JEE Main 2014 Question Paper with Solutions

The current voltage relation of diode is given by I = (e^1000V/T – 1) mA, where the applied voltage V is in
volts and the temperature T is in degree Kelvin. If a student makes an error measuring 0.01 V while
measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?

An 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 sealed and the tube is raised vertically up by additional 46
cm. What will be length of the air column above mercury in the tube now? (Atmospheric pressure = 76 cm
of Hg)

Match List-I (Electromagnetic wave type) with List-II (Its association / application) and select the correct
option from the choices given below the lists:

A parallel plate capacitor is made of two circular plates separated by a distance of 5 mm and with a
dielectric of dielectric constant 2.2 between them. When the electric field in the dielectric is 3 × 10⁴ V/m,
the charge density of the positive plate will be close to :

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

Four 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 speed of each particle is :

In a large building, there are 15 bulbs of 40 W, 5 bulbs of 100 W, 5 fans of 80 W and 1 heater of 1kW. The
voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be :

A particle moves with simple harmonic motion in a straight line. In first s, after starting from rest it travels
a distance a, and in next s it travels 2a, in same direction, then :

The coercivity of a small magnet where the ferromagnet gets demagnetized is 3 x 103 Am^-1. The current
required to be passed in a solenoid of length 10 cm and number of turns 100, so that the magnet gets
demagnetized when inside the solenoid, is:

The forward biased diode connection is:

During the propagation of electromagnetic waves in a medium:

In the circuit shown here, the point ‘C’ is kept connected to point ‘A’ till the current flowing through the circuit becomes constant. Afterward, suddenly, point ‘C’ is disconnected from point ‘A’ and connected to point ‘B’ at time t = 0. Ratio of the voltage across resistance and the inductor at t = L/R will be equal to :

A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct
statement:

From 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 it to reach the highest point of its path. The relation
between H, u and n is:

A 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 has the focal lengths f₁ and f₂ respectively. The correct
relation between the focal lengths is:

Three rods of Copper, Brass and Steel are welded together to from a Y –shaped structure. Area of cross –
section of each rod = 4 cm². End of copper rod is maintained at 100^oC where as ends of brass and steel are
kept at 0^oC. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are
thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are
0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is :

A 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. The velocity of sound in air is 340 m/s.

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends 900 angle at centre. Radius joining their interface makes an angle α with
vertical. ratio d₁/d₂ is

A green light is incident from the water to the air - water interface at the critical angle (9). Select the correct statement

Hydrogen (₁H¹), Deuterium (₁H²), singly ionised Helium (₂He⁴)⁺ and doubly ionised lithium (₃Li⁶)⁺⁺ all have
one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wave lengths of
emitted radiation are λ₁, λ₂, λ₃ and λ₄ respectively then approximately which one of the following is
correct?

The radiation corresponding to 3 → 2 transition of hydrogen atom falls on a metal surface to produce
photoelectrons. These electrons are made to enter a magnetic field of 3 x 10^-4T. If the radius of the largest
circular path followed by these electrons is 10.0 mm, the work function of the metal is close to :

A 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 the ground at which the block can be placed without slipping
is :

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx² where a and b are constants. The work done in stretching the unstretched rubber band by L is :

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r < < R, and the surface tension of water is T, value of r just before bubbles detach is : (density of water is ρ_w)

Two 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 has maximum intensity (and beam B has zero
intensity), a rotation of Polaroid through 300 makes the two beams appear equally bright. If the initial
intensities of the two beams are IA and IB respectively, then I_A/I_B equals :

Assume that an electric field  exists in space. Then the potential difference V_A – V_O, where V_O is
the potential at the origin and V_A the potential at x = 2 m is :

Q. No 31- 60 carry 4 marks each and 1 mark is deducted for  every incorrect answer.Q.

Q.

