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JEE Main 2016 April 09 Question Paper with Solutions

All 90 questions from the JEE Main 2016 (April 09) 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 correctPhysics and Measurement
In the following 'I' refers to current and 'a' to acceleration of a point mass falling vertically in a viscous medium. Choose the option that corresponds to the dimensions of electrical conductivity :
(A)
(B)
(C)
(D)
Q2Single correctLaws of Motion
Which of the following option correctly describes the variation of the speed and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force , where 'k' is a constant, on the body ? (Graphs are schematic and not drawn to scale)
(A)
(B)
(C)
(D)
Q3Single correctLaws of Motion
A rocket is fired vertically from the earth with an acceleration of , where g is the gravitational acceleration. On an inclined plane inside the rocket, making an angle with the horizontal, a point object of mass m is kept. The minimum coefficient of friction between the mass and the inclined surface such that the mass does not move is :
(A)
(B)
(C)
(D)
Q4Single correctWork, Energy and Power
A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km and applies a constant frictional force on the car. While moving uphill on the road at a speed of , the car needs power P. If it needs power while moving downhill at speed v then value of v is :
(A)
(B)
(C)
(D)
Q5Single correctRotational Motion
A cubical block of side 30 cm is moving with velocity on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :
A square (side view of a cube), side 30 cm, sitting on a horizontal surface and moving to the right with velocity 2 m/s (arrow pointing right from the block). At the bottom-right corner of the block on the surface is a small bump/peg marked O about which the block will tip and rotate.
(A)
(B)
(C)
(D)
Q6Single correctGravitation
Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If is the time taken for planet to go over path abc and for path taken over cda then :
An ellipse with four points marked on it: d at upper-left, b at the right vertex (end of major axis), a at the left vertex, and c at the lower part. The sun S is marked at a focus inside the ellipse. db is the semimajor axis and ca the semiminor axis; triangle csa (from c to sun S to a) is shaded/indicated as one quarter of the ellipse area. Path abc and path cda are the two arcs.
(A)
(B)
(C)
(D)
Q7Single correctProperties of Solids and Liquids
Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then :
A cylindrical water jar of radius R (top width marked R), filled with water to height H (water level shown with horizontal dashed lines), resting on a stand of height h. A small hole of diameter 2r is at the bottom centre of the jar. Below the hole a funnel-shaped stream of water narrows as it falls; at the ground the stream diameter is marked 2x. Vertical distance from hole to ground is h.
(A)
(B)
(C)
(D)
Q8Single correctThermodynamics
200 g water is heated from to . Ignoring the slight expansion of water, the change in its internal energy is (Given specific heat of water ) :
(A)
(B)
(C)
(D)
Q9Single correctThermodynamics
The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :
(A)
(B)
(C)
(D)
Q10Single correctOscillations and Waves
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time one particle has displacement A while the other one has displacement and they are moving towards each other. If they cross each other at time t, then t is :
(A)
(B)
(C)
(D)
Q11Single correctOscillations and Waves
Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec is :
(A)
(B)
(C)
(D)
Q12Single correctElectrostatics
The potential (in volts) of a charge distribution is given by
for
for
V(z) does not depend on x and y. If this potential is generated by a constant charge per unit volume (in units of ) which is spread over a certain region, then choose the correct statement.
(A)
(B)
(C)
(D)
Q13Single correctElectrostatics
Three capacitors each of are to be connected in such a way that the effective capacitance is . This can be done by connecting them :
(A)
(B)
(C)
(D)
Q14Single correctCurrent Electricity
In the circuit shown, the resistance is a variable resistance. If for , the heat generation in is maximum then the value of is :
A series circuit: a battery (cell) connected to a resistor R in series, which then connects to a parallel combination of a fixed resistor R (top branch) and a variable resistor r (bottom branch, drawn with an arrow through it). The parallel pair returns to the other terminal of the battery.
(A)
(B)
(C)
(D)
Q15Single correctMagnetic Effects of Current and Magnetism
A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of . One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of with this field. The magnitude of the other field (in mT) is close to :
(A)
(B)
(C)
(D)
Q16Single correctCurrent Electricity
