JEE Main 2013 · 07 Apr 2013 · Offline

Q1.In an LCR circuit as shown below both switches are open initially. Now switch ${\mathrm{S}}_1$ is closed, ${\mathrm{S}}_2$ kept open. ( q is charge on the capacitor and $\tau =\mathrm{RC}$ is capacitive time constant). Which of the following statement is correct?

Q2.A diode detector is used to detect an amplitude modulated wave of $60\%$ modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.

Q3.The supply voltage to a room is 120 V . The resistance of the lead wires is $6\Omega$. A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb?

Q4.A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring …

Q5.Two charges, each equal to q , are kept at $\mathrm{x}=-\mathrm{a}$ and $\mathrm{x}=\mathrm{a}$ on the x -axis. A particle of mass m and charge ${\mathrm{q}}_0=\frac{\mathrm{q}}{2}$ is placed at the origin. If charge ${\mathrm{q}}_0$ is given a small displacement ( …

Q6.A beam of unpolarised light of intensity ${\mathrm{I}}_0$ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of $45^{\circ }$ relative to that of A. The intensity of the emergent light is:

Q7.The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows:

Q8.Two coherent point sources ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are separated by a small distance 'd' as shown. The fringes obtained on the screen will be:

Q9.A metallic rod of length ' $\ell$ ' is tied to a string of length $2\ell$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ' B ' in the region, the e.m.f. induced across the ends of …

Q10.In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number ( $\mathrm{n}-1$ ). If $\mathrm{n}\gg 1$, the frequency of radiation emitted is proportional to

Q11.Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T , density of liquid is $\rho$ and L is its latent heat of vapori …

Q12.The graph between angle of deviation ( $\delta$ ) and angle of incidence (i) for a triangular prism is represented by:

Q13.Let $[{\epsilon }_0]$ denote the dimensional formula of the permittivity of vacuum. If $\mathrm{M}=$ mass, $\mathrm{L}=$ length, $\mathrm{T}=$ time and $\mathrm{A}=$ electric current, then:

Q14.The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is

Q15.A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of $1\%$. What is the fundamental frequency of steel if density and elasticity of steel are $7.7\times 10^3\mathrm{kg}/{\mathrm{m}}^3$ and …

Q16.This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-I: Higher the range, greater is the resistance of ammeter.
Statement- II: To increase the range of ammeter, additional …

Q17.What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2 R ?

Q18.A projectile is given an initial velocity of $(\hat{i}+2\hat{j})\mathrm{m}/\mathrm{s}$, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$, the equation of its trajectory is:

Q19.Two capacitors $C_1$ and $C_2$ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then :

Q20.A hoop of radius $r$ and mass $m$ rotating with an angular velocity ${\omega }_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

Q21.An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M . The piston and cylinder have equal cross sectional area A . When the piston is in equilibrium, the volume of the gas is ${\mathrm{V}}_0$ and its pressure is ${\mathrm{P}}_0$. …

Q22.A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is:

Q23.A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm . The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm . If a current of 2.0 A flows through the smaller loop, then the flux linked …

Q24.If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature ${\theta }_0$ the graph between the temperature T of the metal and time t will be closest to :

Q25.The I-V characteristic of an LED is

Q26.This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement I : A point particle of mass m moving with speed v collides with stationary point particle of mass M . If the maximum e …

Q27.The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5 s . In another 10 s it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals.

Q28.Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm . If speed of light in material of lens is $2\times 10^8\mathrm{m}/\mathrm{s}$, the focal length of the lens is :

Q29.The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT . The peak value of electric field strength is :

Q30.Two short bar magnets of length 1 cm each have magnetic moments $1.20{\mathrm{Am}}^2$ and $1.00{\mathrm{Am}}^2$ respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are …

Q1.An unknown alcohol is treated with the "Lucas reagent" to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:

Q2.The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of ${\mathrm{Na}}^{+}$ will be:

Q3.Stability of the species ${\mathrm{Li}}_2,{\mathrm{Li}}_2^{-}$ and ${\mathrm{Li}}_2^{+}$ increases in the order of:

Q4.The molarity of a solution obtained by mixing 750 mL of $0.5(\mathrm{M})\mathrm{HCl}$ with 250 mL of $2(\mathrm{M})\mathrm{HCl}$ will be:

Q5.Which of the following is the wrong statement?

