JEE Advanced 2009 · 12 Apr 2009 · Paper 2

Q1.The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point P is

Q2.A piece of wire is bent in the shape of a parabola $y=k{x}^2$ ( $y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to …

Q3.Photoelectric effect experiments are performed using three different metal plates $\mathrm{p},\mathrm{q}$ and r having work functions ${\varphi }_p=2.0\mathrm{eV},{\varphi }_q=2.5\mathrm{eV}$ and ${\varphi }_r=3.0\mathrm{eV}$, respectively. A light beam containing wavelengths of …

Q4.A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is ge …

Q5.Two metallic rings A and B, identical in shape and size but having different resistivities ${\rho }_A$ and ${\rho }_B$, are kept on top of two identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in identical manner, the rings A an …

Q6.A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-col …

Q7.The figure shows the $P-V$ plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse. Then,

Q8.Under the influence of the Coulomb field of charge $+Q$, a charge $-q$ is moving around it in an elliptical orbit. Find out the correct statement(s).

Q11.Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$. In each of these cases …

Q12.A metal rod AB of length $10x$ has its one end A in ice at 0°C and the other end B in water at $100^{\circ }\mathrm{C}$. If a point P on the rod is maintained at $400^{\circ }\mathrm{C}$, then it is found that equal amounts of water and ice evaporate and melt per unit time …

Q13.A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height H. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice an …

Q14.Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure $8\mathrm{N}/{\mathrm{m}}^2$. The radii of bubbles A and B are 2 cm and 4 cm, respectively. Surface tension of the soap-water used to make bubbles is …

Q15.Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses $m,2m$ and $m$, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes completely inelastic collis …

Q16.A steady current $I$ goes through a wire loop PQR having shape of a right angle triangle with $\mathrm{PQ}=3x,\mathrm{PR}=4x$ and $\mathrm{QR}=5x$. If the magnitude of the magnetic field at P due to this loop is $k\left(\frac{{\mu }_{0}I}{48\pi x}\right)$, find the val …

Q17.A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg . Taking $g=10\mathrm{m}/{\mathrm{s}}^2$, find the work done (in joules) by the string on the block of mass 0.36 kg during the first sec …

Q18.A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho =\kappa r^a$, where $\kappa$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r=\frac{R}{2}$ is $\frac{1}{8}$ times that at …

Q19.A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz . Find the separation (in cm) between the successive nodes on the string.

Q1.For a first order reaction $\mathrm{A}\to \mathrm{P}$, the temperature ( T ) dependent rate constant ( $k$ ) was found to follow the equation $\log k=-(2000)\frac{1}{\mathrm{T}}+6.0$. The pre-exponential factor A and the activation energy …

Q2.The spin only magnetic moment value (in Bohr magneton units) of $\mathrm{Cr}(\mathrm{CO}{)}_6$ is

Q3.In the following carbocation, $\mathrm{H}/{\mathrm{CH}}_3$ that is most likely to migrate to the positively charged carbon is

Q4.The correct stability order of the following resonance structures is

${\mathrm{H}}_2\mathrm{C}=\stackrel{+}{\mathrm{N}}=\stackrel{-}{\mathrm{N}}$ (I)

${\mathrm{H}}_2\stackrel{+}{\mathrm{C}}-\mathrm{N}=\stackrel{-}{\mathrm{N}}$ (II) …

Q5.For the reduction of ${\mathrm{NO}}_3^{-}$ion in an aqueous solution, ${\mathrm{E}}^0$ is +0.96 V. Values of ${\mathrm{E}}^0$ for some metal ions are given below …

Q6.Among the following, the state function(s) is(are)

Q7.In the reaction

the amine(s) $\mathbf{X}$ is(are)

Q8.The nitrogen oxide(s) that contain(s) N-N bond(s) is(are)

Q9.The correct statement(s) about the following sugars $\mathbf{X}$ and $\mathbf{Y}$ is(are)

Q10.Match each of the reactions given in Column I with the corresponding product(s) given in Column II.
| (C …

Q11.Match each of the compounds given in Column I with the reaction(s), that they can undergo, given in Column II.

Column I

(A) (see structure)

(B) (see structure)

(C) (see structure)

(D) (see structure)

Column II

(p) Nucleophilic substitution

(q) Elimination

(r) Nucleophili …

Q12.In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt in excess oxygen at 298.0 K. The temperature of the calorimeter was found to increase from 298.0 K to 298.45 K due to the combustion process. Given that the heat capacity of the calorimeter is …

Q13.At 400 K, the root mean square (rms) speed of a gas $\mathbf{X}$ (molecular weight $=40$ ) is equal to the most probable speed of gas $\mathbf{Y}$ at 60 K . The molecular weight of the gas $\mathbf{Y}$ is

Q14.The dissociation constant of a substituted benzoic acid at $25^{\circ }\mathrm{C}$ is $1.0\times 10^{-4}$. The pH of a 0.01 M solution of its sodium salt is

Q15.The total number of $\alpha$ and $\beta$ particles emitted in the nuclear reaction ${}_{92}^{238}\mathrm{U}\to {}_{82}^{214}\mathrm{Pb}$ is

Q16.The oxidation number of Mn in the product of alkaline oxidative fusion of ${\mathrm{MnO}}_2$ is

Q17.The number of water molecule(s) directly bonded to the metal centre in ${\mathrm{CuSO}}_4\cdot 5{\mathrm{H}}_2\mathrm{O}$ is

Q18.The coordination number of Al in the crystalline state of ${\mathrm{AlCl}}_3$ is

Q19.The total number of cyclic structural as well as stereo isomers possible for a compound with the molecular formula ${\mathrm{C}}_5{\mathrm{H}}_{10}$ is

Q1.If the sum of first $n$ terms of an A.P. is $c{n}^2$, then the sum of squares of these $n$ terms is

Q2.A line with positive direction cosines passes through the point $P(2,-1,2)$ and makes equal angles with the coordinate axes. The line meets the plane

at point $Q$. The length of the line segment $PQ$ equals

Q3.The normal at a point $P$ on the ellipse $x^2+4y^2=16$ meets the $x$-axis at $Q$. If $M$ is the mid point of the line segment $PQ$, then the locus of $M$ intersects the latus rectums of the given ellipse at the points

Q4.The locus of the orthocentre of the triangle formed by the lines

and $y=0$, where $p\ne q$, is

Q5.If

then

Q6.An ellipse intersects the hyperbola $2x^2-2y^2=1$ orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then

Q7.For the function

Q8.The tangent $PT$ and the normal $PN$ to the parabola $y^2=4ax$ at a point $P$ on it meet its axis at points $T$ and $N$, respectively. The locus of the centroid of the triangle $PTN$ is a parabola whose

Q9.For $0<\theta <\frac{\pi }{2}$, the solution(s) of

is(are)

Q10.Match the statements/expressions given in Column I with the values given in Column II.

Column I
(A) Root(s) of the equation $2{\sin }^2\theta +{\sin }^{2}2\theta =2$
(B) Points of discontinuity of the function …

Q12.The maximum value of the function $f(x)=2x^3-15x^2+36x-48$ on the set $A=\left\{x\mid x^2+20\le 9x\right\}$ is

Q13.Let $(x,y,z)$ be points with integer coordinates satisfying the system of homogeneous equations:

Then the number of such points for which $x^2+y^2+z^2\le 100$ is

Q14.Let $ABC$ and $AB{C}^{\prime }$ be two non-congruent triangles with sides $AB=4$, $AC=A{C}^{\prime }=2\sqrt{2}$ and angle $B=30^{\circ }$. The absolute value of the difference between the areas of these triangles is

Q16.Let $f:\mathbf{R}\to \mathbf{R}$ be a continuous function which satisfies

Then the value of $f(\ln 5)$ is

Q17.The centres of two circles $C_1$ and $C_2$ each of unit radius are at a distance of 6 units from each other. Let $P$ be the mid point of the line segment joining the centres of $C_1$ and $C_2$ and $C$ be a circle touching circles $C_1$ and $C_2$ extern …

Q18.The smallest value of $k$, for which both the roots of the equation

are real, distinct and have values at least 4, is

Q19.If the function $f(x)=x^3+e^{\frac{x}{2}}$ and $g(x)=f^{-1}(x)$, then the value of $g^{\prime }(1)$ is