**JEE MAIN OFFLINE EXAM 04.04.2015**

**SET-A**

**PHYSICS**

1. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first?

(Assume stones do not rebound after hitting the ground and neglect air resistance, take g=10 m/s^{2})

(The figures are schematic and not drawn to scale)

(1)

(2)

(3)

(4)

2. The period of oscillation of a simple pendulum is Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of g is :

(1) 2%

(2) 3%

(3) 1%

(4) 5%

3.

Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is :

(1) 100 N

(2) 80 N

(3) 120 N

(4) 150 N

4. A particle of mass m moving in the x direction with speed 2υ is hit by another particle of mass 2m moving in the y direction with speed υ. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to :

(1) 44%

(2) 50%

(3) 56%

(4) 62%

**Answer: (3)**

5. Distance of the centre of mass of a solid uniform cone from its vertex is z_{0}^{.} If the radius of its base is R and its height is h then z_{0} is equal to :

(1)

(2)

(3)

(4)

6. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is :

(1)

(2)

(3)

(4)

7. From a solid sphere of mass M and radius R, a spherical portion of radius is removed, as shown in the figure. Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is :

(G = gravitational constant)

(1)

(2)

(3)

(4)

8. A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to T_{M}^{.} If the Young’s modulus of the material of the wire is Y then is equal to :

(g = gravitational acceleration)

(1)

(2)

(3)

(4)

9. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume and pressure If the shell now undergoes an adiabatic expansion the relation between T and R is :

(1)

(2)

(3)

(4)

10. A solid body of constant heat capacity 1 J/°C is being heated by keeping it in contact with reservoirs in two ways :

(i) Sequentially keeping in contact with 2 reservoirs such that reservoir supplies same amount of heat.

(ii) Sequentially keeping in contact with 8 reservoirs such that reservoir supplies same amount of heat.

In both the cases body is brought from initial temperature 100°C to final temperature 200°C. Entropy change of the body in the two cases respectively is :

(1) In2, 4In2

(2) In2, In2

(3) In2, 2In2

(4) 2In2, 8In2

11. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as V^{q}, where V is the volume of the gas. The value of q is :

(1)

(2)

(3)

(4)

12. For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly?

(graphs are schematic and not drawn to scale)

(1)

(2)

(3)

(4)

13. A train is moving on a straight track with speed 20 ms^{−}^{1}. It is blowing its whistle at the frequency heard by a person standing near the track as the train passes him is (passed of sound = 320 ms^{−}^{1}) close to :

(1) 6%

(2) 12%

(3) 18%

(4) 24%

14. A long cylindrical shell carries positive surface charge σ in the upper half and negative surface charge – σ in the lower half. The electric field lines around the cylinder will look like figure given in :

(figures are schematic and not drawn to scale)

(1)

(2)

(3)

(4)

15. A uniformly charged solid sphere of radius R has potential V_{0} (measured with respect to ∞) on its surface. For this sphere the equipotential surfaces with potentials have radius R_{1}, R_{2}, R_{3} and R_{4} Then

(1)

(2)

(3)

(4)

16. In the given circuit, charge Q_{2} on the 2μF capacitor changes as C is varied from 1μF to 3μ Q_{2} as a function of ‘C’ is given properly by : (figures are drawn schematically and are not to scale)

(1)

(2)

(3)

(4)

17. When 5V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is 2.5×10^{−}^{4 }ms^{−}^{1}. If the electron density in the wire is 8×10^{28} m^{−}^{3}, the resistivity of the material is close to :

(1)

(2)

(3)

(4)

18.

In the circuit shown, the current in the 1Ω resistor is :

(1) 1.3 A, from P to Q

(2) 0A

(3) 0.13 A, from Q to P

(4) 0.13 A, from P to Q

19. Two coaxial solenoids of different radii carry current I in the same direction. Let be the magnetic force on the outer solenoid due to the inner one. Then :

(1)

(2) is radially inwards and is radially outwards

(3) is radially inwards and

(4) is radially outwards and

20.

Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making as angle ‘θ’ with the vertical. If wires have mass λ per unit length then the value of I is :

(g = gravitational acceleration)

(1)

(2)

(3)

(4)

21. A rectangular loop of sides 10 cm and 5 cm carrying a current 1 of 12 A is placed in different orientations as shown in the figures below :

(a)

(b)

(c)

(d)

If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?

