullet = 127°C, Melting point of the bullet = 327°C, Latent heat of fusion…
Thermal Properties of Matter Calorimetry Bullet Impact Melting
MediumSingle correctNew idea
Q40
The equation of a particle executing simple harmonic motion is given by $x = \sin \pi\left(t + \frac{1}{3}\right)$ m. At $t$ = 1s, the speed of particle will be (Given: $\pi$ = 3.14) -
Oscillations SHM Equations Velocity and Accel vs Time
EasySingle correctIdea asked in 4 years
Q41
If a charge $q$ is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :
Electric Charges and Fields Gauss's Law Flux Through a Hemisphere
MediumSingle correct · figureNew idea
Q42
Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m. The ratio of net force on a charged ball to the force between any two charged…
Electric Charges and Fields Coulomb's Law Superposition of Forces
EasySingle correct · figureIdea asked in 3 yearsAsked the year before
Q43
Two long parallel conductors S $_1$ and S $_2$ are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along $x$ – axis in X-Y plane. There is a point P located between the conductors (as shown in figure). A…
Moving Charges and Magnetism Biot-Savart Law Superposition of magnetic fields
HardSingle correct · figureIdea asked in 4 years
Q44
If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?
Alternating Current Inductance Dimensional Analysis of Inductance
EasySingle correctNew idea
Q45
Given below are two statements : Statement I: A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves. Statement II: In a material medium, the EM wave travels with…
Electromagnetic Waves
EasyTwo statements
Q46
A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.
Ray Optics and Optical Instruments Lens Maker's Formula Cutting a Thin Lens
MediumSingle correct · figureNew ideaIdea asked in 2 years
Q47
If a wave gets refracted into a denser medium, then which of the following is true?
Wave Optics Refraction and Snell's Law Invariance of Frequency in Refraction
EasySingle correctNew ideaIdea asked in 2 years
Q48
Given below are two statements: Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E $_1$ ) to higher energy orbit (E $_2$ ), is given as $hf = E_1 - E_2$ Statement II: The jumping of electron from…
Atoms Bohr's Atomic Model Energy Level Calculations
EasyTwo statementsIdea asked in 6 yearsAsked the year before
Q49
For a transistor to act as a switch, it must be operated in
Semiconductor Electronics: Materials, Devices and Simple Circuits Transistors Transistor as a Switch
EasySingle correctNew idea
Q50
We do not transmit low frequency signal to long distances because- (a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength. (b) Effective power radiated by a long wavelength baseband…
Communication Systems
MediumOther
Q51
A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta = \tan^{-1}(x \times 10^{-1})$ .…
Laws of Motion Newton's Laws of Motion Equilibrium of a String Junction (Knot)
MediumNumerical valueNew ideaIdea asked in 2 years
Q52
A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches…
System of Particles and Rotational Motion Work and Kinetic Energy Conservation of Mechanical Energy
HardNumerical value · figureIdea asked in 4 yearsAsked the year before
Q53
A diatomic gas ( $\gamma$ = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.
Thermodynamics First Law of Thermodynamics Heat in Isochoric and Isobaric Processes
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q54
A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ___________ s.
Oscillations SHM Equations Standard Time Fractions in SHM
MediumNumerical valueNew idea
Q55
A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $\frac{x}{15}\frac{\epsilon_0 A}{b}$ , The value of…
Electrostatic Potential and Capacitance Parallel Plate Capacitors Series and Parallel Combinations
HardNumerical value · figureIdea asked in 6 yearsAsked the year before
Q56
The current density in a cylindrical wire of radius $r$ = 4.0 mm is $1.0 \times 10^{6}$ A/m $^2$ . The current through the outer portion of the wire between radial distances $\frac{r}{2}$ and $r$ is $x\pi$ A; where $x$ is ________.
Current Electricity Ohm's Law and Resistance Integrating Non-Uniform Current Density
MediumNumerical valueNew idea
Q57
In the given circuit 'a' is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum, will be $\sqrt{\frac{x}{2}}$ . The value of $x$ is ______.
Current Electricity
MediumNumerical value · figure
Q58
A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If $r_d$ and $r_p$ are the radii of their circular paths respectively, then the ratio $\frac{r_d}{r_p}$ will be $\sqrt{x}:1$ where…
Moving Charges and Magnetism Lorentz Force Trajectory Radii Ratio for Same Kinetic Energy
EasyNumerical valueIdea asked in 3 yearsAsked the year before
Q59
A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth’s magnetic field at that place is $4 \times 10^{-3}$ T and the angle of dip is 45°. The emf…
Electromagnetic Induction Faraday's Law Linear Motional EMF
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q60
The cut-off voltage of the diodes (shown in figure) in forward bias is 0.6 V. The current through the resister of 40 $\Omega$ is ________ mA.
Semiconductor Electronics: Materials, Devices and Simple Circuits Semiconductor Diodes Ideal vs. Practical Diode Circuit Analysis
MediumNumerical value · figureIdea asked in 7 yearsAsked the year before

Chemistry30 questions

14 easy15 medium1 hard

Q61
Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas?
States of Matter Ideal Gas Laws Gas Density and Molar Mass
EasyDiagram based · figureIdea asked in 2 yearsAsked the year before
Q62
Identify the **incorrect** statement for $\mathrm{PCl_5}$ from the following.
Chemical Bonding and Molecular Structure VSEPR Theory Trigonal Bipyramidal Positions
EasySingle correctIdea asked in 5 yearsAsked the year before
Q63
**Statement I:** Leaching of gold with cyanide ion in absence of air / $\mathrm{O_2}$ leads to cyano complex of Au(III). **Statement II:** Zinc is oxidized during the displacement reaction carried out for gold extraction. In the light of the above…
General Principles and Processes of Isolation of Elements Metallurgical Extraction MacArthur-Forrest Cyanide Process
MediumTwo statementsIdea asked in 2 yearsAsked the year before
Q64
The correct order of increasing intermolecular hydrogen bond strength is
Chemical Bonding and Molecular Structure
MediumSingle correct
Q65
The correct order of increasing ionic radii is
Classification of Elements and Periodicity in Properties Periodic Trends Isoelectronic Species Radii Comparison
EasySingle correctIdea asked in 5 yearsAsked the year before
Q66
The gas produced by treating an aqueous solution of ammonium chloride with sodium nitrite is
The p-Block Elements Group 15 & 16 Preparation of Dinitrogen
EasySingle correctIdea asked in 2 years
Q67
Given below are two statements: one is labelled as **Assertion A** and the other is labelled as **Reason R**. **Assertion A:** Flourine forms one oxoacid. **Reason R:** Flourine has smallest size amongst all halogens and is highly electronegative. In the…
The p-Block Elements Group 17 & 18 Anomalous Properties of Fluorine
EasyAssertion–reasonNew ideaIdea asked in 2 years
Q68
In 3d series, the metal having the highest $\mathrm{M^{2+}/M}$ standard electrode potential is
The d- and f-Block Elements d-Block Elements Standard Electrode Potential Trends
EasySingle correctIdea asked in 3 yearsAsked the year before
Q69
The 'f' orbitals are half and completely filled, respectively in lanthanide ions [Given : Atomic no. Eu, 63; Sm, 62; Tm, 69; Tb, 65; Yb, 70; Dy, 66]
The d- and f-Block Elements f-Block Elements Lanthanide Electronic Configuration
MediumSingle correctIdea asked in 5 yearsAsked the year before
Q70
Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers: Mn = 25; Fe = 26) A. $\mathrm{[FeF_6]^{3-}}$ B. $\mathrm{[Fe(CN)_6]^{3-}}$ C. $\mathrm{[MnCl_6]^{3-}}$ (high spin) D. $\mathrm{[Mn(CN)_6]^{3-}}$ Choose…
Coordination Compounds Crystal Field Theory Spin-only Magnetic Moment
MediumOtherIdea asked in 7 yearsAsked the year before
Q71
On the surface of polar stratospheric clouds, hydrolysis of chlorine nitrate gives A and B while its reaction with HCl produces B and C. A, B and C are, respectively
Environmental Chemistry Role of Polar Stratospheric Clouds (PSCs)
MediumSingle correctNew idea
Q72
Which of the following is most stable?