A resistance is connected to a battery of 5 V. A galvanometer of resistance is to be used as an ammeter to measure current through the resistance, for this a resistance is connected to the galvanometer. Which of the following connections should be employed if the measured current is within of the current without the ammeter in the circuit ?
(A)
(B)
(C)
(D)
Q17Single correctAlternating Current
A series LR circuit is connected to a voltage source with . After very large time, current I(t) behaves as :
(A)
(B)
(C)
(D)
Q18Single correctElectromagnetic Waves
Microwave oven acts on the principle of :
(A)
(B)
(C)
(D)
Q19Single correctRay Optics and Optical Instruments
A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of :
Optical bench arrangement on a horizontal axis. From left: an upright object arrow, then a biconvex (convex) lens labelled |Focal length| = 30 cm, then a biconcave (concave) lens labelled |Focal length| = 120 cm, then a vertical hatched plane mirror at the right end. Dimension brackets below: 60 cm from convex lens to concave lens, 20 cm from concave lens to the plane mirror, and a separate 70 cm bracket starting at the concave lens and extending to the right past the mirror.
(A)
(B)
(C)
(D)
Q20Single correctWave Optics
In Young's double slit experiment, the distance between slits and the screen is 1.0 m and monochromatic light of 600 nm is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance between the slits. If the angular resolution of the eye is , the value of is close to :
(A)
(B)
(C)
(D)
Q21Single correctDual Nature of Radiation and Matter
When photons of wavelength are incident on an isolated sphere, the corresponding stopping potential is found to be V. When photons of wavelength are used, the corresponding stopping potential was thrice that of the above value. If light of wavelength is used then find the stopping potential for this case :
(A)
(B)
(C)
(D)
Q22Single correctAtoms and Nuclei
A hydrogen atom makes a transition from to and emits a photon. This photon strikes a doubly ionized lithium atom in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :
(A)
(B)
(C)
(D)
Q23Single correctSemiconductor Electronics
The truth table given in fig. represents :
A truth table with three columns headed A, B, Y and four data rows. Rows: A=0 B=0 Y=0; A=0 B=1 Y=1; A=1 B=0 Y=1; A=1 B=1 Y=1. (This is the OR-gate truth table; KaTeX cannot render the bordered table, so it must be drawn as a bordered image.)
(A)
(B)
(C)
(D)
Q24Single correctCommunication Systems
An audio signal consists of two distinct sounds : one a human speech signal in the frequency band of 200 Hz to 2700 Hz, while the other is a high frequency music signal in the frequency band of 10200 Hz to 15200 Hz. The ratio of the AM signal bandwidth required to send both the signals together to the AM signal bandwidth required to send just the human speech is :
(A)
(B)
(C)
(D)
Q25Single correctOscillations
A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at . If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature, the resulting graph is a line of slope S. If the coefficient of linear expansion of metal is then the value of S is :
(A)
(B)
(C)
(D)
Q26Single correctMechanical Properties of Solids
A uniformly tapering conical wire is made from a material of Young's modulus and has a normal, unextended length . The radii, at the upper and lower ends of this conical wire, have values and , respectively. The upper end of the wire is fixed to a rigid support and a mass is suspended from its lower end. The equilibrium extended length, of this wire, would equal :
(A)
(B)
(C)
(D)
Q27Single correctCurrent Electricity
To know the resistance G of a galvanometer by half deflection method, a battery of emf and resistance R is used to deflect the galvanometer by angle . If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :
(A)
(B)
(C)
(D)
Q28Single correctRay Optics and Optical Instruments
To find the focal length of a convex mirror, a student records the following data :
Object Pin : 22.2 cm; Convex Lens : 32.2 cm; Convex Mirror : 45.8 cm; Image Pin : 71.2 cm.
The focal length of the convex lens is and that of mirror is . Then taking index correction to be negligibly small, and are close to :
(A)
(B)
(C)
(D)
Q29Single correctSemiconductor Electronics
An experiment is performed to determine the I - V characteristics of a Zener diode, which has a protective resistance of , and a maximum power of dissipation rating of 1 W. The minimum voltage range of the DC source in the circuit is :
(A)
(B)
(C)
(D)
Q30Single correctSemiconductor Electronics
An unknown transistor needs to be identified as a or type. A multimeter, with ve and ve terminals, is used to measure resistance between different terminals of transistor. If terminal 2 is the base of the transistor then which of the following is correct for a transistor ?
(A)
(B)
(C)
(D)