(1) (a) and (b), respectively

(2) (a) and (c), respectively

(3) (b) and (d), respectively

(4) (b) and (c), respectively

22. An introductory (L = 0.03H) and a resistor (R = 0.15 kΩ) are connected in series to a battery of 15V EMF in a circuit shown below. The key K_{1} has been kept closed for a long time. Then at t=0, K_{1} is opened and key K_{2} is closed simultaneously. At t=1ms, the current in the circuit will be : (e^{5}≅150)

(1) 100 mA

(2) 67 mA

(3) 6.7 mA

(4) 0.67 mA

23. A red LED emits light at 0.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is :

(1) 1.73 V/m

(2) 2.45 V/m

(3) 5.48 V/m

(4) 7.75 V/m

24. Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ, a ray, incident at an angle θ, on the face AB would get transmitted through the face AC of the prism provided :

(1)

(2)

(3)

(4)

25. On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens’ principle leads us to conclude that as it travels, the light beam :

(1) become narrower

(2) goes horizontally without any deflection

(3) bends downwards

(4) bends upwards

26. Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is :

(1) 1 μm

(2) 30 μm

(3) 100 μm

(4) 300 μm

27. As an electron makes a transition from an excited state to the ground state of a hydrogen – like atom/ion :

(1) Its kinetic energy increases but potential energy and total energy decrease

(2) Kinetic energy, potential energy and total energy decrease

(3) Kinetic energy decreases, potential energy increases but total energy remains same

(4) Kinetic energy and total energy decrease but potential energy increases

28. Match **List – I **( Fundamental Experiment) with **List-II **(its conclusion) and select the correct option from the choices given below the list :

(1)(A) – (i) (B) – (iv) (C) – (iii)

(2) (A) – (ii) (B) – (iv) (C) – (iii)

(3)(A) – (ii) (B) – (i) (C) – (iii)

(4) (A) – (iv) (B) – (iii) (C) – (ii)

29. A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is/are :

(1) 2MHz only

(2)2005 kHz, and 1995 kHz

(3) 2005 kHz, 2000 kHz and 1995 kHz

(4) 2000 kHz and 1995 kHz

30. An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to Q_{0} and then connected to the L and R as shown below :

If a student plots graphs of the square of maximum charge on the capacitor with time(t) for two different values L_{1} and L_{2} (L_{2}>L_{2}) of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)

(1)

(2)

(3)

(4)

**CHEMISTRY**

1. The molecular formula of a commercial resin used for exchanging ions in water softening is C_{8}H_{7}SO_{3}Na (Mol. Wt. 206). What would be the maximum uptake of Ca^{2+} ions by the resin when expressed in mole per gram resin?

(1)

(2)

(3)

(4)

2. Sodium metal crystallizes in a body centered cubic lattice with a unit cell edge of 4.29Å. The radius of sodium atom is approximately:

(1)

(2)

(3)

(4)

3. Which of the following is the energy of a possible excited state of hydrogen?

(1) +13.6 eV

(2) −6.8 eV

(3) −3.4 eV

(4) +6.8 eV

4. The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is:

(1) ion – ion interaction

(2) ion – dipole interaction

(3) London force

(4) hydrogen bond

5. The following reaction is performed at 298 K.

2NO(g) + O_{2}(g) ⇌ 2NO_{2}(g)

The standard free energy of formation of NO(g) is 86.6 kj/mol at 298 K. What is the standard free energy of formation of NO_{2}(g) at 298 K? (K_{p} = 1.6×10^{12})

(1)

(2)

(3)

(4)

6. The vapour pressure of acetone at 20°C is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at 20°C, its vapour pressure was 183 torr. The molar mass (g mol^{−}^{1}) of the substance is:

(1) 32

(2) 64

(3) 128

(4) 488

7. The standard Gibbs energy change at 300 K for the reaction 2A ⇌ B+C is 2494.2 J. At a given time, the composition of the reaction mixture is [A] =1/2, [B] = 2 and [C] =1/2. The reaction proceeds in the : [R =8.314 J/K/mol, e=2.718]

(1) forward direction because

(2) reserve direction because

(3) forward direction because

(4) reserve direction because

8. Two Faraday of electricity is passed through a solution of CuSO_{4}. The mass of copper deposited at the cathode is : (at.mass of Cu = 63.5 amu)

(1) 0 g

(2) 63.5 g

(3) 2 g

(4) 127 g

9. Higher order (>3) reactions are rare due to :

(1) Low probability of simultaneous collision of all the reacting species

(2) Increase in entropy and activation energy as more molecules are involved

(3) Shifting of equilibrium towards reactants due to elastic collisions

(4) Loss of active species on collision

10. 3 g of activated charcoal was added to 50 mL of acetic acid solution (0.06N) in a flask. After an hour it was filtered and the strength of the filterate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram of charcoal) is :