Q6.Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is expected to have the highest ${\mathrm{E}}_{{\mathrm{M}}^{3+}/{\mathrm{M}}^{2+}}^0$ value?

Q7.A solution of (-) -1-chloro -1 - phenylethane is toluene racemises slowly in the presence of a small amount of ${\mathrm{SbCl}}_5$, due to the formation of :

Q8.The coagulating power of electrolytes having ions ${\mathrm{Na}}^{+},{\mathrm{Al}}^{3+}$ and ${\mathrm{Ba}}^{2+}$ for arsenic sulphide sol increases in the order:

Q9.How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2 ?

Q10.Experimentally it was found that a metal oxide has formula ${\mathrm{M}}_{0.98}\mathrm{O}$. Metal M , is present as ${\mathrm{M}}^{2+}$ and ${\mathrm{M}}^{3+}$ in its oxide. Fraction of the metal which exists as ${\mathrm{M}}^{3+}$ would be:

Q11.A compound with molecular mass 180 is acylated with ${\mathrm{CH}}_3\mathrm{COCl}$ to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is:

Q12.Given
${\mathrm{E}}_{{\mathrm{Cr}}^{3+}/\mathrm{Cr}}^0=-0.74\mathrm{V};{\mathrm{E}}_{{\mathrm{MnO}}_4^{-}/{\mathrm{Mn}}^{2+}}^0=1.51\mathrm{V}$ …

Q13.Arrange the following compounds in order of decreasing acidity:

Q14.The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation energy of such a reaction will be:
( $\mathrm{R}=8.314{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$ and $\log 2=0.301$ )

Q15.Synthesis of each molecule of glucose in photosynthesis involves:

Q16.Which of the following complex species is not expected to exhibit optical isomerism?

Q17.A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of $37.0^{\circ }\mathrm{C}$. As it does so, it absorbs 208J of heat. The values of q and w for the process will be: ( …

Q18.A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of ${\mathrm{CO}}_2$. The empirical formula of the hydrocarbon is:

Q19.The order of stability of the following carbocations:

Q20.Which of the following represents the correct order of increasing first ionization enthalpy for $\mathrm{Ca},\mathrm{Ba},\mathrm{S},\mathrm{Se}$ and Ar?

Q21.For gaseous state, if most probable speed is denoated by $C^{\ast }$, average speed by $\bar{C}$ and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

Q22.The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:

Q23.Consider the following reaction:

The values of $\mathrm{x},\mathrm{y}$ and z in the reaction are, res …

Q24.Which of the following exists as covalent crystals in the solid state?

Q25.Compound (A), ${\mathrm{C}}_8{\mathrm{H}}_9\mathrm{Br}$, gives a white precipitate when warmed with alcoholic ${\mathrm{AgNO}}_3$. Oxidation of (A) gives a acid (B), ${\mathrm{C}}_8{\mathrm{H}}_6{\mathrm{O}}_4$. (B) easily forms anhydride on heating. Identify the compound (A) …

Q26.Energy of an electron is given by $E=-2.178\times 10^{-18}\frac{Z^2}{n^2}$ J. Wavelength of light required to excite an electron in an hydrogen atom from level $\mathrm{n}=1$ to $\mathrm{n}=2$ will be ( $\mathrm{h}=6.62\times 10^{-34}$ Js and $\mathrm{c}=3.0\times 10^8$ …

Q27.An organic compound $A$ upon reacting with ${\mathrm{NH}}_3$ gives $B$. On heating $B$ gives $C$. $C$ in presence of KOH reacts with ${\mathrm{Br}}_2$ to give ${\mathrm{CH}}_3{\mathrm{CH}}_2{\mathrm{NH}}_2$. A is

Q28.In which of the following pairs of molecules/ions, both the species are not likely to exist?

Q29.Which of the following molecules are expected to exhibit diamagnetic behaviour?

Q30.Which of the following arrangements does not represent the correct order of the property stated against it?

Q1.The circle passing through $(1,-2)$ and touching the axis of x at $(3,0)$ also passes through the point

Q2.ABCD is a trapezium such that AB and CD are parallel and $\mathrm{BC}\perp \mathrm{CD}$. If $\angle \mathrm{ADB}=\theta ,\mathrm{BC}=\mathrm{p}$ and $\mathrm{CD}=\mathrm{q}$, then AB is equal to

Q3.Given: A circle, $2x^2+2y^2=5$ and a parabola, $y^2=4\sqrt{5}x$.

