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JEE Main 2014 Session Shift 1 Question Paper with Solutions | JEE Arc

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JEE Main 2014Session, Shift 1

Physics 22Chemistry 24Mathematics 28

Physics

Q5975The radiation corresponding to 3 → 2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a…Atoms and Nuclei
Q5976Hydrogen (₁H¹), Deuterium (₁H²), singly ionised Helium (₂H e⁴)⁺ and doubly ionised lithium (₃L i⁶)⁺⁺ all have one electron around the nucleus. Consider an…Atoms and Nuclei
Q6148A parallel plate capacitor is made of two circular plates separated by a distance 5 mm and with a dielectric of dielectric constant 2.2 between them. When the…Electrostatics
Q6419In a large building, three are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1 kW. The voltage of electric mains is 220 V. The minimum…Current Electricity
Q6734During the propagation of electromagnetic waves in a medium:Electromagnetic Waves
Q6863The current voltage relation of diode is given by I = (e^(100V/T) - 1)mA, where the applied voltage V is in volts and the temperature T is in degree kelvin…Electronic Devices
Q7002Assume that an electric field E = 30x² i exists in space. Then the potential difference V A - V O, where V O is the potential at the origin and V A the…Electrostatics
Q7030A thin convex lens made from crown glass (μ = 3/2) has focal length f. When it is measured in two different liquids having refractive indices 4/3 and 5/3, it…Optics
Q7096A green light is incident from the water to the air - water interface at the critical angle (θ). Select the correct statement.Optics
Q7251Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The…Gravitation
Q7340Three rods of Copper, Brass and Steel are welded together to form a Y shaped structure. Area of cross - section of each rod = 4c m². End of copper rod is…Properties of Solids and Liquids
Q7550A block of mass m is placed on a surface with a vertical cross section given by y = (x³)/6. If the coefficient of friction is 0.5, the maximum height above…Laws of Motion
Q7636The coercivity of a small magnet where the ferromagnet gets demagnetized is 3 × 10³ A m⁻¹. The current required to be passed in a solenoid of length 10 cm and…Magnetic Effects of Current and Magnetism
Q7857From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by…Kinematics
Q7977An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and…Properties of Solids and Liquids
Q8001The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100° C is: (For…Properties of Solids and Liquids
Q8045A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular…Rotational Motion
Q8141A particle moves with simple harmonic motion in a straight line. In first τ s, after starting from rest it travels a distance a, and in next τ s it travels…Oscillations and Waves
Q8327A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?Units and Measurements
Q8458Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A…Optics
Q8544A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz…Oscillations and Waves
Q8616When a rubber-band is stretched by a distance x, it exerts restoring force of magnitude F = ax + b x² where a and b are constants. The work done in stretching…Work, Energy and Power

Chemistry

Q6The most suitable reagent for the conversion of R - CH₂ - OH → R - CHO is:Organic Compounds Containing Oxygen
Q112For the estimation of nitrogen, 1.4 g of organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of M/10 sulphuric…Some Basic Principles of Organic Chemistry
Q229Which one of the following bases is not present in DNA?Biomolecules
Q404For the reaction SO₂ (g) + 1/2 O₂(g) SO₃(g). if K P = K C (RT)ˣ where the symbols have usual meaning then the value of x is: (assuming ideality)Equilibrium
Q495For the non – stoichiometre reaction 2A + B → C + D, the following kinetic data were obtained in three separate experiments, all at 298 K. Initial…Chemical Kinetics
Q523Considering the basic strength of amines in aqueous solution, which one has the smallest pK b value?Organic Compounds Containing Nitrogen
Q586The equation which is balanced and represents the correct product(s) is:Coordination Compounds
Q605The octahedral complex of a metal ion M³⁺ with four monodentate ligands L₁, L₂, L₃ and L₄ absorb wavelengths in the region of red, green, yellow and blue…Coordination Compounds
Q855Which series of reactions correctly represents chemical relations related to iron and its compound?d- and f-Block Elements
Q932Resistance of 0.2 M solution of an electrolyte is 50 Ω. The specific conductance of the solution is 1.4 S m⁻¹. The resistance of 0.5 M solution of the same…Redox Reactions and Electrochemistry
Q933The equivalent conductance of NaCl at concentration C and at infinite dilution are λ C and λ _∞, respectively. The correct relationship between λ C and λ _∞…Redox Reactions and Electrochemistry
Q979Given below are the half-cell reactions: Mn²⁺ + 2e⁻ → Mn; E^(o) = -1.18 V 2(Mn³⁺ + e⁻ → Mn²⁺); E^(o) = +1.51 V The E^(o) for 3Mn²⁺ → Mn + 2Mn³⁺ will be:Redox Reactions and Electrochemistry
Q1125If Z is a compressibility factor, van der Waals equation at low pressure can be written as:Gaseous State
Q1141In S N 2 reactions, the correct order of reactivity for the following compounds: CH₃Cl, CH₃CH ₂Cl, (CH₃)₂CHCl and (CH₃)₃CCl is:Organic Compounds Containing Halogens
Q1483Which one of the following properties is not shown by NO?p-Block Elements
Q1526The correct statement for the molecule, CsI₃ is:p-Block Elements
Q1674Which one is classified as a condensation polymer?Polymers
Q1795In which of the following reactions H₂O₂ acts as a reducing agent? 1. H₂O₂ + 2H⁺ + 2e⁻ → 2H₂O 2. H₂O₂ - 2e⁻ → O₂ + 2H⁺ 3. H₂O₂ + 2e⁻ → 2OH⁻ 4. H₂O₂ + 2OH⁻…Redox Reactions and Electrochemistry
Q1871The metal that cannot be obtained by electrolysis of an aqueous solution of its salts is:S Block Elements
Q1942CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following expressions is correct?Solid State
Q1958Consider separate solutions of 0.500 M C₂H₅OH(aq), 0.100 M Mg₃(PO₄)₂(aq), 0.250 M KBr(aq) and 0.125 M Na₃PO₄(aq) at 25^(o)C. Which statement is true about…Solutions
Q2057The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1: 4. The ratio of number of their molecule is:Some Basic Concepts in Chemistry
Q2194The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:Atomic Structure
Q2345For complete combustion of ethanol, C₂H₅OH(l) + 3O₂(g) → 2CO₂(g) + 3H₂O(l) the amount of heat produced as measured in bomb calorimeter, is 1364.47 kJ mol^–1…Chemical Thermodynamics