(1) 18 mg

(2) 36 mg

(3) 42 mg

(4) 54 mg

11. The ionic radii (in Å ) of N^{3}^{−}, O^{2}^{−} and F^{−} are respectively :

(1) 1.36, 1.40 and 1.71

(2) 1.36, 1.71 and 1.40

(3) 1.71, 1.40 and 1.36

(4) 1.71, 1.36 and 1.40

12. In the context of the Hall – Heroult process for the extraction of Al, which of the following statements is false?

(1) are produced in this process

(2) is mixed with which lowers the melting point of the mixture and brings conductivity

(3) is reduced at the cathode to from Al

(4) serves as the electrolyte

13. From the following statements regarding H_{2}O_{2}, choose the incorrect statement :

(1) It can act only as an oxidizing agent

(2) It decomposes on exposure to light

(3) It has to be stored in plastic or wax lined glass bottles in dark

(4) It has to be kept away dust

14. Which one of the following alkaline earth metal sulphates has its hydration enthalpy greater than its lattice enthalpy?

(1)

(2)

(3)

(4)

15. Which among the following is the most reactive?

(1)

(2)

(3)

(4)

16. Match the catalysts to the correct processes :

**Catalyst Process**

(A) TiCl_{3} (i) Wacker process

(B) PdCl_{2} (ii) Ziegler – Natta polymerization

(C) CuCl_{2} (iii) Contact process

(D) V_{2}O_{5} (iv) Deacon’s process_{ }

(1) (A) – (iii), (B) – (ii), (C) – (iv), (D) – (i)

(2) (A) – (ii), (B) – (i), (C) – (iv), (D) – (iii)

(3) (A) – (ii), (B) – (iii), (C) – (iv), (D) – (i)

(4) (A) – (iii), (B) – (i), (C) – (ii), (D) – (iv)

17. Which one has the highest boiling point?

(1) He

(2) Ne

(3) Kr

(4) Xe

18. The number of geometric isomers that can exist for square planar [Pt (Cl) (py) (NH_{3}) (NH_{2}OH)]^{+} is (py = pyridine) :

(1) 2

(2) 3

(3) 4

(4) 6

19. The color of KMnO_{4} is due to :

(1) M → L charge transfer transition

(2) d – d transition

(3) L → M charge transfer transition

(4) σ – σ^{*} transition

20. Assertion : Nitrogen and Oxygen are the main components in the atmosphere but these do not react to from oxides of nitrogen.

Reason : The reaction between nitrogen and oxygen requires high temperature.

(1) Both assertion and reason are correct, and the reason is the correct explanation for the assertion

(2) Both assertion and reason are correct, but the reason is not correct explanation for the assertion

(3) The assertion is incorrect, but the reason is correct

(4) Both the assertion and reason are incorrect

21. In Carious method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is :

(at. Mass Ag = 108; Br =80)

(1) 24

(2) 36

(3) 48

(4) 60

22. Which of the following compounds will exhibit geometrical isomerism?

(1) 1 – Phenyl – 2 – butane

(2) 3 – Phenyl – 1 – butane

(3) 2 – Phenyl – 1 – butane

(4) 1, 1 – Biphenyl – 1 – propane

23. Which compound would give 5 – keto – 2 – methyl hexanal upon ozonolysis?

(1)

(2)

(3)

(4)

24. The synthesis of alkyl fluorides is best accomplished by :

(1) Free radical fluorination

(2) Sandmeyer’s reaction

(3) Finkelstein reaction

(4) Swarts reaction

26. In the reaction

the product E is :

(1)

(2)

(3)

(4)

27. Which polymer is used in the manufacture of plaints and lacquers?

(1) Bakelite

(2) Glyptal

(3) Polypropene

(4) Poly vinyl chloride

28. Which of the vitamins given below is water soluble?

(1) Vitamin C

(2) Vitamin D

(3) Vitamin E

(4) Vitamin K

29. Which of the following compounds is not an antacid?

(1) Aluminum hydroxide

(2) Cimetidine

(3) Phenelzine

(4) Ranitidine

30. Which of the following compounds is not colored yellow?

(1)

(2)

(3)

(4)

**MATHEMATICS**

1. Let A and B be two sets containing four and two elements respectively. Then the number of subjects of the set A X B, each having at least three elements is :

(1) 219

(2) 256

(3) 275

(4) 510

2. A complex number z is said to be unimodular if |z| = 1. Suppose z_{1} and z_{2} are complex numbers such that is unimodular and z_{2} is not unimodular. Then the point z_{1} lines on a :

(1) Straight line parallel to x-axis.

(2) Straight line parallel to y-axis.

(3) Circle of radius 2.

(4) Circle of radius √2.

3. Let α and β be the roots of equation x^{2} – 6x – 2 = 0. If a_{n} =α^{n} – β^{n}, for n≥1, then the value of is equal to :

(1) 6

(2) −6

(3) 3

(4) −3

4. If is a matrix satisfying the equation AA^{T} = 91, where I is 3X3 identity matrix, then the ordered pair (a,b) is equal to :

(1) (2, −1)

(2) (−2, 1)

(3) (2, 1)

(4) (−2, −1)

5. The set of all values of λ for which the system of linear equations :

2x_{1} – 2x_{2} + x_{3} = λx_{1}

2x_{1} –3x_{2} +2 x_{3} = λx_{2}

−x_{1 }+ 2x_{2} = λx_{3}

has a non-trivial solution,

(1) is an empty set.

(2) is a singleton.

(3) contains two elements.

(4) contains more than two elements.

6. The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is :

(1) 216

(2) 192

(3) 120

(4) 72

7. The sum of coefficients of integral powers of x in the binomial expansion of is :

(1)

(2)

(3)

(4)

8. If m is the A.M. of the two distinct real numbers l and n (l, n>1) and G_{1}, G_{2} and G_{3} are three geometric means between l and n then equals.

(1)

(2)

(3)

(4)

9. The sum of first 9 terms of the series is :

(1) 71

(2) 96

(3) 142

(4) 192

10. is equal to :

(1) 4

(2) 3

(3) 2

(4) 1/2

11. If function,

is differentiable, then the value of k+m is :

(1) 2

(2) 16/5

(3) 10/3

(4) 4

12. The normal to the curve, x^{2}+2xy−3y^{2}=0, at (1,1) :

(1) Does not meet the curve again.

(2) Meets the curve again in the second quadrant.

(3) Meets the curve again in the third quadrant.

(4) Meets the curve again in the fourth quadrant.

13. Let f(x) be a polynomial of degree four having extreme values at x=1 and x=2.

If then f(2) is equal to :

(1) −8

(2) −4

(3) 0

(4) 4

14. The integral equals :

(1)

(2)

(3)

(4)

15. The integral

is equal to :

(1) 2

(2) 4

(3) 1

(4) 6

16. The area (in sq. units) of the region described by {(x,y) : y^{2 }≤ 4x – 1} is :

(1)

(2)

(3)

(4)

17. Let y(x) be the solution of the differential equation (x log x) log x, (x ≥ 1). Then y(e) is equal to :

(1) e

(2) 0

(3) 2

(4) 2e

18. The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with verticles (0, 0), (0, 41) and (41, 0), is :

(1) 901

(2) 861

(3) 820

(4) 780

19. Locus of the image of the point (2, 3) in the line (2x −3y+4) +k (x−2y+3) = 0, k ε **R, **is a :

(1) Straight line parallel to x-axis.

(2) Straight line parallel to y-axis.

(3) Circle of radius √2.

(4) Circle of radius √3.

20. The number of common tangents to the circles x^{2} + y^{2} −4x −6y – 12 = 0 and x^{2} + y^{2} + 6x +18y +26 = 0, is :

(1) 1

(2) 2

(3) 3

(4) 4

21. The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse is :

(1)

(2)

(3)

(4)

22. Let O be the vertex and Q be any point on the parabola, x^{2} =8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

(1)

(2)

(3)

(4)

23. The distance of the point (1, 0, 2) from the point of intersection of the line and the plane x−y+z = 16, is :

(1) 2√14

(2) 8

(3) 3√21

(4) 13

24. The equation of the plain containing the line 2x – 5y + z = 3; x+y+4z = 5, and parallel to the plane, x+3y+6z = 1, is :

(1) 2x+6y+12z = 13

(2) x+3y+6z = −7

(3) x +3y+6z = 7

(4) 2x + 6y +12z = −13

25. Let be three non-zero vectors such that no two of them are collinear and . If θ is the angle between vectors , then a value of sin θ is :

(1)

(2)

(3)

(4)

26. If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes, then the probability that one of the boxes contains exactly 3 balls is :

(1)

(2)

(3)

(4)

27. The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

(1) 16.8

(2) 16.0

(3) 15.8

(4) 14.0

28. If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60° respectively, then the ratio, AB : BC, is :

(1)

(2)

(3)

(4)

29. Let tan^{−}^{1}y = tan^{−}^{1} x + tan^{−}^{1 } where Then a value of y is :

(1)

(2)

(3)

(4)

30. The negation of ~ s ∨ ( ~ r ∧ s) is equivalent to :

(1) s ∧ ~ r

(2) s ∧ (r ∧ ~ s)

(3) s ∨ (r ∨ ~ s)

(4) s ∧ r

**Latest Govt Job & Exam Updates:**