Chemistry30 questions

Q31Single correctSome Basic Concepts in Chemistry
The amount of arsenic pentasulphide that can be obtained when 35.5 g arsenic acid is treated with excess ( assuming 100% conversion) is :
(A)
(B)
(C)
(D)
Q32Single correctStates of Matter
At very high pressures, the compressibility factor of one mole of a gas is given by :
(A)
(B)
(C)
(D)
Q33Single correctStructure of Atom
The total number of orbitals associated with the principal quantum number 5 is :
(A)
(B)
(C)
(D)
Q34Single correctStates of Matter
Which intermolecular force is most responsible in allowing xenon gas to liquefy ?
(A)
(B)
(C)
(D)
Q35Single correctChemical Thermodynamics
A reaction at 1 bar is non-spontaneous at low temperature but becomes spontaneous at high temperature. Identify the correct statement about the reaction among the following :
(A)
(B)
(C)
(D)
Q36Single correctSolutions
The solubility of in water at 300 K and 500 torr partial pressure is 0.01 g . The solubility (in g ) at 750 mm partial pressure is :
(A)
(B)
(C)
(D)
Q37Single correctChemical Thermodynamics
For the reaction,
and are, respectively, kJ mo and kJ mo at 298 K. The equilibrium constant for the reaction at 298 K is :
(A)
(B)
(C)
(D)
Q38Single correctRedox Reactions and Electrochemistry
What will occur if a block of copper metal is dropped into a beaker containing a solution of ?
(A)
(B)
(C)
(D)
Q39Single correctChemical Kinetics
The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur by a two step process shown below :
----- (i)
L mo
----- (ii)
L mo
The closest rate constant for the overall reaction is :
(A)
(B)
(C)
(D)
Q40Single correctSurface Chemistry
A particular adsorption process has the following characteristics : (i) It arises due to van der Waals forces and (ii) it is reversible. Identify the correct statement that describes the above adsorption process :
(A)
(B)
(C)
(D)
Q41Single correctp-Block Elements
The non-metal that does not exhibit positive oxidation state is :
(A)
(B)
(C)
(D)
Q42Single correctGeneral Principles and Processes of Isolation of Metals
The plot shows the variation of versus temperature for the two reactions.
and

