JEE Main 2015 · 04 Apr 2015 · Offline

Q1.As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:

Q2.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 wrist watch of 1 s resolution. The accuracy in the determination of $g$ …

Q3.A long cylindrical 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 look like figure given in: (figures are schematic and not drawn to scale)

Q4.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:

Q5.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 …

Q6.An inductor ( $\mathrm{L}=0.03\mathrm{H}$ ) and a resistor ( $\mathrm{R}=0.15\mathrm{k}\Omega$ ) are connected in series to a battery of 15 V EMF in a circuit shown. The key ${\mathrm{K}}_1$ has been kept closed for a long time. Then at $\mathrm{t}=0,{\mathrm{K}}_1$ is opene …

Q7.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 ${\mathrm{T}}_{\mathrm{M}}$. If the Young's modulus of the material of the wire is Y then $\frac{1}{\mathrm{Y}}$ is equal to: ( …

Q8.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:

Q9.Two coaxial solenoids of different radii carry current I in the same direction. Let ${\overrightarrow{\mathrm{F}}}_1$ be the magnetic force on the inner solenoid due to the outer one and ${\overrightarrow{\mathrm{F}}}_2$ be the magnetic force on the outer solenoid due to the inne …

Q10.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 ${\mathrm{V}}^{\mathrm{q}}$, where V is the volume of the gas. The value of q is : …

Q11.An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to ${\mathrm{Q}}_0$ and then connected to the L and R as shown.
If a student plots graphs of the square of maximum charge ( ${\mathrm{Q}}_{\text{max }}^2$ ) on the capacitor with time ( …

Q12.From a solid sphere of mass M and radius R , a spherical portion of radius $\mathrm{R}/2$ is removed, as shown in the figure. Taking gravitational potential $\mathrm{V}=0$ at $\mathrm{r}=\infty$, the potential at the centre of the cavity thus formed is ( $\mathrm{G}=$ gravitati …

Q13.A train is moving on a straight track with speed $20{\mathrm{ms}}^{-1}$. 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 $=320{\mathrm{ms}}^{-1}$) cl …

Q14.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 w …

Q15.Distance of the centre of mass of a solid uniform cone from its vertex is ${\mathrm{z}}_0$. If the radius of its base is R and its height is h then ${\mathrm{z}}_0$ is equal to :

Q16.A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below:

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 …

Q17.In the circuit shown, the current in the $1\Omega$ resistor is :

Q18.In the given circuit, charge ${\mathrm{Q}}_2$ on the $2\mu \mathrm{F}$ capacitor changes as C is varied from $1\mu \mathrm{F}$ to $3\mu \mathrm{F}$. ${\mathrm{Q}}_2$ as a function of 'C' is given properly by: (figures are drawn schematically and are not to scale)

Q19.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 perfectly inelastic, the percentage loss in the energy during the collision is close to

Q20.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:

Q21.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 :

Q22.Match List - I (Fundamental Experiment) with List - II (its conclusion) and select the correct option from the choices given below the list:

Q23.When 5 V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is $2.5\times 10^{-4}{\mathrm{ms}}^{-1}$. If the electron density in the wire is $8\times 10^{28}{\mathrm{m}}^{-3}$, the resistivity of the material is close to:

Q24.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)

Q25.Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of $10\mathrm{m}/\mathrm{s}$ and $40\mathrm{m}/\mathrm{s}$ respectively. Which of the following graph best represents the time variation of relative position of the second stone …

Q26.A solid body of constant heat capacity $1\mathrm{J}/{}^{\circ }\mathrm{C}$ 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 keep …

Q27.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:

Q28.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 an angle '$\theta$' with the vertical. If wires have mass $\lambda$ per unit length then the value of I is: ( …

Q29.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:

Q30.A uniformly charged solid sphere of radius R has potential V0 (measured with respect to infinity) on its surface. For this sphere the equipotential surfaces with potentials 3V0/2, 5V0/4, 3V0/4 and V0/4 have radius R1, R2, R3 and R4 respectively. Then: [options — see source PDF]

Q1.Which of the following is the energy of a possible excited state of hydrogen?

Q2.In the following sequence of reactions:

Toluene $\stackrel{{\mathrm{KMnO}}_4}{\to }$ A $\stackrel{{\mathrm{SOCl}}_2}{\to }$ B $\underset{{\mathrm{BaSO}}_4}{\overset{{\mathrm{H}}_2/\mathrm{Pd}}{\to }}$ C,

The product C is:

Q3.Which compound would give 5-keto-2-methyl hexanal upon ozonolysis?

