JEE Main 2014 Question Paper With Solutions (6th-April-2014)

A block of mass m is placed on a surface with a vertical cross-section given by y = x³/6. f 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 :

A 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 speed ω rad/s about the vertical. About the point of suspension

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

The 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 steel Young's modulus is 2 × 10¹¹ Nm^–2 and coefficient of thermal expansion is 1.1 × 10^–5 K^–1)

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 90° angle at centre. Radius joining their interface makes an angle α with vertical. Ratio is

On heating water, bubbles being formed at the bottom of the vessel detatch 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 detatch is (Density of water is ρ_ω)

​Three rods of copper, brass and steel are welded together to form a Y-shaped structure. Area of cross-section of each rod = 4 cm². End of copper rod is maintained at 100°C whereas ends of brass and steel are kept at 0°C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cm 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

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

​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)

A 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 2a in same direction then

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.

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

A 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 electric field in the dielectric is 3 × 10⁴ V/m, the charge density of the positive plate will be close to

​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 1 kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be:

A conductor lies along the z-axis at –1.5 ≤ z < 1.5 m and carries a fixed current of 10.0 A indirection (see figure). For a fieldT, find the power required to move the conductor at constant speed to x = 2.0 m, y = 0 m in 5 × 10^–3 s. Assume parallel motion along the x-axis

The 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 number of turns 100, so that the magnet gets demagnetized when inside the solenoid, is

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

During the propagation of electromagnetic waves in a medium

​A thin convex lens made from crown glass 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

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

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 30° makes the two beams appear equally bright. If the initial intensities of the two beams are I_A and I_B respectively, then equals

​The radiation corresponding to 3→2 transitions of hydrogen atoms falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3 × 10^–4 T. 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

​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 wavelengths of emitted radiation are λ₁, λ₂, λ₃ and λ₄ respectively then approximately which one of the following is correct?

The forward biased diode connection is

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

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

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

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

​For the estimation of nitrogen, 1.4 g of an 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

​Resistance 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 electrolyte is 280 Ω. The molar conductivity of 0.5 M solution of the electrolyte in S m² mol^–1 is

For complete combustion of ethanol,

the amount of heat produced as measured in bomb calorimeter, is 1364.47 kJ mol^–1 at 25°C. Assuming ideality the enthalpy of combustion, Δ_cH, for the reaction will be (R = 8.314 kJ mol^–1)

​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)

​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°C. Which statement is true about these solutions, assuming all salts to be strong electrolytes?

For the reaction If K_P = K_C(RT)^x where the symbols have usual meaning then the value of x is (assuming ideality)

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

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

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

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

In which of the following reactions H₂O₂ acts as a reducing agent?
(a) H₂O₂ + 2H⁺ + 2e^– → 2H₂O
(b) H₂O₂ – 2e^– → O₂ + 2H⁺
(c) H₂O₂ + 2e^– → 2OH^–
(d) H₂O₂ + 2OH^– – 2e^– → O₂ + 2H₂O

The correct statement for the molecule, CsI₃, is

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

Given below are the half-cell reactions


The E° for 3 Mn²⁺ → Mn + 2Mn³⁺ will b

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

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

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

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

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

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

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

The major product C would be

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

For which of the following molecule significant μ ≠ 0?

Which one is classified as a condensation polymer?

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

​In the reaction,the product C is

If X = {4ⁿ – 3n – 1 : n ∈ N} and Y = {9(n – 1) : n ∈ N}, where N is the set of natural numbers, then X ∪ Y is equal to​

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

If a ∈ R and the equation
–3(x – [x])² + 2 (x – [x]) + a² = 0
(where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

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

If α, β ≠ 0, and f(n) = αⁿ + βⁿ and = K(1 – α)²  (1 – β)² (α – β)², then K is equal to

If A is an 3 × 3 non-singular matrix such that AA′ = A′A and B =A⁻¹ A′ , then BB′ equals

If the coefficients of x³ and x⁴ in the expansion of (1 + ax + bx²) (1 – 2x)¹⁸ in powers of x are both zero, then (a, b) is equal to

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

Three 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

is equal to

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

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 c ∈]0, 1[

​If x = –1 and x = 2 are extreme points of f (x) =α log|x|+ βx² + x then

The integral dx is equal to

The integral equals

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

​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 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

​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

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

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

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

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

​If then λ is equal to

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

The variance of first 50 even natural numbers is

Let where x ∈R and k ≥ 1. Then f₄(x) – f₆(x) equals

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 statement ~(p ↔ ~q) is