JEE Main 2014 Question Paper With Solutions (11th-April-2014)

A cone of base radius R and height h is located in a uniform electric field  parallel to its base. The electric flux entering the cone is:

Three identical bars A, B and C are made of different magnetic materials. When kept in a uniform magnetic field, the field lines around them look as follows :

Make the correspondence of these bars with their material being diamagnetic (D) ferromagnetic (F) and paramagnetic (P)

The average mass of rain drops is 3.0 × 10^–5 kg and their average terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square meter of the surface at a place which receives 100 cm of rain in a year.

An ideal monoatomic gas is confinedinacy linder by a spring loaded piston of cross section 8.0 × 10^–3 m². Initially, the gas is at 300K and occupies a volume of 2.4 × 10^–3 m³ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by 0.1 m. The force constant of the spring is 8000 N/m and the atmospheric pressure is 1.0 × 10⁵ N/m² The cylinder and the piston are thermally insulated.
The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible):

The angular frequency of the damped oscillator is given by where k is the spring constant, m is the mass of the oscillator and r is the damping constant. If the ratio is 8%, the change in time period compared to the undamped oscillator is approximate as follows:

A coil of circular cross-section having 1000 turns and 4 cm² face area is placed with its axis parallel to a magnetic field which decreases by 10^-2 Wb m^-2 in 0.01 s. The e.m.f. induced in the coil is:

Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length 25 cm is:

A body of mass 5kg under the action of constant force  has velocity at t = 0 s as and at t = 10 s as  :-

In the circuit diagrams (A, B, C, and D) shown below, R is a high resistance and S is a resistance the order of galvanometer G. The correct circuit, corresponding to the half deflection method for finding the resistance and figure of merit of the galvanometer, is the circuit labelled as:

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity 0.8). The height of water is 3m and that of kerosene 2m. When the hole is opened the velocity of fluid coming out from it is nearly:
(take g = 10 ms^-2 and density of water = 10³ kg m^-3)

A photon of wavelength λ is scattered from an electron, which was at rest. The wavelength shift Δλ is three times of λ and the angle of scattering θ is 60°. The angle at which the electron recoiled is φ The value of tan φ is:
(electron speed is much smaller than the speed of light)

The Bulk moduli of Ethanol, Mercury and Water are given as 0.9, 25 and 2.2 respectively in units of 10⁹ Nm^-2. For a given value of pressure, the fractional compression in volume is  Which of the following statements about  for these three liquids is correct? :-

A hot body, obeying Newton's law of cooling is cooling down from its peak value 80ºC to an ambient temperature of 30ºC. It takes 5 minutes in cooling down from 80°C to 40°C. How much time will it take to cool down from 62°C to 32°C? (Given ln 2 = 0.693, ln 5 = 1.609)

A Zener diode is connected to a battery and a load as shown below :
The currents I, I_Z and I_L are respectively.

An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density 10³ kg/m³. The pressure inside the bubble is 1100 Nm^-2 greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? (g = 9.8 ms^-2):-

In the circuit shown, current (in A) through the 50 V and 30 V batteries are, respectively:-

During an adiabatic compression, 830J of work is done on 2 moles of a diatomic ideal gas to reduce its volume by 50%. The change in its temperature is nearly: (R = 8.3 JK^-1mol^-1)

A small ball of mass m starts at a point A with speed v₀ and moves along a frictionless track AB as shown. The track BC has coefficient of friction μ. The ball comes to stop at C after traveling a distance L which is:

In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be :

A thin bar of length L has a mass per unit length λ, that increases linearly with distance from one end. If its total mass is M and its mass per unit length at the lighter end is λ₀, then the distance of the centre of mass from the lighter end is :

In terms of resistance R and time T, the dimensions of ratio of the permeability μ and permittivity ε is :-

The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target the rifle must be aimed in order to hit the target

An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 2. What is the distance between the screen and the object?

Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is :

From a sphere of mass M and radius R, a smaller sphere of radius R/2 is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is:

An electromagnetic wave of frequency 1 x 10¹⁴ hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If ε₀ = 8.8 × 10^-12 C²/N-m², then average energy density of electric field will be:

Two factories are sounding their sirens at 800 Hz. A man goes from one factory to other at a speed of 2 m/s. The velocity of sound is 320 m/s. The number of beats heard by the person in one second will be :

The appearance of colour in solid alkali metal halides is generally due to:

Complete reduction of benzene-diazonium chloride with Zn/HCl gives:

Which of the following statements about Na₂O₂ is not correct ?

In allene (C₃H₄), the type(s) of hybridization of the carbon atoms is (are):

In the reaction of formation of sulphur trioxide by contact process  the rate of reaction was measured as  The rate of reaction in terms of [SO₂] in mol L^–1s–1 will be

Based on the equation
 
the wavelength of the light that must be absorbed to excite hydrogen electron from level n = 1 to level n = 2 will be (h = 6.625 × 10^–34 Js, C = 3 × 10⁸ ms^–1)

Given :-
Fe³⁺(aq) + e^- → Fe²⁺ (aq); E° = +0.77 V
Al³⁺(aq) + 3e^- → Al (s); E° = -1.66 V
Br₂(aq) + 2e^- → 2Br^- ; E° = + 1.09 V
Considering the electrode potentials, which of the following represents the correct order of reducing power?