Q4.The ionic radii (in $\mathring{A}$) of ${\mathrm{N}}^{3-}$, ${\mathrm{O}}^{2-}$ and ${\mathrm{F}}^{-}$ are respectively:

Q5.The color of ${\mathrm{KMnO}}_4$ is due to:

Q6.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.

Q7.Which of the following compounds is not an antacid?

Q8.In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is false?

Q9.Match the catalysts to the correct processes:

Catalyst
(A) ${\mathrm{TiCl}}_3$
(B) ${\mathrm{PdCl}}_2$
(C) ${\mathrm{CuCl}}_2$
(D) ${\mathrm{V}}_2{\mathrm{O}}_5$

Process
(i) Wacker process
(ii) Ziegler - Natta polymerization
(iii) Contact process
(iv) Deacon's process

Q10.In the reaction:

the product E is

Q11.Which polymer is used in the manufacture of paints and lacquers?

Q12.The number of geometric isomers that can exist for square planar ${\left[\mathrm{Pt}(\mathrm{Cl})(\mathrm{py})({\mathrm{NH}}_3)({\mathrm{NH}}_2\mathrm{OH})\right]}^{+}$ is (py = pyridine):

Q13.Higher order (>3) reactions are rare due to:

Q14.Which among the following is the most reactive?

Q15.Two Faraday of electricity is passed through a solution of ${\mathrm{CuSO}}_4$. The mass of copper deposited at the cathode is: (at. mass of $\mathrm{Cu}=63.5\mathrm{amu}$)

Q16.$3\mathrm{g}$ of activated charcoal was added to 50 mL of acetic acid solution ( 0.06 N ) 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 of charcoal) is:

Q17.The synthesis of alkyl fluorides is best accomplished by:

Q18.The molecular formula of a commercial resin used for exchanging ions in water softening is ${\mathrm{C}}_8{\mathrm{H}}_7{\mathrm{SO}}_3\mathrm{Na}$ (Mol. Wt. 206). What would be the maximum uptake of ${\mathrm{Ca}}^{2+}$ ions by the resin when expressed in mole per gram resin?

Q19.Which of the vitamins given below is water soluble?

Q20.The intermolecular interaction that is dependent on the inverse cube of distance between the molecule is:

Q21.The following reaction is performed at 298 K .
$2\mathrm{NO}(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\rightleftharpoons 2{\mathrm{NO}}_2(\mathrm{g})$
The standard free energy of formation of $\mathrm{NO}(\mathrm{g})$ is $86.6\mathrm{kJ}/\mathrm{mol}$ at 298 K . What is the …

Q22.Which of the following compounds is not colored yellow?

Q23.In 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 $\mathrm{Ag}=108;\mathrm{Br}=80)$

Q24.Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of $4.29\mathring{A}$. The radius of sodium atom is approximately:

Q25.Which of the following compounds will exhibit geometrical isomerism?

Q26.The vapour pressure of acetone at $20^{\circ }\mathrm{C}$ is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at $20^{\circ }\mathrm{C}$, its vapour pressure was 183 torr. The molar mass $(\mathrm{g}{\mathrm{mol}}^{-1})$ of the substance is:

Q27.From the following statements regarding ${\mathrm{H}}_2{\mathrm{O}}_2$, choose the incorrect statement:

Q28.Which one of the following alkaline earth metal sulphates has its hydration enthalpy greater than its lattice enthalpy?

Q29.The standard Gibbs energy change at 300 K for the reaction $2\mathrm{A}\rightleftharpoons \mathrm{B}+\mathrm{C}$ is 2494.2 J . At a given time, the composition of the reaction mixture is $[A]=\frac{1}{2},[B]=2$ and $[C]=\frac{1}{2}$. The reaction proceeds in the: [ …

Q30.Which one has the highest boiling point?