The image of the line   in the plane 2x - y + z + 3 = 0 is the line

If the coefficients of x³ and x⁴ in the expansion of in powers of x are both zero, then (a, b) is equal to

If a  R and the equation  (where [x] denotes the greatest integer x) has no integral solution, then all possible values of a lie in the interval

If , then λ  is equal to

The variance of first 50 even natural numbers is

A 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 flies off horizontally straight away from the point O. After one second, the elevation of the bird from
O is reduced to 30°. Then the speed (in m/s) of the bird is

The integral equals

The statement 

If A is an 3 x 3 non-singular matrix such that equals

The integral is equal to

If z is a complex number such that |z| 2, then the minimum value of 

If g is the inverse of a function f and   then g'(x) is equal to

If α, β 0, and f (n) = α" + β" and 

then K is equal to

Let   Then f₄(x) - f₆(x) equals

Let  α  and β be the roots of equation px² + qx + r = 0, p 0. If p, q, r are in A.P. and  hen the value of |α - β| is

Let A and B be two events such that  stands for the complement of the event A. Then the events A and B are

If 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

Let the population of rabbits surviving at a time t be governed by the differential equation If p(0) = 100, then p(t) equals

Let 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, then the radius of T is equal to

The area of the region described by A = {(x, y) : x² + y² 1 and y² 1 - x} is

Let 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 equidistant from the two axes then

Let 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) and parallel to PS is

If   where N is the set of natural numbers, then XY

The locus of the foot of perpendicular drawn from the centre of the ellipse x² + 3y² = 6 on any tangent to it
is

Three positive numbers from 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

If (10)⁹ + 2(11)¹ (10)⁸ + 3(11)² (10)⁷ + ….. + 10(11)⁹ = k(10)⁹, then k is equal to

The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l² = m² + n² is

The slope of the line touching both the parabolas y² = 4x and x² =-32y is

If x = -1 and x = 2 are extreme points of f(x) = αlog |x| + βx² + x, then 

Which one of the following properties is not shown by NO?

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

The metal that cannot be obtained by electrolysis of an aqueous solution of its salts is:

Resistance of 0.2 M solution of an electrolyte is 50 ?. The specific conductance of the solution is 1.4 S m^-1.
The resistance of 0.5 M solution of the same electrolyte is 280 ?. The molar conductivity of 0.5 M solution
of the electrolyte in S m² mol^-1 is:

CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following
expressions is correct?

Consider 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^oC. Which statement is true about these solutions, assuming all salts to be strong
electrolytes?

In which of the following reactions H₂O₂ acts as a reducing agent?

In S_N2 reactions, the correct order of reactivity for the following compounds:
CH₃Cl, CH₃CH₂Cl, (CH₃)₂CHCl and (CH₃)₃CCl is:

The 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, respectively. The increasing order of ligand
strength of the four ligands is:

For 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 acid. The unreacted acid required 20 ml of M/10 sodium hydroxide for complete neutralization. The percentage of nitrogen in the compound is:

The 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_∞ is given as:
(where the constant B is positive)

For the reaction   where the symbols have usual meaning then the value of x is: (assuming ideality)

In the reaction,

the product C is:

Sodium phenoxide when heated with CO₂ under pressure at 125^oC yields a product which on acetylation
produces C.

The major product C would be:

On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic
compound formed is:

The correct statement for the molecule, CsI3 is:

The equation which is balanced and represents the correct product(s) is:

For which of the following molecule significant μ 0?

a) b)  c) d) 

For the non – stoichiometre reaction 2A+B →C+D , the following kinetic data were obtained in three
separate experiments, all at 298 K.

The rate law for the formation of C is:

Which series of reactions correctly represents chemical reactions related to iron and its compound?

Considering the basic strength of amines in aqueous solution, which one has the smallest pK_b value?

Which one of the following bases is not present in DNA?

The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:

The major organic compound formed by the reaction of 1, 1, 1– trichloroethane with silver powder is:

Given below are the half-cell reactions:

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of
their molecule is:

Which one is classified as a condensation polymer?

Among the following oxoacids, the correct decreasing order of acid strength is:

For complete combustion of ethanol,  the amount of heat produced as measured in bomb calorimeter, is 1364.47 kJ mol^–1 at 25⁰C. Assuming ideality the Enthalpy of combustion, ΔCH, for the reaction will be: (R = 8.314 kJ mol^–1)

The most suitable reagent for the conversion of R -CH₂ -OH→R -CHO is: