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JEE Main 2019 January 09, Shift 2 Question Paper with Solutions

All 90 questions from the JEE Main 2019 (January 09, Shift 2) shift — Physics (30), Chemistry (30) and Mathematics (30) — each with the correct answer (answer key) and a step-by-step solution. Read it free online, or attempt the full paper as a timed mock test.

Physics30 questions

Q1Single correctKinematics
The position co-ordinates of a particle moving in a coordinate system is given by


and
The speed of the particle is:
(A)
(B)
(C)
(D)
Q2Single correctUnits and Measurements
Expression for time in terms of (universal gravitational constant), (Planck constant) and (speed of light) is proportional to:
(A)
(B)
(C)
(D)
Q3Single correctKinematics
In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed v more than that of car B. Both the cars start from rest and travel with constant acceleration and respectively. Then v is equal to:
(A)
(B)
(C)
(D)
Q4Single correctLaws of Motion
A mass of kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is
(A)
(B)
(C)
(D)
Q5Single correctWork, Energy and Power
A force acts on a object so that its position is given as a function of time as . What is the work done by this force in first seconds?
(A)
(B)
(C)
(D)
Q6Single correctRotational Motion
A rod of length is pivoted at one end. It is raised such that it makes an angle of from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in ) will be
A uniform rod pivoted at its lower-left end (drawn as a small circle/hub on a hatched base). The rod is raised so it makes an angle of 30 degrees above the horizontal, sloping up to the right; the angle 30 degrees is marked between the rod and the horizontal dashed line at the pivot.
(A)
(B)
(C)
(D)
Q7Single correctGravitation
The energy required to take a satellite to a height h above the Earth surface (radius of Earth km) is , and the kinetic energy required for the satellite to be in a circular orbit at this height is . The value of h for which and are equal, is
(A)
(B)
(C)
(D)
Q8Single correctProperties of Solids and Liquids
The top of a water tank is open to air and its water level is maintained. It is giving out water per minute through a circular opening of radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to:
(A)
(B)
(C)
(D)
Q9Single correctThermodynamics
Two Carnot engines A and B are operated in series. The first one, A, receives heat at and rejects to a reservoir at temperature . The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at . Calculate the temperature if the work outputs of the two engines are equal:
(A)
(B)
(C)
(D)
Q10Single correctKinetic Theory of Gases
A mass of nitrogen gas is enclosed in a vessel at a temperature, . The amount of heat transferred to the gas, so that R.M.S. velocity of molecules is doubled, is about:
(A)
(B)
(C)
(D)
Q11Single correctOscillations and Waves
A particle is executing simple harmonic motion () of amplitude , along the -axis, about . When its potential energy () equals kinetic energy (), the position of the particle will be:
(A)
(B)
(C)
(D)
Q12Single correctRotational Motion
A rod of mass M and length is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses, each of mass m, are attached at distance from its centre on both sides, it reduces the oscillation frequency by . The value of ratio is close to:
(A)
(B)
(C)
(D)
Q13Single correctOscillations and Waves
A musician using an open flute of length produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of . If the wave speed is , the frequency heard by the running person shall be close to:
(A)
(B)
(C)
(D)
Q14Single correctElectrostatics
Charge is distributed within a sphere of radius R with a volume charge density , where A and a are constants. If Q is the total charge of this charge distribution, the radius R is:
(A)
(B)
(C)
(D)
Q15Single correctElectrostatics
Two point charges and are placed on the x-axis at and respectively. The electric field (in V/m) at a point on y-axis is,
(A)
(B)
(C)
(D)
Q16Single correctElectrostatics
A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants arranged as shown in the figure. The effective dielectric constant K will be:
Parallel plate capacitor cross-section shown as a rectangle split into a 2x2 grid of dielectric blocks. Top-left = K1, top-right = K2 (top row labelled height L/2). Bottom-left = K3, bottom-right = K4 (bottom row labelled height L/2). Total width labelled d/2 + d/2 (i.e. each vertical column is half the plate width), each horizontal layer is half the plate gap L/2. K1 K2 on the upper half, K3 K4 on the lower half.
