Solved papers for JEE Main & Advanced JEE Main Solved Paper-2015
done JEE Main Solved Paper-2015 Total Questions - 90
question_answer1) 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 :
[JEE Main Solved Paper-2015 ]
question_answer2) 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 1m from the diode is :
[JEE Main Solved Paper-2015 ]
question_answer3) 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 change to \[{{T}_{M}}.\]If the Young's modulus of the material of the wire is Y then\[\frac{1}{Y}\]is equal to : (g = gravitational acceleration)
[JEE Main Solved Paper-2015 ]
question_answer4) 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? (graph are schematic and not drawn to scale)
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question_answer5) A train is moving on a straight track with speed \[20m{{s}^{-1}}.\]. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound \[=320m{{s}^{-1}}\] ) close to
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question_answer6) When 5V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons \[2.5\times {{10}^{-4}}m{{s}^{-1}}.\]If the electron density in the wire is \[8\times {{10}^{28}}{{m}^{-3}},\]the resistivity of the material is close to
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question_answer7) 4 Two long current carrying thin wires, both with current I, and held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle \['\theta '\] with the vertical. If wires have mass \[\lambda \]per unit length then the value of I is : (g = gravitational acceleration)
[JEE Main Solved Paper-2015 ]
question_answer9) 5 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
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question_answer10) An inductor (L = 0.03 H) and a resistor \[(R=0.15k\Omega )\]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 : \[\left( {{e}^{5}}\cong 150 \right)\]
[JEE Main Solved Paper-2015 ]
question_answer11) 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 \[\left( Q_{Max}^{2} \right)\]on the capacitor with time (t) for two different values \[{{L}_{1}}\] and \[{{L}_{2}}\] \[\left( {{L}_{1}}>{{L}_{2}} \right)\]of L then which of the following represents this graph correctly ? (plots are schematic and not drawn ot scale)
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question_answer12) In the given circuit, charge \[{{Q}_{2}}\] on the \[2\mu F\] capacitor changes as C is varied from \[1\mu F\] to \[3\mu F.{{Q}_{2}}\] as a function of 'C' is given properly by : (figures are drawn schematically and are not to scale)
[JEE Main Solved Paper-2015 ]
question_answer13) 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 :
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question_answer14) The period of oscillation of a simple pendulum is \[T=2\pi \sqrt{\frac{L}{g}}.\]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 :
[JEE Main Solved Paper-2015 ]
question_answer15) 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 :
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question_answer16) 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 :
[JEE Main Solved Paper-2015 ]
question_answer17) A solid body of constant heat capacity \[1J/{}^\circ C\] is being heated by keeping it in contact with reservoirs in two ways : (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature \[100{}^\circ C\] to final temperature \[200{}^\circ C\]. Entropy change of the body in the two cases respectively is :
[JEE Main Solved Paper-2015 ]
question_answer18) 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\[u=\frac{U}{V}\propto {{T}^{4}}\]and pressure\[p=\frac{1}{3}\left( \frac{U}{V} \right).\]If the shell now undergoes an adiabatic expansion the relation between T and R is :
[JEE Main Solved Paper-2015 ]
question_answer19) Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 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 of the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s2) (The figure are schematic and not drawn to scale)
[JEE Main Solved Paper-2015 ]
question_answer20) A uniformly charged solid sphere of radius R has potential V0 (measured with respect to \[\infty \] ) on its surface. For this sphere the equipotential surfaces with potentials \[\frac{3{{V}_{0}}}{2},\frac{5{{V}_{0}}}{4},\frac{3{{V}_{0}}}{4}\]and \[\frac{{{V}_{0}}}{4}\]have radius \[{{R}_{1}},{{R}_{2}},{{R}_{3}}\] and\[{{R}_{4}}\] respectively. Then
[JEE Main Solved Paper-2015 ]
question_answer21) Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is \[\mu ,\] a ray, incident at an angle \[\theta ,\] on the face AB would get transmitted through the face AC of the prism provided.