Consider the following equilibrium ​White precipitate of AgCl appears on adding which of the following?

Tischenko reaction is a modification of

Which one of the following does not have a pyramidal shape?

The following reaction 

is known as

Chlorobenzne reacts with trichloro acetaldehyde in the presence of H₂SO₄ 

The major product formed is

Shapes of certain interhalogen compounds are stated below. Which one of them is not correctly stated?

Which one of the following statements is not correct?

Which of the following series correctly represents relations between the elements from X to Y?

Which of the following statement s about the depletion of ozone layer is correct?

The initial volume of a gas cylinder is 750.0 mL. If the pressure of gas inside the cylinder changes from 840.0 mm Hg to 360.0 mm Hg, the final volume the gas will be

If λ₀ and λ be threshold wavelength and wavelength of incident light, the velocity of photoelectron ejected from the metal surface is:

Which one of the following is used as Antihistamine?

The molar heat capacity (C_p) of CD₂O is 10 cals at 1000 K. The change in entropy associated with cooling of 32 g of CD₂O vapour from 1000 K to 100 K at constant pressure will be (D = deuterium, at. mass = 2u)

The gas liberated by the electrolysis of Dipotassium succinate solution is

Which of the following name formula combinations is not correct?

For the reaction, 2N₂O₅ → 4NO₂ + O₂, the rate equation can be expressed in two ways  k and k' are related as

An organic compound A, C₅H₈O; reacts with H₂O, NH₃ and CH₃COOH as described below:

A is

A gaseous compound of nitrogen and hydrogen contains 12.5%(by mass) of hydrogen. The density of the compound relative to hydrogen is 16. The molecular formula of the compound is :

Assuming that the degree of hydrolysis is small, the pH of 0.1 M solution of sodium acetate (K_a = 1.0 × 10^–5) will be

The reagent needed for converting  is

Consider the coordination compound, [Co(NH₃)₆]Cl₃.  In the formation of this complex, the species which acts as the Lewis acid is:

The correct order of bond dissociation energy among N₂, O₂, O₂^– is shown in which of the following arrangements?

In some solutions, the concentration of H₃O⁺ remains constant even when small amounts of strong acid or strong base are added to them. These solutions are known as:-

If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(X), the mean of variable X, is

The integral  is equal to

Let f be an odd function defined on the set of real numbers such that for x ≥ 0,
f(x) = 3sinx + 4cosx
Then f(x) at 

The plane containing the line  and parallel to the line  passes through the point

The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius = √3 is

The proposition ~(pv~q)v~ (pvq) is logically equivalent to

If the general solution of the differential equation for some function is given by y ln |cx| = x, where c is an arbitrary constant, then (2) is equal to

For the curve y = 3 sinθ cosθ , x = e^θsinθ, 0 ≤ θ  ≤ π, the tangent is parallel to x-axis when θ is

 is equal to

Let f(x) = x|x|, g(x) = sinx and h(x) = (gof)(x). Then

A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that x∈A is

 then k is equal to

Let P(3secθ, 2tanθ) and Q(3secφ, 2tanφ) where θ + φ = π/2 be two distinct points on the hyperbola Then the ordinate of the point of intersection of the normals at P and Q is

In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is

Let A {2, 3, 5}, B (– 1, 3, 2) and C(λ, 5, μ) be the vertices of a ΔABC. If the median through A is equally inclined to the coordinate axes, then

The set of all real values of λ for which exactly two common tangents can be drawn to the circles
x² + y² - 4x - 4y + 6 = 0
and x² + y² - 10x - 10y + λ = 0 is the interval

If z₁, z₂ and z₃, z₄ are 2 pairs of complex conjugate numbers, then 

If 2cosθ + sinθ =  then 7cosθ + 6sinθ is equal to

An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is :

The coefficient of x⁵⁰ in the binomial expansion of
(1 + x)¹⁰⁰⁰ + x(1 + x)⁹⁹⁹ + x²(1 + x)⁹⁹⁸ + ......... + x¹⁰⁰⁰  is

Let L₁ be the length of the common chord of the curves x² + y² = 9 and y² = 8x, and L₂ be the length of the latus rectum of y² = 8x then

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be α. After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to β. Then the height (in metres) of the tower is

Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120°. At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr)

If α and β are roots of the equation  for some k, and α² + β² = 66, then α³ + β³ is equal to

Let for i = 1, 2, 3 p_i(x) be a polynomial of degree 2 in x, p_i'(x) and p_i''(x) be the first and second order derivatives of p_i(x) respectively.

and B(x) = [A(x)]^TA(x). Then determinant of B(x)

The sum of the first 20 terms common between the series 3 + 7 +11 +15 +.....and 1 + 6 + 11 +16 +....., is :

 then a value of 

Let A be a 3 × 3 matrix such that
 
Then A^–1 is

A stair-case of length l rests against a vertical wall and a floor of a room,. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio 1 : 2. If the stair-case begins to slide on the floor, then the locus of P is :

The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is :