(A)
(B)
(C)
(D)
Q17Single correctCurrent Electricity
A carbon resistance has a following colour code. What is the value of the resistance?
A horizontal carbon resistor (cylindrical body with axial leads on both sides) carrying four colour bands. Reading left to right the bands are labelled G O Y Golden (Green, Orange, Yellow, Gold).
(A)
(B)
(C)
(D)
Q18Single correctCurrent Electricity
In the given circuit the internal resistance of the cell is negligible. If , and and the reading of an ideal voltmeter across is , then the value of will be:
DC circuit. An 18 V cell at the bottom drives current up the left side. The top branch has R3 then R4 in series (R3 left, R4 right, drawn across the top). R1 is on the left vertical arm in series with the supply. R2 is a vertical resistor in the middle of the circuit, in parallel with the series combination of R3 and R4. An ideal voltmeter reads 5 V across R4.
(A)
(B)
(C)
(D)
Q19Single correctMagnetic Effects of Current and Magnetism
A particle having the same charge as of electron moves in a circular path of radius under the influence of a magnetic field of . If an electric field of makes it to move in a straight path, then the mass of the particle is (Given charge of electron )
(A)
(B)
(C)
(D)
Q20Single correctMagnetic Effects of Current and Magnetism
One of the two identical conducting wires of length L is bent in the form of a circular loop and the other into a circular coil of N identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop to that at the centre of the coil , i.e. will be:
(A)
(B)
(C)
(D)
Q21Single correctElectromagnetic Induction and Alternating Currents
A power transmission line feeds input power at to a step down transformer with its primary windings having turns. The output power is delivered at by the transformer. If the current in the primary of the transformer is and its efficiency is , the output current would be:
(A)
(B)
(C)
(D)
Q22Single correctElectromagnetic Induction and Alternating Currents
A series AC circuit containing an inductor , a capacitor and a resistor is driven by an AC source of . The energy dissipated in the circuit in is:
(A)
(B)
(C)
(D)
Q23Single correctElectromagnetic Waves
The energy associated with electric field is and with magnetic field is for an electromagnetic wave in free space. Then:
(A)
(B)
(C)
(D)
Q24Single correctOptics
Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror and parallel to the second mirror is finally reflected from the second mirror parallel to the first mirror . The angle between the two mirrors will be:
(A)
(B)
(C)
(D)
Q25Single correctOptics
In a young's double slit experiment, the slits are placed apart. Light of wavelength is incident on the slits. The total number of bright fringes that are observed in the angular range is:
(A)
(B)
(C)
(D)
Q26Single correctDual Nature of Matter and Radiation
The magnetic field associated with a light wave is given, at the origin, by
. If this light falls on a silver plate having a work function of , what will be the maximum kinetic energy of the photoelectrons?
(A)
(B)
(C)
(D)
Q27Single correctAtoms and Nuclei
At a given instant, say , two radioactive substance A and B have equal activities. The ratio of their activities after time t itself decays with time t as . If the half-life of A is , the half-life of B is:
(A)
(B)
(C)
(D)
Q28Single correctSemiconductor Electronics: Materials, Devices and Simple Circuits
Ge and Si diodes start conducting at and respectively. In the following figure if Ge diode connection are reversed, the value of changes by: (assume that the Ge diode has large breakdown voltage)
Circuit with a 12 V battery on the left. Two diodes in parallel between the input node and the output node Vo: the upper diode is Ge, the lower diode is Si, both drawn pointing toward the output (forward). A 5 K resistor connects the output node Vo to ground. Output terminal Vo at the top right. Bottom rail grounded.
(A)
(B)
(C)
(D)
Q29Single correctCommunication Systems
In a communication system operating at wavelength , only one percent of source frequency is available as signal bandwidth. The number of channels accommodated for transmitting TV signals of band width are (Take velocity of light
(A)
(B)
(C)
(D)
Q30Single correctExperimental Skills
The pitch and the number of divisions, on the circular scale, for a given screw gauge are and respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies divisions below the mean line.
The readings of the main scale and the circular scale, for a thin sheet, are and respectively, the thickness of this sheet is:
(A)
(B)
(C)
(D)