Organic Chemistry: Some Basic Principles and Techniques Resonance and Hyperconjugation Huckel's Rule
MediumDiagram based · figureIdea asked in 5 yearsAsked the year before
Q73
What will be the major product of following sequence of reactions? $\mathrm{n-Bu-}$ [drawn: terminal triple bond] $\xrightarrow[\text{(ii) Lindlar cat, H}_2]{\text{(i) n-BuLi, n-C}_5\text{H}_{11}\text{Cl}}$
Hydrocarbons Alkenes and Alkynes Alkylation of Terminal Alkynes
MediumDiagram based · figureIdea asked in 2 years
Q74
Product 'A' of following sequence of reactions is Ethylbenzene $\xrightarrow[\text{(b) Cl}_2\text{, }\Delta]{\text{(a) Br}_2\text{, Fe}}$ 'A' (c) alc. KOH Major Product
Haloalkanes and Haloarenes Aromatic Hydrocarbons Role of Lewis Acids in Halogenation
MediumDiagram based · figureNew idea
Q75
Match List I with List II. List I | List II A. [drawn: benzene ring bearing OH $\rightarrow$ benzene ring bearing OH and, on a neighbouring ring carbon, CHO] | I. $\mathrm{Br_2}$ in $\mathrm{CS_2}$ B. [drawn: benzene ring bearing OH $\rightarrow$ plain…
Alcohols, Phenols and Ethers Alcohols and Phenols Reimer-Tiemann Reaction
MediumMatch the list · figureIdea asked in 4 yearsAsked the year before
Q76
Decarboxylation of all six possible forms of diaminobenzoic acids $\mathrm{C_6H_3(NH_2)_2COOH}$ yields three products A, B and C. Three acids give a product 'A', two acids gives a product 'B' and one acid give a product 'C'. The melting point of product 'C' is
Amines
HardSingle correct
Q77
Which is true about Buna-N?
Polymers Buna-N Monomers and Properties
EasySingle correctNew idea
Q78
Given below are two statements. Statement I: Maltose has two $\alpha$ -D-glucose units linked at $\mathrm{C_1}$ and $\mathrm{C_4}$ and is a reducing sugar. Statement II: Maltose has two monosaccharides: $\alpha$ -D-glucose and $\beta$ -D-glucose linked at…
Biomolecules Carbohydrates Maltose Structure and Linkage
EasyTwo statementsIdea asked in 3 yearsAsked the year before
Q79
Match List I with List II. List I | List II A. Antipyretic | I. Reduces pain B. Analgesic | II. Reduces stress C. Tranquilizer | III. Reduces fever D. Antacid | IV. Reduces acidity(stomach) Choose the correct answer from the options given below:
Chemistry in Everyday Life Mechanism and Dual Use of Aspirin
EasyMatch the listNew idea
Q80
Match List I with List II. List I (Anion) | List II (gas evolved on reaction with dil. $\mathrm{H_2SO_4}$ ) A. $\mathrm{CO_3^{2-}}$ | I. Colourless gas which turns lead acetate paper black. B. $\mathrm{S^{2-}}$ | II. Colourless gas which turns acidified…
Practical Chemistry (Qualitative Analysis)Anion Analysis Dilute Acid Group Identification
MediumMatch the listNew idea
Q81
116 g of a substance upon dissociation reaction, yields 7.5 g of hydrogen, 60 g of oxygen and 48.5 g of carbon. Given that the atomic masses of H, O and C are 1, 16 and 12, respectively. The data agrees with how many formulae of the following ? ________. A.…
Some Basic Concepts of Chemistry Mole Concept Empirical Formula from Mass Percentage
MediumNumerical valueIdea asked in 3 years
Q82
Consider the following set of quantum numbers. n l $\mathrm{m_l}$ A. 3 3 $-3$ B. 3 2 $-2$ C. 2 1 $+1$ D. 2 2 $+2$ The number of correct sets of quantum numbers is ________.
Structure of Atom Quantum Numbers Validity of Quantum Number Sets
EasyNumerical valueNew idea
Q83
BeO reacts with HF in presence of ammonia to give [A] which on thermal decomposition produces [B] and ammonium fluoride. Oxidation state of Be in [A] is ______
The s-Block Elements
MediumNumerical value
Q84
When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20 litre, the magnitude of the maximum work obtained is ________J. [nearest integer](Given : R = 8.3 J $\mathrm{K^{-1}mol^{-1}}$ and log 2 = 0.3010)
Thermodynamics (Chemistry)First Law of Thermodynamics Work and Heat in Isothermal Processes
EasyNumerical valueNew ideaIdea asked in 3 years
Q85
A solution containing $2.5 \times 10^{-3}$ kg of a solute dissolved in $75 \times 10^{-3}$ kg of water boils at 373.535 K. The molar mass of the solute is ________ $\mathrm{g\ mol^{-1}}$ . [nearest integer] (Given : $\mathrm{K_b(H_2O)}$ = 0.52 K kg…
Solutions Colligative Properties Boiling Point Elevation
EasyNumerical valueIdea asked in 6 yearsAsked the year before
Q86
pH value of 0.001 M NaOH solution is ________.
Equilibrium pH and Buffers pH of Strong Acids and Bases
EasyNumerical valueIdea asked in 4 yearsAsked the year before
Q87
For the reaction taking place in the cell: $\mathrm{Pt(s)|H_2(g)|H^{+}(aq)\,||\,Ag^{+}(aq)|Ag(s)}$ $\mathrm{E^\circ_{cell}}$ = + 0.5332 V. The value of $\Delta_f G^{\ominus}$ is __________ $\mathrm{kJ\ mol^{-1}}$ . (in nearest integer)
Electrochemistry Nernst Equation Gibbs Energy and EMF
MediumNumerical valueIdea asked in 3 years
Q88
It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be __________ $\mathrm{kJ\ mol^{-1}}$ . [nearest integer]…
Chemical Kinetics Arrhenius Equation Activation Energy Calculation
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q89
[figure: graph with vertical axis $\log\frac{x}{m}$ (arrow pointing up) and horizontal axis $\log p$ (arrow pointing right); a straight line rising to the right, partly dashed towards the vertical axis, with a small right triangle marked 'slope = 1'; the…
Surface Chemistry Adsorption Freundlich Logarithmic Plot
MediumNumerical value · figureIdea asked in 4 yearsAsked the year before
Q90
0.25 g of an organic compound containing chlorine gave 0.40 g of silver chloride in Carius estimation. The percentage of chlorine present in the compound is __________. [in nearest integer] (Given: Molar mass of Ag is 108 g $\mathrm{mol^{-1}}$ and that of Cl…
Organic Chemistry: Some Basic Principles and Techniques
EasyNumerical value

Maths30 questions

1 easy18 medium11 hard

Q1
The number of points of intersection of $|z-(4+3i)|=2$ and $|z|+|z-4|=6$ , $z\in\mathbb{C}$ , is
Complex Numbers and Quadratic Equations
MediumSingle correct
Q2
Let $f(x)=\begin{vmatrix} a & -1 & 0\\ ax & a & -1\\ ax^2 & ax & a\end{vmatrix}$ , $a\in\mathbb{R}$ . Then the sum of the squares of all the values of $a$ , for which $2f'(10)-f'(5)+100=0$ , is
Determinants
MediumSingle correct
Q3
Let for some real numbers $\alpha$ and $\beta$ , $a=\alpha-i\beta$ . If the system of equations $4ix+(1+i)y=0$ and $8\left(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\right)x+\bar{a}y=0$ has more than one solution, then $\frac{\alpha}{\beta}$ is equal to
Determinants Cramer's Rule Complex Coefficients in Cramer's Rule
MediumSingle correctNew idea
Q4
Let $A$ and $B$ be two $3\times3$ matrices such that $AB=I$ and $|A|=\frac{1}{8}$ . Then $|adj\,(B\,adj(2A))|$ is equal to
Determinants Matrix Inverse Determinant of Adjoint of Inverse
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q5
Let $S=2+\frac{6}{7}+\frac{12}{7^2}+\frac{20}{7^3}+\frac{30}{7^4}+\dots..$ Then $4S$ is equal to
Sequences and Series Arithmetico-Geometric Series Second-Order AGP Summation
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q6