[JEE Main Solved Paper-2015 ]
question_answer22) A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12A is placed in different orientations as shown in the figures below :
[JEE Main Solved Paper-2015 ]
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 eqilibrium?
question_answer23) Two coaxial solenoids of different radii carry current I in the same direction. Let \[{{\vec{F}}_{1}}\]be the magnetic force on the inner soleoid due to the outer one and \[{{\vec{F}}_{2}}\]be the magnetic force on the outer solenoid due to the inner one. Then :
[JEE Main Solved Paper-2015 ]
A)
\[{{\vec{F}}_{1}}\]is radially inwards and \[{{\vec{F}}_{2}}=0\]
doneclear
B)
\[{{\vec{F}}_{1}}\]is radially outwards and \[{{\vec{F}}_{2}}=0\]
doneclear
C)
\[{{\vec{F}}_{1}}={{\vec{F}}_{2}}=0\]
doneclear
D)
\[{{\vec{F}}_{1}}\]is radially inwards and \[{{\vec{F}}_{2}}\]is radially onwards
question_answer24) A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectely inelastic, the percentage loss in the energy during the collision is close to :
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question_answer25) Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molcules increases as \[{{V}^{q}},\] where V is the volume of the gas. The value of q is : \[\left( \gamma =\frac{{{C}_{p}}}{{{C}_{v}}} \right)\]
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question_answer26) From a solid sphere of mass M and radius R, a spherical portion of radius \[\frac{R}{2}\]is removed, as shown in the figure. Taking gravitional potential V = 0 at \[r=\infty ,\] the potential at the centre of cavity thus formed is: (G = gravitational constant)
[JEE Main Solved Paper-2015 ]
question_answer27) Given in the figure are two blocks A and B of weight 20 N and 100N respectively. There 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 :
[JEE Main Solved Paper-2015 ]
question_answer28) D / Physics A long cylinderal shell carries positive surface charge \[\sigma \] in the upper half and negative surface charge \[-\sigma \]in the lower half. The electric field lines around the cylinder will looke like figure given in : (Figures are schematic and not drawn to scale)
[JEE Main Solved Paper-2015 ]
question_answer29) As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom / ion:
[JEE Main Solved Paper-2015 ]
A)
kinetic energy decrease, potential energy increase but total energy remians same
doneclear
B)
kinetic energy and total energy decrease but potential energy increases
doneclear
C)
its kinetic energy increases but potential energy and total energy decrease
doneclear
D)
kinetic energy, potential energy and total energy decrease
question_answer30) Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choices given below the list :
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question_answer33) Which one of the following alkaline earth metal sulphates has its hydration enthalpy greater than its lattice enthalpy ?
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question_answer35) Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of \[4.29\overset{\text{o}}{\mathop{\text{A}}}\,\]. The radius of sodium atom is approximately :
[JEE Main Solved Paper-2015 ]
question_answer40) In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is false?
[JEE Main Solved Paper-2015 ]
A)
\[A{{l}^{3+}}\] is reduced at the cathode to form Al
doneclear
B)
\[N{{a}_{3}}Al{{F}_{6}}\] serves as the electrolyte
doneclear
C)
\[CO\] and \[C{{O}_{2}}\] are produced in this process
doneclear
D)
\[A{{l}_{2}}{{O}_{3}}\]is mixed with \[Ca{{F}_{2}}\] which lowers the melting point of the mixture and brings conductivity
question_answer41) In the following sequence of reactions : Toluene \[\xrightarrow[{}]{KMn{{O}_{4}}}A\xrightarrow[{}]{SOC{{l}_{2}}}B\xrightarrow[BaS{{O}_{4}}]{{{H}_{2}}/Pd}C,\]the product C is:
[JEE Main Solved Paper-2015 ]
question_answer45) The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is:
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question_answer46) The molecular formula of a commercial resin used for exchanging ions in water softening is \[{{C}_{8}}{{H}_{7}}S{{O}_{3}}Na\] (Mol. wt. 206). \[C{{a}^{2+}}\] ions by the resin when expressed in mole per gram resin ?