Mathematics

Q2374The angle between the lines whose direction cosines satisfy the equations l+m+n=0 and l² = m² + n² is:Three Dimensional Geometry
Q2393The image of the line (x - 1)/3 = (y - 3)/1 = (z - 4)/(- 5) in the plane 2x-y+z+3=0 is the line:Three Dimensional Geometry
Q2631If x=-1 and x=2 are extreme points of f(x) = α log | x |+β x² + x thenLimit, Continuity and Differentiability
Q2696If f and g are differentiable functions in [ 0,1 ] satisfying f(0) = 2 = g(1),g(0) = 0 and f(1) = 6, then for some c ] 0,1 [Limit, Continuity and Differentiability
Q2803The area of the region described by A = (x,y):x² + y² ≤ 1. and. y² ≤ 1 - x is:Integral Calculus
Q2973If the coefficints of x³ and x⁴ in the expansion of (1 + ax + b x²)(1 - 2x)¹⁸ in powers of x are both zero, then (a, b) is equal to:Binomial Theorem and Its Simple Applications
Q3090Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally…Coordinate Geometry
Q3250If z is a complex number such that | z | ≥ 2, then the minimum value of | z + 1/2 |:Complex Numbers and Quadratic Equations
Q3350The integral ∫₀^π √(1 + 4 sin ²x/2 - 4 sin x/2 1mu) dx equals:Integral Calculus
Q3583Let the population of rabbits surviving at time t be governed by the differential equation (dp(t))/dt = 1/2p(t) - 200. If p(0)=100, then p(t) equals:Differential Equations
Q3656If g is the inverse of a function f and f'(x) = 1/(1 + x⁵), then g'(x) is equal to:Limit, Continuity and Differentiability
Q3723The locus of the foot of perpendicular drawn from the centre of the ellipse x² + 3y² = 6 on any tangent to it is:Coordinate Geometry
Q3903A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45°. It files off horizontally straight away from…Height and Distance
Q4268lim x → 0 (sin (π cos ²x))/(x²) is equal to:Limit, Continuity and Differentiability
Q4311The statement (p q) is:Mathematical Reasoning
Q4440If α,β ≠ 0, and f(n) = α ⁿ + β ⁿ and | 3 1 + f(1) 1 + f(2) 1 + f(1) 1 + f(2) 1 + f(3) 1 + f(2) 1 + f(3) 1 + f(4) | = K (1 - α)² (1 - β)² (α - β)², then K is…Matrices and Determinants
Q4477If A is a 3 × 3 non-singular matrix such that AA'=A'A and B = A⁻¹A', then BB' equals:Matrices and Determinants
Q4735The slope of the line touching both the parabolas y² = 4x and x² = - 32y isCoordinate Geometry
Q4941Let A and B be two events such that P(A B) = 1/6, P(A B) = 1/4 and P(A) = 1/4, where A stands for the complement of the event A. Then the events A and B are:Statistics and Probability
Q5059If a R and the equation - 3(x - [ x ])² + 2(x - [ x ]) + a² = 0 (where [ x ] denotes the greater integer ≤ x) has no integral solution, then all possible…Complex Numbers and Quadratic Equations
Q5122Let α and β be the roots of equation p x² + qx + r = 0, p ≠ 0. If p, q, r in A.P. and 1/(α) + 1/(β) = 4, then the value of | α - β | is:Complex Numbers and Quadratic Equations
Q5245Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is:Sequence and Series
Q5291If (10)⁹ + 2(11)¹ (10⁸) + 3(11)² (10)⁷ +......... + 10(11)⁹ = k (10)⁹,, then k is equal to:Sequence and Series
Q5431The variance of first 50 even natural numbers isStatistics and Probability
Q5588Let PS be the median of the triangle with vertices P(2, 2), Q(6, -1) and R(7, 3). The equation of the line passing through (1, -1) band parallel to PS is:Coordinate Geometry
Q5598Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is…Coordinate Geometry
Q5644Let f k (x) = 1/k(sin ^(k)x + cos ^(k)x) where x R and k ≥ 1. Then f₄(x) - f₆(x) equals:Trigonometry
Q5716If [ a × b b × c c × a ] = λ [ a b c ]² then λ is equal to:Vector Algebra