Identify the correct statement :
A plot of -ln Kp (vertical axis, marked at value 20) versus temperature T(K) (horizontal axis, marked at 1200). Two straight lines start from a common region near the left. The upper line is labelled 'M -> MO' and rises (positive slope) with increasing T. The lower line is labelled 'C -> CO' and falls (negative slope) with increasing T. The two lines cross near T = 1200 K; above 1200 K the C->CO line lies below the M->MO line.
(A)
(B)
(C)
(D)
Q43Single correctHydrogen
Identify the incorrect statement regarding heavy water :
(A)
(B)
(C)
(D)
Q44Single corrects-Block Elements
The correct order of the solubility of alkaline-earth metal sulphates in water is :
(A)
(B)
(C)
(D)
Q45Single correctp-Block Elements
Match the items in Column I with their use mentioned in Column II :
Column IColumn II
(A). Silica gel(i). Transistor
(B). Silicon(ii). Ion-exchanger
(C). Silicone(iii). Drying agent
(D). Silicate(iv). Sealant
(A)
(B)
(C)
(D)
Q46Single correctChemical Bonding and Molecular Structure
The group of molecules having identical shape is :
(A)
(B)
(C)
(D)
Q47Single correctThe d- and f-Block Elements
Which one of the following species is stable in aqueous solution ?
(A)
(B)
(C)
(D)
Q48Single correctCoordination Compounds
Which one of the following complexes will consume more equivalents of aqueous solution of ?
(A)
(B)
(C)
(D)
Q49Single correctCoordination Compounds
Identify the correct trend given below :
(Atomic No. = Ti : 22, Cr : 24 and Mo : 42)
(A)
(B)
(C)
(D)
Q50Single correctEnvironmental Chemistry
BOD stands for :
(A)
(B)
(C)
(D)
Q51Single correctSome Basic Concepts in Chemistry
An organic compound contains C, H and S. The minimum molecular weight of the compound containing 8% sulphur is :
(atomic weight of S = 32 amu)
(A)
(B)
(C)
(D)
Q52Single correctHydrocarbons
The hydrocarbon with seven carbon atoms containing a neopentyl and a vinyl group is :
(A)
(B)
(C)
(D)
Q53Single correctHydrocarbons
5 L of an alkane requires 25 L of oxygen for its complete combustion. If all volumes are measured at constant temperature and pressure, the alkane is :
(A)
(B)
(C)
(D)
Q54Single correctOrganic Compounds Containing Halogens
The gas evolved on heating in methanol is :
(A)
(B)
(C)
(D)
Q55Single correctAldehydes, Ketones and Carboxylic Acids
Bouveault-Blanc reduction reaction involves :
(A)
(B)
(C)
(D)
Q56Single correctOrganic Compounds Containing Nitrogen
The test to distinguish primary, secondary and tertiary amines is :
(A)
(B)
(C)
(D)
Q57Single correctPolymers
Assertion : Rayon is a semisynthetic polymer whose properties are better than natural cotton.
Reason : Mechanical and aesthetic properties of cellulose can be improved by acetylation.
(A)
(B)
(C)
(D)
Q58Single correctBiomolecules
Consider the following sequence for aspartic acid :
The (isoelectric point) of aspartic acid is :
A four-step acid-base dissociation sequence of aspartic acid shown as four skeletal amino-acid structures connected by equilibrium arrows labelled with pK values. Structure 1 (fully protonated): central CH carbon bearing H3N+ on the left, an upper COOH (CO2H) group, a lower side chain CH2CO2H, and an H on the right. An equilibrium arrow labelled pK1 = 1.88 leads to Structure 2: same backbone but the upper carboxyl is now deprotonated CO2- (H3N+ retained, side chain still CH2CO2H). An equilibrium arrow labelled pKR = 3.65 leads to Structure 3 (drawn on the second row): backbone with H3N+ left, upper CO2-, side chain now deprotonated CH2CO2-. An equilibrium arrow labelled pK2 = 9.60 leads to Structure 4: amino group now neutral H2N, upper CO2-, side chain CH2CO2-, H on right. Each structure drawn as a vertical carbon with the amino group and an H on the horizontal bonds and the two carboxyl-bearing groups above and below.
(A)
(B)
(C)
(D)
Q59Single correctChemistry in Everyday Life
The artificial sweetener that has the highest sweetness value in comparison to cane sugar is :
(A)
(B)
(C)
(D)
Q60Single correctSurface Chemistry
The most appropriate method of making egg-albumin sol is :
(A)
(B)
(C)
(D)