Chemistry30 questions

Q31Single correctSome Basic Concepts in Chemistry
For the following reaction, the mass of water produced from is:
(A)
(B)
(C)
(D)
Q32Single correctAtomic Structure
Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?
(A) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.
(B) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.
(C) According to wave mechanics, the ground state angular momentum is equal to .
(D) The plot of Vs r for various azimuthal quantum numbers, shows peak shifting towards higher r value.
(A)
(B)
(C)
(D)
Q33Single correctClassification of Elements and Periodicity in Properties
When the first electron gain enthalpy of oxygen is , its second electron gain enthalpy is:
(A)
(B)
(C)
(D)
Q34Single correctChemical Bonding and Molecular Structure
In which of the following processes, the bond order has increased and paramagnetic character has changed to diamagnetic?
(A)
(B)
(C)
(D)
Q35Single correctChemical Thermodynamics
The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapour are 4.2 and 2.0 ; heat of liquid fusion and vaporization of water are 334 and 2491 , respectively.) ( )
(A)
(B)
(C)
(D)
Q36Single correctp-Block Elements
The temporary hardness of water is due to:
(A)
(B)
(C)
(D)
Q37Single correctp-Block Elements
The metal that forms nitride by reacting directly with of air is:
(A)
(B)
(C)
(D)
Q38Single correctHydrocarbons
Which of the following compounds is not aromatic?
(A)
(B)
(C)
(D)
Q39Single correctEquilibrium
The pH of rain water is approximately:
(A)
(B)
(C)
(D)
Q40Single correctp-Block Elements
Which of the following conditions in drinking water causes methemoglobinemia?
(A)
(B)
(C)
(D)
Q41Single correctSome Basic Concepts in Chemistry
At , copper (Cu) has FCC unit cell structure with cell edge length of . What is the approximate density of Cu (in ) at this temperature?
[Atomic Mass of ]
(A)
(B)
(C)
(D)
Q42Single correctSolutions
A solution containing 62 g ethylene glycol in 250 g water is cooled to . If for water is 1.86 K , the amount of water (in g ) separated as ice is:
(A)
(B)
(C)
(D)
Q43Single correctRedox Reactions and Electrochemistry
If the standard electrode potential for a cell is 2 V at 300 K, the equilibrium constant (K) for the reaction.

at 300 K is approximately
(A)
(B)
(C)
(D)
Q44Single correctChemical Kinetics
For the reaction, products, when the concentration of A and B both were doubled, the rate of the reaction increased from to . When the concentration of A alone is doubled, the rate increased from to . Which one of the following statements is correct?
(A)
(B)
(C)
(D)
Q45Single correctEquilibrium
Consider the following reversible chemical reactions:


