JEE Main 2009 · 12 Apr 2009 · Offline

Q1.This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement - 1: For a charged particle moving from point P to point Q , the net work done by an electrostatic field on the par …

Q2.The above is a plot of binding energy per nucleon ${\mathrm{E}}_{\mathrm{b}}$, against the nuclear mass $\mathrm{M};\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D},\mathrm{E},\mathrm{F}$ correspond to different nuclei. Consider four reactions:
(i) …

Q3.A p-n junction (D) shown in the figure can act as a rectifier. An alternating current source ($\mathrm{V}$) is connected in the circuit.

Q4.The logic circuit shown below has the input waveforms 'A' and 'B' as shown. Pick out the correct output waveform.

Q5.If $\mathrm{x},\mathrm{v}$ and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?

Q6.In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v$, from the lens, …

Q7.A thin uniform rod of length $\ell$ and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of

Q8.Let $P(r)=\frac{Q}{\pi R^4}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. for a point ' $p$ ' inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is

Q9.The transition from the state $\mathrm{n}=4$ to $\mathrm{n}=3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from

Q10.One kg of a diatomic gas is at a pressure of $8\times 10^4\mathrm{N}/{\mathrm{m}}^2$. The density of the gas is $4\mathrm{kg}/{\mathrm{m}}^{-3}$. What is the energy of the gas due to its thermal motion?

Q11.This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-1: The temperature dependence of resistance is usually given as …

Q12.A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $=b$ ) and $DA$ (radius $=a$ ) of the loop are joined by two straight wires AB and CD . A steady current I is flowing in the loop. Angle made by AB and CD at the or …

Q13.A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe …

Q14.Two points P and Q are maintained at the potentials of 10 V and -4 V respectively. The work done in moving 100 electrons from $P$ to $Q$ is

Q15.The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc $=1240\mathrm{eV}\mathrm{nm}$)

Q16.A particle has an initial velocity $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed after 10 s is

Q17.A motor cycle starts from rest and accelerates along a straight path at $2\mathrm{m}/{\mathrm{s}}^2$. At the starting point of the motor cycle there is a stationary electric sire. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\%$ …

Q18.Consider a rubber ball freely falling from a height $\mathrm{h}=4.9\mathrm{m}$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as funct …

Q19.A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on Q is zero, then the $\mathrm{Q}/\mathrm{q}$ equals

Q20.A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length x of the bar from its hot end is best described by which of the following figure.

Q21.A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the …

Q22.Three sound waves of equal amplitudes have frequencies $(v-1),v,(v+1)$. They superpose to give beats. The number of beats produced per second will be

Q23.The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g=$ the acceleration due to gravity on the surface of the earth) in terms of $R$, the radius of the earth is

Q24.Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire-2 has cross-sectional area 3A. If the length of wire 1 increases by $\Delta x$ on applying force F, how much force is needed to stretch wire 2 by the same amount?

Q25.In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree ($=0.5^{\circ }$), then the least count of the instr …

Q26.An inductor of inductance L = 400 mH and resistors of resistances $R_1=2\Omega$ and $R_2=2\Omega$ are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L …

Q27.Assuming the gas to be ideal the work done on the gas in taking it from A to B is

Q28.The work done on the gas in taking it from D to A is

Q29.The net work done on the gas in the cycle ABCDA is

Q1.Knowing that the Chemistry of lanthanoids (Ln) is dominated by its +3 oxidation state, which of the following statements in incorrect ?

Q2.A liquid was mixed with ethanol and a drop of concentrated ${\mathrm{H}}_2{\mathrm{SO}}_4$ was added. A compound with a fruity smell was formed. The liquid was :

Q3.Arrange the carbanions, $({\mathrm{CH}}_3{)}_3\overline{\mathrm{C}},\overline{\mathrm{C}}{\mathrm{Cl}}_3,({\mathrm{CH}}_3{)}_2\overline{\mathrm{C}}\mathrm{H},{\mathrm{C}}_6{\mathrm{H}}_5\overline{\mathrm{C}}{\mathrm{H}}_2$, in order of their decreasing stability :

Q4.The alkene that exhibits geometrical isomerism is :

Q5.In which of the following arrangements, the sequence is not strictly according to the property written against it ?

Q6.The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is :

Q7.Which of the following statements is incorrect regarding physissorptions ?

Q8.Which of the following on heating with aqueous KOH , produces acetaldehyde ?

Q9.In an atom, an electron is moving with a speed of $600\mathrm{m}/\mathrm{s}$ with an accuracy of $0.005\%$. Certainity with which the position of the electron can be located is $(\mathrm{h}=6.6\times 10^{-34}\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$, …

Q10.In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is ${\mathrm{CH}}_3\mathrm{OH}(\ell )+\frac{3}{2}{\mathrm{O}}_2(\mathrm{g})\to {\mathrm{CO}}_2(\mathrm{g})+2{\mathrm{H}}_2\mathrm{O}(\ell )$ At 298 K standard Gibb's energie …

Q11.Two liquids X and Y form an ideal solution. At 300 K , vapour pressure of the solution containing 1 mol of $X$ and 3 mol of $Y$ is 550 mm Hg . At the same temperature, if 1 mol of $Y$ is further added to this solution, vapour pressure of the solution increases by 10 mm Hg . …

Q12.The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of $99\%$ of the chemical reaction will be ( $\log 2=0.301$ ) :

Q13.Given : ${\mathrm{E}}_{{\mathrm{Fe}}^{3+}/\mathrm{Fe}}^{\circ }=-0.036\mathrm{V},{\mathrm{E}}_{{\mathrm{Fe}}^{2+}/\mathrm{Fe}}^{\circ }=-0.439\mathrm{V}$. The value of standard electrode potential for the change, …

Q14.On the basis of the following thermochemical data : ( $\Delta {\mathrm{fG}}^{\circ }{\mathrm{H}}_{(\mathrm{aq})}^{+}=0$ )
${\mathrm{H}}_2\mathrm{O}(\ell )\to {\mathrm{H}}^{+}(\mathrm{aq})+{\mathrm{OH}}^{-}(\mathrm{aq});\Delta \mathrm{H}=57.32\mathrm{kJ}$ …

Q15.Copper crystallizes in fcc with a unit cell length of 361 pm . What is the radius of copper atom ?

Q16.Which of the following has an optical isomer ?

Q17.Solid $\mathrm{Ba}{\left({\mathrm{NO}}_3\right)}_2$ is gradually dissolved in a $1.0\times 10^{-4}\mathrm{M}{\mathrm{Na}}_2{\mathrm{CO}}_3$ solution. At what concentration of ${\mathrm{Ba}}^{2+}$ will a precipitate begin to form? $({\mathrm{K}}_{\mathrm{sp}}$ …

Q18.Which one of the following reactions of Xenon compounds is not feasible ?

Q19.Using MO theory predict which of the following species has the shortest bond length ?

Q20.In context with the transition elements, which of the following statements is incorrect ?
(1) In addition to the normal oxidation states, the zero oxidation state is also shown by these elements in complexes.
(2) In the highest oxidation states, the transition metal show basic ch …

Q21.Calculate the wavelength (in nanometer) associated with a proton moving at $1.0\times 10^3{\mathrm{ms}}^{-1}$ (Mass of proton $=1.67\times 10^{-27}\mathrm{kg}$ and $\mathrm{h}=6.63\times 10^{-34}\mathrm{Js}$ ) :

Q22.A binary liquid solution is prepared by mixing $n$-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution ?

Q23.The number of stereoisomers possible for a compound of the molecular formula ${\mathrm{CH}}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}(\mathrm{OH})-\mathrm{Me}$ is :

Q24.The IUPAC name of neopentane is

Q25.The set representing the correct order of ionic radius is :

Q26.The two functional groups present in a typical carbohydrate are :

Q27.The bond dissociation energy of $\mathrm{B}-\mathrm{F}$ in ${\mathrm{BF}}_3$ is $646\mathrm{kJ}{\mathrm{mol}}^{-1}$ whereas that of $\mathrm{C}-\mathrm{F}$ in ${\mathrm{CF}}_4$ is 515 kJ ${\mathrm{mol}}^{-1}$. The correct reason for higher B-F bond dissociation energy …

Q28.In Cannizzaro reaction given below
…

Q29.Which of the following pairs represents linkage isomers ?

Q30.Buna-N synthetic rubber is a copolymer of :

Q1.Let $a,b,c$ be such that $b(a+c)\ne 0$. If $\left|\begin{array}{ccc}a& a+1& a-1\\ -b& b+1& b-1\\ c& c-1& c+1\end{array}\right|+\left|\begin{array}{ccc}a+1& b+1& c-1\\ a-1& b-1& c+1\\ (-1{)}^{n+2}a& (-1{)}^{n+1}b& (-1{)}^{n}c\end{array}\right|=0$, then the v …

Q2.If the mean deviation of number $1,1+d,1+2d,\dots ,1+100d$ from their mean is 255, then the $d$ is equal to

Q3.If the roots of the equation $b{x}^2+cx+a=0$ be imaginary, then for all real values of $x$, the expression $3b^2{x}^2+6bcx+2c^2$ is

Q4.Let $A$ and $B$ denote the statements
A: $\cos \alpha +\cos \beta +\cos \gamma =0$
B: $\sin \alpha +\sin \beta +\sin \gamma =0$
If $\cos (\beta -\gamma )+\cos (\gamma -\alpha )+\cos (\alpha -\beta )=-\frac{3}{2}$, then

Q5.The lines $p\left(p^2+1\right)x-y+q=0$ and ${\left(p^2+1\right)}^{2}x+\left(p^2+1\right)y+2q=0$ are perpendicular to a common line for

Q6.If $A,B$ and $C$ are three sets such that $A\cap B=A\cap C$ and $A\cup B=A\cup C$, then

Q7.If $\vec{u},\vec{v},\vec{w}$ are non-coplanar vectors and $p,q$ are real numbers, then the equality …

Q8.Let the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ lies in the plane $x+3y-\alpha z+\beta =0$. Then $(\alpha ,\beta )$ equals

Q9.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

Q10.${\int }_0^{\pi }[\cot x]dx$, $[\bullet ]$ denotes the greatest integer function, is equal to

Q11.For real $x$, let $f(x)=x^3+5x+1$, then

Q12.In a binomial distribution $B\left(n,p=\frac{1}{4}\right)$, if the probability of at least one success is greater than or equal to $\frac{9}{10}$, then n is greater than

Q13.If $P$ and $Q$ are the points of intersection of the circles $x^2+y^2+3x+7y+2p-5=0$ and $x^2+y^2+2x+2y-p^2=0$, then there is a circle passing through $P,Q$ and $(1,1)$ for

Q14.The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are

Q15.If $\left|Z-\frac{4}{Z}\right|=2$, then the maximum value of $|Z|$ is equal to

Q16.Three distinct points $\mathrm{A},\mathrm{B}$ and C are given in the $2-$ dimensional coordinate plane such that the ratio of the distance of any one of them from the point ( 1,0 ) to the distance from the point ( $-1,0$ ) is equal to $\frac{1}{3}$. Then the circumcentre …

Q17.The remainder left out when $8^{2n}-(62{)}^{2n+1}$ is divided by 9 is

Q18.The ellipse $x^2+4y^2=4$ is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point $(4,0)$. Then the equation of the ellipse is

Q19.The sum to the infinity of the series $1+\frac{2}{3}+\frac{6}{3^2}+\frac{10}{3^3}+\frac{14}{3^4}+\dots \dots$. is

Q20.The differential equation which represents the family of curves $y=c_1{e}^{c_{2}x}$, where $c_1$ and $c_2$ are arbitrary constants is

Q21.One ticket is selected at random from 50 tickets numbered $00,01,02,\dots .,49$. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

Q22.Let $y$ be an implicit function of $x$ defined by $x^{2x}-2x^x\cot y-1=0$. Then $y^{\prime }(1)$ equals

Q23.The area of the region bounded by the parabola $(y-2{)}^2=x-1$, the tangent to the parabola at the point $(2,3)$ and the $x$-axis is

Q24.Given $\mathrm{P}(\mathrm{x})={\mathrm{x}}^4+{\mathrm{ax}}^3+{\mathrm{bx}}^2+\mathrm{cx}+\mathrm{d}$ such that $\mathrm{x}=0$ is the only real root of ${\mathrm{P}}^{\prime }(\mathrm{x})=0$. If $\mathrm{P}(-1)<\mathrm{P}(1)$, then in the interval $[-1,1]$

Q25.The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

Q26.Let $f(x)=(x+1{)}^2-1,x\ge -1$

Statement-1: The set $\{x:f(x)=f^{-1}(x)\}=\{0,-1\}$
Statement-2: $f$ is a bijection.

Q27.Let $f(x)=x|x|$ and $g(x)=\sin x$.

Statement-1: $g\circ f$ is differentiable at $x=0$ and its derivative is continuous at that point.
Statement-2: $g\circ f$ is twice differentiable at $x=0$.

Q28.Statement-1: The variance of first $n$ even natural numbers is $\frac{n^2-1}{4}$
Statement-2: The sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n(n+1)(2n+1)}{6}$

Q29.Statement-1: $\sim (p\leftrightarrow \sim q)$ is equivalent to $p\leftrightarrow q$.

Statement-2: $\sim (p\leftrightarrow \sim q)$ is a tautology.

Q30.Let $A$ be a $2\times 2$ matrix

Statement-1: $\text{adj}(\text{adj }A)=A$
Statement-2: $|\text{adj }A|=|A|$