Mathematics30 questions

Q61Single correctRelations and Functions
For , let and Then the value of is equal to :
(A)
(B)
(C)
(D)
Q62Single correctComplex Numbers
The point represented by in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by :
(A)
(B)
(C)
(D)
Q63Single correctComplex Numbers and Quadratic Equations
If the equations and have a common root different from , then is equal to :
(A)
(B)
(C)
(D)
Q64Single correctMatrices and Determinants
If , and , then is :
(A)
(B)
(C)
(D)
Q65Single correctMatrices and Determinants
The number of distinct real roots of the equation, in the interval is :
(A)
(B)
(C)
(D)
Q66Single correctPermutations and Combinations
If the four letter words (need not be meaningful) are to be formed using the letters from the word "MEDITERRANEAN" such that the first letter is R and the fourth letter is E, then the total number of all such words is :
(A)
(B)
(C)
(D)
Q67Single correctBinomial Theorem
For , if , then is equal to :
(A)
(B)
(C)
(D)
Q68Single correctAlgebra
Let x, y, z be positive real numbers such that and . Then is equal to :
(A)
(B)
(C)
(D)
Q69Single correctBinomial Theorem
The value of is equal to :
(A)
(B)
(C)
(D)
Q70Single correctLimits, Continuity and Differentiability
If , then 'a' is equal to :
(A)
(B)
(C)
(D)
Q71Single correctLimits, Continuity and Differentiability
If the function is differentiable at , then is equal to :
(A)
(B)
(C)
(D)
Q72Single correctApplication of Derivatives
If the tangent at a point P, with parameter t, on the curve , , , meets the curve again at a point Q, then the coordinates of Q are :
(A)
(B)
(C)
(D)
Q73Single correctApplication of Derivatives
The minimum distance of a point on the curve from the origin is :
(A)
(B)
(C)
(D)
Q74Single correctIntegral Calculus
If , where k is a constant of integration, then equals :
(A)
(B)
(C)
(D)
Q75Single correctIntegral Calculus
If , then is equal to :
(A)
(B)
(C)
(D)
Q76Single correctIntegral Calculus
The area (in sq. units) of the region described by is :
(A)
(B)
(C)
(D)
Q77Single correctDifferential Equations
If f is a differentiable function in the interval such that and , for each , then is equal to :
(A)
(B)
(C)
(D)
Q78Single correctCoordinate Geometry
If a line drawn through the intersection of the lines and , meets the coordinate axes at A and B, , then the locus of the mid-point of AB is :
(A)
(B)
(C)
(D)
Q79Single correctCoordinate Geometry
The point is translated parallel to the line by units. If the new point Q lies in the third quadrant, then the equation of the line passing through Q and perpendicular to L is :
(A)
(B)
(C)
(D)
Q80Single correctCoordinate Geometry
A circle passes through and touches the -axis at . Which one of the following equations can represent a diameter of this circle ?
(A)
(B)
(C)
(D)
Q81Single correctCoordinate Geometry
Let a and b be respectively the semi-transverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation . If is a focus and is the corresponding directrix of this hyperbola, then is equal to :
(A)
(B)
(C)
(D)
Q82Single correctCoordinate Geometry
If the tangent at a point on the ellipse meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle OAB is :
(A)
(B)
(C)
(D)
Q83Single correctThree Dimensional Geometry
The shortest distance between the lines and lies in the interval :
(A)
(B)
(C)
(D)
Q84Single correctThree Dimensional Geometry
The distance of the point from the plane passing through the point and perpendicular to the planes and , is :
(A)
(B)
(C)
(D)
Q85Single correctVector Algebra
In a triangle ABC, right angled at the vertex A, if the position vectors of A, B and C are respectively , and , then the point (p, q) lies on a line :
(A)
(B)
(C)
(D)
Q86Single correctStatistics
If the mean deviation of the numbers from their mean is , then a value of d is :
(A)
(B)
(C)
(D)
Q87Single correctProbability
If A and B are any two events such that and , then the conditional probability, , where A' denotes the complement of A, is equal to :
(A)
(B)
(C)
(D)
Q88Single correctTrigonometry
The number of for which is :
(A)
(B)
(C)
(D)
Q89Single correctTrigonometry
If m and M are the minimum and the maximum values of , then is equal to :
(A)
(B)
(C)
(D)
Q90Single correctMathematical Reasoning
Consider the following two statements :
P : If 7 is an odd number, then 7 is divisible by 2.
Q : If 7 is a prime number, then 7 is odd.
If is the truth value of the contrapositive of P and is the truth value of contrapositive of Q, then the ordered pair equals :
(A)
(B)
(C)
(D)

More JEE Main 2016 papers

Frequently Asked Questions

How many questions are in the JEE Main 2016 April 09 paper?

The JEE Main 2016 April 09 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.

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

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