The relationship between and is:
(A)
(B)
(C)
(D)
Q46Single correctSurface Chemistry
For coagulation of arsenious sulphide sol, which of the following salt solutions will be most effective?
(A)
(B)
(C)
(D)
Q47Single correctSurface Chemistry
Match Item I with Item II
Item IItem II
(A). Benzaldehyde(P). Mobile phase
(B). Alumina(Q). Adsorbent
(C). Acetonitrile(R). Adsorbate
(A)
(B)
(C)
(D)
Q48Single correctGeneral Principles and Processes of Isolation of Metals
The correct statement regarding the given Ellingham diagram is:
Ellingham diagram of Delta G versus temperature showing oxide-formation lines for Cu, Zn, C and Al.
(A)
(B)
(C)
(D)
Q49Single correctp- Block Elements
Good reducing nature of is attributed to the presence of:
(A)
(B)
(C)
(D)
Q50Single correctd- and f-Block Elements
The transition element that has the lowest enthalpy of atomisation is:
(A)
(B)
(C)
(D)
Q51Single correctCoordination Compounds
Homoleptic octahedral complexes of a metal ion with three monodentate ligands , and absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is:
(A)
(B)
(C)
(D)
Q52Single correctCoordination Compounds
The complex that has highest crystal field splitting energy , is:
(A)
(B)
(C)
(D)
Q53Single correctHydrocarbons
The major product of the following reaction is:
Succinic anhydride plus o-cresol (benzene with OH and ortho CH3), arrow labelled AlCl3, heat.
(A)
(B)
(C)
(D)
Q54Single correctOrganic Compounds Containing Oxygen
The products formed in the reaction of cumene with followed by treatment with dil HCl are:
(A)
(B)
(C)
(D)
Q55Single correctOrganic Compounds Containing Oxygen
The major product formed in the following reaction is:
Acetone plus acetophenone (benzene ring bearing a CO-CH3), arrow labelled dilute NaOH.
(A)
(B)
(C)
(D)
Q56Single correctOrganic Compounds Containing Oxygen
The test performed on compound x and their inferences are:
Test | Inference |
(a) 2, 4 - test | Coloured precipitate yellow |
(b) Iodoform test | Yellow precipitate |
(c) Azo-dye test | No dye formation |
Compound is:
(A)
(B)
(C)
(D)
Q57Single correctOrganic Compounds Containing Nitrogen
The major product obtained in the following reaction is:
Benzene with ortho phenol OH and a gem-dimethyl benzylic carbon linked to CH(CH3)NH2; arrow (CH3CO)2O / pyridine (1 eqv.), RT.
(A)
(B)
(C)
(D)
Q58Single correctOrganic Compounds Containing Nitrogen
The increasing basicity order of the following compounds is:
(A)
(B)
(C)
(D)
(A)
(B)
(C)
(D)
Q59Single correctOrganic Compounds Containing Nitrogen
The major product of the following reaction is:
Benzene with ortho C(=O)NH2 and CH2CH3; arrow (i) Br2/hv (ii) KOH dilute.
(A)
(B)
(C)
(D)
Q60Single correctBiomolecules
The correct sequence of amino acids present in the tripeptide given below is:
Tripeptide drawn N-terminal to C-terminal with the three alpha-carbon side chains and two amide linkages.
(A)
(B)
(C)
(D)

Mathematics30 questions

Q61Single correctComplex Numbers and Quadratic Equations
The number of all possible positive integral value of for which the roots of the quadratic equation are rational numbers is:
(A)
(B)
(C)
(D)
Q62Single correctComplex Numbers and Quadratic Equations
If both the roots of the quadratic equation are real and distinct and they lie in the interval , then m lies in the interval:
Note: In the actual JEE paper interval was
(A)
(B)
(C)
(D)
Q63Single correctComplex Numbers and Quadratic Equations
Let be a root of quadratic equation, . If , then is equal to:
(A)
(B)
(C)
(D)
Q64Single correctPermutations and Combinations
The number of natural numbers less than 7000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to:
(A)
(B)
(C)
(D)
Q65Single correctSequence and Series
The sum of the following series up to 15 terms, is:
(A)
(B)
(C)
(D)
Q66Single correctSequence and Series
Let a, b and c be the , and terms respectively of a non-constant A.P. . If these are also the three consecutive terms of a G.P. , then is equal to:
(A)
(B)
(C)
(D)
Q67Single correctBinomial Theorem and its Simple Applications
The coefficient of in the expansion of is
(A)
(B)
(C)
(D)
Q68Single correctTrigonometry
If , then the number of values of x for which , is:
(A)
(B)
(C)
(D)
Q69Single correctCo-ordinate Geometry
Let be the set of all triangles in the -plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in has area 50 sq. units, then the number of elements in the set is:
(A)
(B)
(C)
(D)
Q70Single correctCo-ordinate Geometry
Let the equations of two sides of a triangle be and . If the orthocenter of this triangle is at then the equation of it's third side is:
(A)
(B)
(C)
(D)
Q71Single correctCo-ordinate Geometry
If the circles and intersect at two distinct points, then:
(A)
(B)
(C)
(D)
Q72Single correctCo-ordinate Geometry
Let and be points on the parabola, . Let C be chosen on the arc AOB of the parabola, where O is the origin, such that the area of is maximum. Then, the area (in sq. units) of , is:
(A)
(B)
(C)
(D)
Q73Single correctCo-ordinate Geometry
A hyperbola has its centre at the origin, passes through the point and has transverse axis of length 4 along the -axis. Then the eccentricity of the hyperbola is:
(A)
(B)
(C)
(D)
Q74Single correctLimit, Continuity and Differentiability
For each , let [x] be the greatest integer less than or equal to x. Then is equal to
(A)
(B)
(C)
(D)
Q75Single correctSets, Relations and Functions
The logical statement is equivalent to
(A)
(B)
(C)
(D)
Q76Single correctStatistics and Probability
A data consists of n observations: . If and , then the standard deviation of this data is
(A)
(B)
(C)
(D)
Q77Single correctMatrices and Determinants
If , then A is:
(A)
(B)
(C)
(D)
Q78Single correctMatrices and Determinants
If the system of linear equations ; ; is consistent, then:
(A)
(B)
(C)
(D)
Q79Single correctTrigonometry
If and , then is equal to:
(A)
(B)
(C)
(D)
Q80Single correctDifferential Equations
Let be such that , for all , and . If satisfies the differential equation, with then is equal to:
(A)
(B)
(C)
(D)
Q81Single correctSets, Relations and Functions
Let . Define a function as , then f is:
(A)
(B)
(C)
(D)
Q82Single correctIntegral Calculus
Let f be a differentiable function from R to R such that , for all . If then is equal to
(A)
(B)
(C)
(D)
Q83Single correctLimit, Continuity and Differentiability
If and , then the value of at , is:
(A)
(B)
(C)
(D)
Q84Single correctIntegral Calculus
If , , and , then the value of is
(A)
(B)
(C)
(D)
Q85Single correctIntegral Calculus
If , , then the value of k is
(A)
(B)
(C)
(D)
Q86Single correctIntegral Calculus
The area of the region in sq. units, is
(A)
(B)
(C)
(D)
Q87Single correctVector Algebra
Let , and be three vectors such that the projection vector of on is . If is perpendicular to , then is equal to:
(A)
(B)
(C)
(D)
Q88Single correctThree Dimensional Geometry
If the lines and are perpendicular, then
(A)
(B)
(C)
(D)
Q89Single correctThree Dimensional Geometry
The equation of the plane containing the straight line and perpendicular to the plane containing the straight lines and is:
(A)
(B)
(C)
(D)
Q90Single correctStatistics and Probability
An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:
(A)
(B)
(C)
(D)

More JEE Main 2019 papers

Frequently Asked Questions

How many questions are in the JEE Main 2019 January 09, Shift 2 paper?

The JEE Main 2019 January 09, Shift 2 paper has 90 questions — Physics (30), Chemistry (30) and Mathematics (30). Every question is on this page with its correct answer and a step-by-step solution.

What is the marking scheme for JEE Main?

JEE Main awards +4 marks for each correct answer and −1 for a wrong answer, with 0 for questions left unattempted. The paper covers Physics, Chemistry and Mathematics.

Are the answer key and step-by-step solutions provided for the 2019 January 09, Shift 2 paper?

Yes — every question shows the correct answer (answer key) and a detailed step-by-step solution, free to read online.

Can I take the JEE Main 2019 January 09, Shift 2 paper as a timed mock test?

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