[JEE Main Solved Paper-2015 ]
question_answer47) Two Faraday of electricity is passed through a solution of \[CuS{{O}_{4}}.\] The mass of copper deposited at the cathode is : (at. mass of Cu = 63.5 amu)
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question_answer48) The number of geometric isomers that can exist for square planar \[{{\left[ Pt\left( Cl \right)\left( py \right)\left( N{{H}_{3}} \right)\left( N{{H}_{2}}OH \right) \right]}^{+}}\] is \[\text{(py}\,\text{=}\,\,\text{pyridine):}\]
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question_answer49) Carius 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)
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question_answer52) 3g of activated charcoal was added to 50mL acetic solution (0.06N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram charcoal) is :
[JEE Main Solved Paper-2015 ]
question_answer53) The vapour pressure of acetone at 200C is 185 torr. When 1.2 g of a non ? volatile substance was dissolved in 100 g of acetone at 200C, its vapour pressure was 183 torr. The molar mass (g mol?1) of the substance is
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question_answer55) The standard Gibbs energy change at 300K for the reaction \[2AB+C\]At a given time, the composition of the reaction mixture is\[\left[ A \right]=\frac{1}{2},\left[ B \right]=2\]and \[\left[ C \right]=\frac{1}{2}.\] The reaction proceeds in the : \[[R=8.314J/Kmol,e=2.718]\]
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question_answer56) Assertion : Nitrogen and oxygen are the main components in the atmosphere but these do not react to form oxides of nitrogen. Reason : The reaction between nitrogen and oxygen requires high temperature.
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A)
The assertion is incorrect, but the reason is correct
doneclear
B)
Both the assertion and reason are incorrect
doneclear
C)
Both assertion and reason are correct, and the reason is the correct explanation for the assertion
doneclear
D)
Both assertion and reason are correct, but reason is not the correct explanation for the assertion
question_answer59) The following reaction is performed at \[298K.2NO(g)+{{O}_{2}}2N{{O}_{2}}(g)\] 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 \[N{{O}_{2}}(g)\] at 298K? \[\left( {{K}_{p}}=1.6\times {{10}^{12}} \right)\]
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question_answer61) Let\[\vec{a},\vec{b}\]and\[\vec{c}\]be three non - zero vectors such that no two of them are collinear and\[\left( \vec{a}\times \vec{b} \right)\times \vec{c}=\frac{1}{3}\left| {\vec{b}} \right|\left| {\vec{c}} \right|\vec{a}.\]If \[\theta \]is the angle between vectors \[\vec{b}\]and \[\vec{c},\]then a value of \[\sin \theta \]is :
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question_answer62) 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 locus of P is :
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question_answer63) 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 300, 450 and 600 respectively, then the ratio, AB : BC, is :
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question_answer64) The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices \[\left( 0,0 \right),\left( 0,41 \right)\] and \[\left( 41,0 \right),\] is
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question_answer65) The equation of the plane containing the line \[2x-5y+z=3;x+y+4z=5,\] and parallel to the plane, \[x+3y+6z=1,\] is :
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question_answer66) Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set \[A\times B,\] each having at least three elements is :
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question_answer68) The distance of the point \[\left( 1,0,2 \right)\]from the point of intersection of the line \[\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\]and the plane \[x-y+z=16,\] is :
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question_answer69) The sum of coefficients of integral powers of x in the binomial expansion of \[{{\left( 1-2\sqrt{x} \right)}^{50}}\]is