If $a_1, a_2, a_3\,......$ and $b_1, b_2, b_3......$ are A.P., and $a_1=2,\ a_{10}=3,\ a_1b_1=1=a_{10}b_{10}$ , then $a_4\,b_4$ is equal to -
Sequences and Series AP and GP AP General Term
MediumSingle correctIdea asked in 4 yearsAsked the year before
Q7
If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $f(x)=\int_0^{x^2}\frac{t^2-5t+4}{2+e^t}\,dt$ , then the ordered pair $(m, n)$ is equal to
Application of Derivatives Maxima and Minima Extrema of Integral Functions
MediumSingle correctIdea asked in 2 years
Q8
Let $f$ be a differentiable function in $\left(0,\frac{\pi}{2}\right)$ . If $\int_{\cos x}^{1}t^2f(t)\,dt=\sin^3x+\cos x$ , then $\frac{1}{\sqrt{3}}f'\left(\frac{1}{\sqrt{3}}\right)$ is equal to
Integrals Leibniz Rule Variable Limit Leibniz
MediumSingle correctNew idea
Q9
The integral $\int_0^1\frac{1}{7^{\left[\frac{1}{x}\right]}}\,dx$ , where $[\cdot]$ denotes the greatest integer function, is equal to
Integrals Definite Integral Properties Greatest Integer Function Integrals
HardSingle correctIdea asked in 7 yearsAsked the year before
Q10
If the solution curve of the differential equation $((\tan^{-1}y)-x)\,dy=(1+y^2)\,dx$ passes through the point $(1, 0)$ , then the abscissa of the point on the curve whose ordinate is $\tan(1)$ , is
Differential Equations Linear Differential Equations Change of Independent Variable to form LDE
MediumSingle correctNew idea
Q11
If the equation of the parabola, whose vertex is at $(5, 4)$ and the directrix is $3x+y-29=0$ , is $x^2+ay^2+bxy+cx+dy+k=0$ , then $a+b+c+d+k$ is equal to
Conic Sections General Conic Section Focus-Directrix Form Extraction
MediumSingle correctIdea asked in 3 yearsAsked the year before
Q12
The set of values of $k$ , for which the circle $C: 4x^2+4y^2-12x+8y+k=0$ lies inside the fourth quadrant and the point $\left(1,-\frac{1}{3}\right)$ lies on or inside the circle $C$ , is
Conic Sections
MediumSingle correct
Q13
Let the foot of the perpendicular from the point $(1, 2, 4)$ on the line $\frac{x+2}{4}=\frac{y-1}{2}=\frac{z+1}{3}$ be $P$ . Then the distance of $P$ from the plane $3x+4y+12z+23=0$ is
Three Dimensional Geometry Lines in 3D Foot of the Perpendicular
MediumSingle correctIdea asked in 6 yearsAsked the year before
Q14
The shortest distance between the lines $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1}$ and $\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}$ , is
Three Dimensional Geometry Skew Lines Cartesian Shortest Distance
MediumSingle correctIdea asked in 6 years
Q15
Let $\vec{a}$ and $\vec{b}$ be the vectors along the diagonals of a parallelogram having area $2\sqrt{2}$ . Let the angle between $\vec{a}$ and $\vec{b}$ be acute, $|\vec{a}|=1$ , and $|\vec{a}\cdot\vec{b}|=|\vec{a}\times\vec{b}|$ . If…
Vector Algebra Cross Product Area of Quadrilateral via Diagonals
HardSingle correctNew ideaIdea asked in 3 years
Q16
The mean and variance of the data $4, 5, 6, 6, 7, 8, x, y$ , where $x<y$ , are $6$ and $\frac{9}{4}$ respectively. Then $x^4+y^2$ is equal to
Statistics Variance and SD Finding Unknown Observations from Mean and Variance
MediumSingle correctIdea asked in 7 yearsAsked the year before
Q17
If a point $A(x, y)$ lies in the region bounded by the $y$ -axis, straight lines $2y+x=6$ and $5x-6y=30$ , then the probability that $y<1$ is
Probability
MediumSingle correct
Q18
The value of $\cot\left(\sum_{n=1}^{50}\tan^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is
Inverse Trigonometric Functions Inverse Trig Identities Telescoping cot^-1 Quadratic Trick
MediumSingle correctNew idea
Q19
$\alpha=\sin 36^\circ$ is a root of which of the following equation?
Trigonometric Functions Trigonometric Identities Values of Non-Standard Specific Angles
HardSingle correctIdea asked in 3 yearsAsked the year before
Q20
Which of the following statement is a tautology ?