Statement-I : An equation of a common tangent to these curves is $\mathrm{y}=\mathrm{x}+\sqrt{5}$.

Statement - II: If the line, $y=mx+\frac{\sqrt{5}}{m}(m\ne 0)$ is their common tangent, then …

Q4.A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching $x$-axis, the equation of the reflected rays is

Q5.All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

Q6.If $\mathrm{x},\mathrm{y},\mathrm{z}$ are in A.P. and ${\tan }^{-1}\mathrm{x},{\tan }^{-1}\mathrm{y}$ and ${\tan }^{-1}\mathrm{z}$ are also in A.P., then

Q7.If $\int f(x)dx=\Psi (x)$, then $\int x^{5}f\left(x^3\right)dx$ is equal to

Q8.The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, and having centre at $(0,3)$ is

Q9.The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0,1)(1,1)$ and $(1,0)$ is

Q10.The intercepts on x -axis made by tangents to the curve, $\mathrm{y}={\int }_0^{\mathrm{x}}|\mathrm{t}|\mathrm{dt},\mathrm{x}\in \mathrm{R}$, which are parallel to the line $\mathrm{y}=2\mathrm{x}$, are equal to

Q11.The sum of first 20 terms of the sequence $0.7,0.77,0.777$ $\_\_\_\_$ is

Q12.Consider :

Statement - I: $(p\wedge \sim q)\wedge (\sim p\wedge q)$ is a fallacy.

Statement - II : $(p\to q)\leftrightarrow (\sim q\to \sim p)$ is a tautology.

Q13.The area (in square units) bounded by the curves $y=\sqrt{x}$, $2y-x+3=0$, $x$-axis, and lying in the first quadrant is

Q14.The expression $\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$ can be written as

Q15.The real number $k$ for which the equation, $2x^3+3x+k=0$ has two distinct real roots in $[0,1]$

Q16.${\lim }_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to

Q17.Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_n=10$, then the value of $n$ is

Q18.At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production $P$ w.r.t. additional number of workers $x$ is given by $\frac{dP}{dx}=100-12\sqrt{x}$. If the firm employs 25 more workers, then the new level of production of items is

Q19.Statement - I : The value of the integral ${\int }_{\pi /6}^{\pi /3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\frac{\pi }{6}$.

Statement - II : ${\int }_a^{b}f(x)dx={\int }_a^{b}f(a+b-x)dx$.

Q20.If $P=\left[\begin{array}{ccc}1& \alpha & 3\\ 1& 3& 3\\ 2& 4& 4\end{array}\right]$ is the adjoint of a $3\times 3$ matrix $A$ and $|A|=4$, then $\alpha$ is equal to

Q21.The number of values of $k$, for which the system of equations
$(k+1)x+8y=4k$
$kx+(k+3)y=3k-1$
has no solution, is

Q22.If $y=\sec ({\tan }^{-1}x)$, then $\frac{dy}{dx}$ at $x=1$ is equal to

Q23.If the lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, then $k$ can have

Q24.Let $A$ and $B$ be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A\times B$ having 3 or more elements is

Q25.If the vectors $\overrightarrow{\mathrm{AB}}=3\hat{\mathrm{i}}+4\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{AC}}=5\hat{\mathrm{i}}-2\hat{\mathrm{j}}+4\hat{\mathrm{k}}$ are the sides of a triangle ABC, then the length of the median through A is

Q26.A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

Q27.If z is a complex number of unit modulus and argument $\theta$, then $\arg \left(\frac{1+\mathrm{z}}{1+\overline{\mathrm{z}}}\right)$ equals

Q28.If the equations ${\mathrm{x}}^2+2\mathrm{x}+3=0$ and ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0,\mathrm{a},\mathrm{b},\mathrm{c}\in \mathrm{R}$, have a common root, then $\mathrm{a}:\mathrm{b}:\mathrm{c}$ is

Q29.Distance between two parallel planes $2x+y+2z=8$ and $4x+2y+4z+5=0$ is

Q30.The term independent of x in expansion of ${\left(\frac{\mathrm{x}+1}{{\mathrm{x}}^{2/3}-{\mathrm{x}}^{1/3}+1}-\frac{\mathrm{x}-1}{\mathrm{x}-{\mathrm{x}}^{1/2}}\right)}^{10}$ is