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question_answer70) The sum of first 9 terms of the series\[\frac{{{1}^{3}}}{1}+\frac{{{1}^{3}}+{{2}^{3}}}{1+3}+\frac{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}{1+3+5}\]...............is:
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question_answer72) The set of all values of \[\lambda \]for which the system of linear equations: \[2{{x}_{1}}-2{{x}_{2}}+{{x}_{3}}=\lambda {{x}_{1}}\] \[2{{x}_{1}}-3{{x}_{2}}+2{{x}_{3}}=\lambda {{x}_{2}}\] \[-{{x}_{1}}+2{{x}_{2}}=\lambda {{x}_{3}}\]has a non- trivial solution,
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question_answer73) A complex number z is said to be unimodular if \[\left| z \right|=1.\]Suppose \[{{z}_{1}}\] and \[{{z}_{2}}\] are complex numbers such that \[\frac{{{z}_{1}}-2{{z}_{2}}}{2-{{z}_{1}}{{\overline{z}}_{2}}}\]is unimodular and \[{{z}_{2}}\] is not unimodular. Then the point \[{{z}_{1}}\] lies on a :
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question_answer74) The number of common tangents to the circles \[{{x}^{2}}+{{y}^{2}}-4x-6y-12=0\] and \[{{x}^{2}}+{{y}^{2}}+6y+18y+26=0,\] is
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question_answer75) The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8, without repetition is :
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question_answer76) Let y(x) be the solution of the differential equation \[\left( x\log x \right)\frac{dy}{dx}+y=2x\log x,(x\ge 1).\] The y (e)is equal to
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question_answer77) If \[A=\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \\ \end{matrix} \right]\]is a matrix satisfying the equation \[A{{A}^{T}}=9I,\] where I is \[3\times 3\] identity matrix, then the ordered pair (a,b) is equal to :
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question_answer78) ) If m is the A.M. of two distinct real numbers \[l\] and \[n\left( l,n>1 \right)\]and \[{{G}_{1}},{{G}_{2}}\]and \[{{G}_{3}}\] are three geometric means between \[l\] and n, then \[G_{1}^{4}+2G_{2}^{4}+G_{3}^{4}\]equals.
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question_answer80) The integral\[\int_{{}}^{{}}{\frac{dx}{{{x}^{2}}{{\left( {{x}^{4}}+1 \right)}^{{}^{3}/{}_{4}}}}}\]equals:
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question_answer82) Let \[{{\tan }^{-1}}y={{\tan }^{-1}}x+{{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right),\]where \[|x|<\frac{1}{\sqrt{3}}.\]Then a value of y is :
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question_answer83) If the function. \[g\left( x \right)=\left\{ \begin{align} & k\sqrt{x+1},\,\,\,\,\,\,0\le x\le 3 \\ & mx+2,\,\,\,\,\,\,\,\,3<x\le 5 \\ \end{align} \right.\]is differentiable, then the value of k + m is :
[JEE Main Solved Paper-2015 ]
question_answer84) 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:
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question_answer85) The integral \[\int\limits_{2}^{4}{\frac{\log {{x}^{2}}}{\log {{x}^{2}}+\log \left( 36-12x+{{x}^{2}} \right)}dx}\] is equal to :
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question_answer86) Let \[\alpha \] and \[\beta \] be the roots of equation \[{{x}^{2}}-6x-2=0.\] If \[{{a}_{n}}={{\alpha }^{n}}-{{\beta }^{n}},\] for \[n\ge 1,\] then the value \[\frac{{{a}_{10}}-2{{a}_{8}}}{2{{a}_{9}}}\]is equal to :
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question_answer87) Let f (x) be a polynomial of degree four having extreme values at x = 1 and x =2. If\[\underset{x\to 0}{\mathop{\lim }}\,\left( 1+\frac{f\left( x \right)}{{{x}^{2}}} \right)=3,\]then f(2) is equal to :
[JEE Main Solved Paper-2015 ]
question_answer88) The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse\[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{5}=1,\]is:
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question_answer89) If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :
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question_answer90) Locus of the image of the point \[\left( 2,3 \right)\]in the line\[\left( 2x-3y+4 \right)+k\left( x-2y+3 \right)=0,\]\[k\in R,\] is a :
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