JEE Main 2010 Paper -1 with Solutions - JEE MCQ

A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the
clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength
B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is

A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tan θ > μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P₁ = mg(sinθ − μ cosθ) to

P₂ = mg(sinθ + μ cosθ), the frictional force f versus P graph will look like

A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is

Consider a thin square sheet of side L and thickness t, made of a material of resistivity ρ. The resistance
between two opposite faces, shown by the shaded areas in the figure is

A real gas behaves like an ideal gas if its

SECTION – II (Multiple Correct Choice Type)

This section contains 5 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONE OR MORE may be correct. Partially correct answers will be not be awarded any marks.

Q.  A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg
mass reverses its direction and moves with a speed of 2 ms⁻¹. Which of the following statement(s) is (are)
correct for the system of these two masses?

One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is P₀. Choose the correct option(s) from the following

A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He
uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this
observation, which of the following statement(s) is (are) true?

A few electric field lines for a system of two charges Q₁ and Q₂ fixed at two different points on the x-axis are shown in the figure. These lines suggest that 

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60° (see figure). If the refractive index of the material of the prism is , which of the following is (are) correct?

SECTION –III (Paragraph Type)
This section contains 2 paragraphs. Based upon the first paragraph 2 multiple choice questions and based upon the second paragraph 3 multiple choice questions have to be answered. Each of these questions has four choices A), B), C) and D) out of WHICH ONLY ONE CORRECT.

Paragraph for Questions 14 to 15

Q. Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature T_c(0). An interesting property of superconductors is that their critical temperature becomes smaller than T_c(0) if they are placed in a magnetic field, i.e., the critical temperature T_c(B) is a function of the magnetic field strength B. The dependence of T_c(B) on B is shown in the figure. 

Q. In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for
two different magnetic fields B₁ (solid line) and B₂ (dashed line). If B₂ is larger than B₁ which of the following graphs shows the correct variation of R with T in these fields?

Paragraph for Questions 14 to 15

Q. Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature T_c(0). An interesting property of superconductors is that their critical temperature becomes smaller than T_c(0) if they are placed in a magnetic field, i.e., the critical temperature T_c(B) is a function of the magnetic field strength B. The dependence of T_c(B) on B is shown in the figure. 

Q. A superconductor has T_c (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its T_c decreases to
75 K. For this material one can definitely say that when

Paragraph for Questions 16 to 18

When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx² it performs simple harmonic motion. The corresponding time period is proportional to ,  as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx² and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx⁴ (α > 0) for |x| near the origin and becomes a constant equal to V₀ for |x| ≥ X₀ (see figure).

Q. If the total energy of the particle is E, it will perform periodic motion only if

Paragraph for Questions 16 to 18

When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx² it performs simple harmonic motion. The corresponding time period is proportional to ,  as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx² and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx⁴ (α > 0) for |x| near the origin and becomes a constant equal to V₀ for |x| ≥ X₀ (see figure).

Q. For periodic motion of small amplitude A, the time period T of this particle is proportional to

Paragraph for Questions 16 to 18

When a particle of mass m moves on the x-axis in a potential of the form V(x) = kx² it performs simple harmonic motion. The corresponding time period is proportional to ,  as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x = 0 in a way different from kx² and its total energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x-axis. Its potential energy is V(x) = αx⁴ (α > 0) for |x| near the origin and becomes a constant equal to V₀ for |x| ≥ X₀ (see figure).

Q. The acceleration of this particle for |x| > X₀ is

SECTION –IV (Integer Type)

This section contains TEN questions. The answer to each question is a single digit integer ranging from 0 to 9. 

Enter only the numerical value in the space provided below.

Q. Gravitational acceleration on the surface of a planet is  where g is the gravitational acceleration on
the surface of the earth. The average mass density of the planet is  times that of the earth. If the escape
speed on the surface of the earth is taken to be 11 kms^-1, the escape speed on the surface of the planet in
kms^-1 will be

A piece of ice (heat capacity = 2100 J kg^-1 °C^-1 and latent heat = 3.36 ×105J kg^-1) of mass m grams is at
-5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the
ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat
exchange in the process, the value of m is

A stationary source is emitting sound at a fixed frequency f₀, which is reflected by two cars approaching the
source. The difference between the frequencies of sound reflected from the cars is 1.2% of f₀. What is the
difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant
speeds much smaller than the speed of sound which is 330 ms^-1.

The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in
front of it to 50 cm, the magnification of its image changes from m25 to m50. The ratio

An α- particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de
Broglie wavelengths are λ_α and λ_p respectively. The ratio , to the nearest integer, is

When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R, the
rate of heat produced in R is J₁. When the same batteries are connected in parallel across R, the rate is J₂.
If J₁ = 2.25 J₂ then the value of R in Ω is

Two spherical bodies A (radius 6 cm ) and B(radius 18 cm ) are at temperature T₁ and T₂, respectively.
The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm.
Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that
of B?

When two progressive waves y₁ = 4 sin(2x - 6t) and  are superimposed, the
amplitude of the resultant wave is

A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its crosssectional area is 4.9 × 10^-7 m². If the mass is pulled a little in the vertically downward direction and
released, it performs simple harmonic motion of angular frequency 140 rad s⁻¹. If the Young’s modulus of
the material of the wire is n × 10⁹ Nm^-2, the value of n is

A binary star consists of two stars A (mass 2.2M_s) and B (mass 11M_s), where M_s is the mass of the sun.
They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio
of the total angular momentum of the binary star to the angular momentum of star B about the centre of
mass is

SECTION – I (Single Correct Choice Type)

This Section contains 8 multiple choice questions. Each question has four choices A), B), C) and D) out of which ONLY ONE is correct.

Q. The synthesis of 3 – octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an
alkyne. The bromoalkane and alkyne respectively are

The correct statement about the following disaccharide is