Mathematical Reasoning
EasySingle correct
Q21
Let $S=\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ . Define $f: S\to S$ as $f(n)=\begin{cases}2n, & \text{if } n=1,2,3,4,5\\ 2n-11, & \text{if } n=6,7,8,9,10\end{cases}$ Let $g: S\to S$ be a function such that…
Relations and Functions
HardNumerical value
Q22
Let $\alpha, \beta$ be the roots of the equation $x^2-4\lambda x+5=0$ and $\alpha, \gamma$ be the roots of the equation $x^2-\left(3\sqrt{2}+2\sqrt{3}\right)x+7+3\lambda\sqrt{3}=0$ , $\lambda>0$ . If $\beta+\gamma=3\sqrt{2}$ , then $(\alpha+2\beta+\gamma)^2$ is…
Complex Numbers and Quadratic Equations Quadratic Roots Symmetric Functions
HardNumerical valueIdea asked in 5 yearsAsked the year before
Q23
Let $A$ be a matrix of order $2\times2$ , whose entries are from the set $\{0, 1, 2, 3, 4, 5\}$ . If the sum of all the entries of $A$ is a prime number $p$ , $2<p<8$ , then the number of such matrices $A$ is ___________.
Permutations and Combinations Distribution of Identical Objects
HardNumerical valueIdea asked in 6 yearsAsked the year before
Q24
If the sum of the coefficients of all the positive powers of $x$ , in the Binomial expansion of $\left(x^n+\frac{2}{x^5}\right)^7$ is $939$ , then the sum of all the possible integral values of $n$ is ___________.
Binomial Theorem
HardNumerical value
Q25
Let $[t]$ denote the greatest integer $\leq t$ and $\{t\}$ denote the fractional part of $t$ . The integral value of $\alpha$ for which the left hand limit of the function $f(x)=[1+x]+\frac{\alpha^{2[x]+\{x\}}+[x]-1}{2[x]+\{x\}}$ at $x=0$ is equal to…
Limits and Derivatives Continuity and Differentiability Continuity involving GIF and Fractional Part
MediumNumerical valueIdea asked in 6 yearsAsked the year before
Q26
If $y(x)=\left(x^x\right)^x$ , $x>0$ , then $\frac{d^2x}{dy^2}+20$ at $x=1$ is equal to ___________.
Continuity and Differentiability Chain Rule Logarithmic Differentiation for Power Towers
HardNumerical valueNew idea
Q27
If the area of the region $\left\{(x,y): x^{\frac{2}{3}}+y^{\frac{2}{3}}\leq1,\ x+y\geq0,\ y\geq0\right\}$ is $A$ , then $\frac{256A}{\pi}$ is equal to ___________.
Application of Integrals Area Under Curves Area of Inequalities
HardNumerical valueIdea asked in 8 yearsAsked the year before
Q28
Let $y=y(x)$ be the solution of the differential equation $\left(1-x^2\right)dy=\left(xy+\left(x^3+2\right)\sqrt{1-x^2}\right)dx$ , $-1<x<1$ , and $y(0)=0$ . If $\int_{-\frac{1}{2}}^{\frac{1}{2}}\sqrt{1-x^2}\,y(x)dx=k$ , then $k^{-1}$ is equal to ___________.
Differential Equations Linear Differential Equations Integrating Factors with Trigonometric Functions
HardNumerical valueNew ideaIdea asked in 4 years
Q29
Let a circle $C$ of radius $5$ lie below the $x$ -axis. The line $L_1: 4x+3y+2=0$ passes through the centre $P$ of the circle $C$ and intersects the line $L_2: 3x-4y-11=0$ at $Q$ . The line $L_2$ touches $C$ at the point $Q$ . Then the distance of $P$ from the…
Straight Lines Straight Line Distance Perpendicular distance from point
MediumNumerical valueIdea asked in 3 yearsAsked the year before
Q30
Let $S=\{E_1, E_2,\dots\dots\dots E_8\}$ be a sample space of a random experiment such that $P(E_n)=\frac{n}{36}$ for every $n=1, 2, \dots\dots, 8$ . Then the number of elements in the set $\left\{A\subseteq S: P(A)\geq\frac{4}{5}\right\}$ is ___________.
Probability
HardNumerical value

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 2022 shifts.