Q1.The sum of coefficients of integral powers of $x$ in the binomial expansion of $(1-2\sqrt{x}{)}^{50}$ is :

Q2.Let $\mathrm{f}(\mathrm{x})$ be a polynomial of degree four having extreme values at $\mathrm{x}=1$ and $\mathrm{x}=2$. If ${\lim }_{\mathrm{x}\to 0}\left[1+\frac{\mathrm{f}(\mathrm{x})}{{\mathrm{x}}^2}\right]=3$, then $f(2)$ is equal to :

Q3.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 :

Q4.The sum of first 9 terms of the series $\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\dots \dots$. is :

Q5.Let O be the vertex and Q be any point on the parabola, ${\mathrm{x}}^2=8\mathrm{y}$. If the point P divides the line segment OQ internally in the ratio $1:3$, then the locus of P is :

Q6.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 of $\frac{a_{10}-2a_8}{2a_9}$ is equal to :

Q7.A complex number z is said to be unimodular if $|\mathrm{z}|=1$. Suppose ${\mathrm{z}}_1$ and ${\mathrm{z}}_2$ are complex numbers such that $\frac{z_1-2z_2}{2-z_1{\bar{z}}_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on $a$ :

Q8.The integral $\int \frac{\mathrm{dx}}{{\mathrm{x}}^2{\left({\mathrm{x}}^4+1\right)}^{3/4}}$ equals :

Q9.The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0,0),(0,41)$ and $(41,0)$, is :

Q10.The distance of the point $(1,0,2)$ from the point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ and the plane $\mathrm{x}-\mathrm{y}+\mathrm{z}=16$, is :

Q11.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 :

Q12.The area (in sq. units) of the region described by $\{(\mathrm{x},\mathrm{y}):{\mathrm{y}}^2\le 2\mathrm{x}$ and $\mathrm{y}\ge 4\mathrm{x}-1\}$ is :

Q13.If m is the A.M. of two distinct real numbers $\ell$ and $\mathrm{n}(\ell ,\mathrm{n}>1)$ and ${\mathrm{G}}_1,{\mathrm{G}}_2$ and ${\mathrm{G}}_3$ are three geometric means between $\ell$ and n , then ${\mathrm{G}}_1^4+2{\mathrm{G}}_2^4+{\mathrm{G}}_3^4$ equals :

Q14.Locus of the image of the point $(2,3)$ in the line $(2x-3y+4)+k(x-2y+3)=0,k\in R$, is a :

Q15.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 :

Q16.The number of integers greater than 6,000 that can be formed, using the digits $3,5,6,7$ and 8 , without repetition, is :

Q17.Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $\mathrm{A}\times \mathrm{B}$, each having at least three elements is :

Q18.Let ${\tan }^{-1}\mathrm{y}={\tan }^{-1}\mathrm{x}+{\tan }^{-1}\left(\frac{2\mathrm{x}}{1-{\mathrm{x}}^2}\right)$, where $|\mathrm{x}|<\frac{1}{\sqrt{3}}$. Then a value of y is :

Q19.The integral ${\int }_2^4\frac{\log {\mathrm{x}}^2}{\log {\mathrm{x}}^2+\log \left(36-12\mathrm{x}+{\mathrm{x}}^2\right)}\mathrm{dx}$ is equal to :

Q20.The negation of $\sim \mathrm{s}\vee (\sim \mathrm{r}\wedge \mathrm{s})$ is equivalent to :

Q21.If the angles of elevation of the top of a tower from three collinear points $\mathrm{A},\mathrm{B}$ and C , on a line leading to the foot of the tower, are $30^{\circ },45^{\circ }$ and $60^{\circ }$ respectively, then the ratio, $\mathrm{AB}:\mathrm{BC}$, is :

Q22.${\lim }_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :

Q23.Let $\overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}}$ and $\overrightarrow{\mathrm{c}}$ be three non-zero vectors such that no two of them are collinear and …

Q24.If $\mathrm{A}=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& -2\\ \mathrm{a}& 2& \mathrm{b}\end{array}\right]$ is a matrix satisfying the equation ${\mathrm{AA}}^{\mathrm{T}}=9\mathrm{I}$, where I is $3\times 3$ identity matrix, then ordered pair $(\mathrm{a},\mathrm{b})$ is …

Q25.If the function. $g(x)=\{\begin{array}{cc}k\sqrt{x+1},& 0\le x\le 3\\ mx+2,& 3<x\le 5\end{array}$ is differentiable, then the value of $k+m$ is :

Q26.The set of all values of $\lambda$ for which the system of linear equations : …

Q27.The normal to the curve, $x^2+2xy-3y^2=0$, at $(1,1)$ :

Q28.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 :

Q29.Let $\mathrm{y}(\mathrm{x})$ be the solution of the differential equation $(\mathrm{x}\log \mathrm{x})\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}=2\mathrm{x}\log \mathrm{x},(\mathrm{x}\ge 1)$. Then $\mathrm{y}(\mathrm{e})$ is equal to :