JEE Advanced 2010 · 11 Apr 2010 · Paper 2

Q1.A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is

Q2.A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is $320{\mathrm{ms}}^{-1}$, t …

Q3.A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

Q4.A block of mass 2 kg is free to move along the x-axis. It is at rest and from $t=0$ onwards it is subjected to a time-dependent force $F(t)$ in the x direction. The force $F(t)$ varies with $t$ as shown in the figure. The kinetic energy of the block after 4.5 seconds is

Q5.A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81\pi }{7}\times 10^5{\mathrm{Vm}}^{-1}$. When the field is switched off, the drop is observed to fall with terminal velocity …

Q6.A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to

Q7.A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. In the initial temperature of the gas is $T_i$ (in Kelvin) and the final temperature is $a{T}_i$, the value of $a$ is

Q8.At time $t=0$, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?
[Take : $\ell n5=1.6,\ell n3=1.1$ ]

Q9.Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3}\mathrm{m}$ to $\frac{50}{7}\mathrm{m}$ in 30 seconds. What is the speed of the object in km per hour ?

Q10.A large glass slab $(\mu =5/3)$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R\mathrm{cm}$. What is the value of $R$ ?

Q11.To determine the half life of a radioactive element, a student plots a graph of $\ell n\left|\frac{\mathrm{dN}(\mathrm{t})}{\mathrm{dt}}\right|$ versus $t$. Here $\frac{dN(t)}{dt}$ is the rate of radioactive decay at time $t$. If the number of radioactive nuclei of this element …

Q12.When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at t …

Q13.When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at t …

Q14.When liquid medicine of density $\rho$ is to be put in the eye, it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at t …

Q15.The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rig …

Q16.The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rig …

Q17.The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rig …

Q18.Two transparent media of refractive indices ${\mu }_1$ and ${\mu }_3$ have a solid lens shaped transparent material of refractive index ${\mu }_2$ between them as shown in figures in Column II. A ray traversing these media is also shown in the figures. In Column I different relation …

Q19.You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current $I$ (steady state fo …

Q1.The complex showing a spin-only magnetic moment of $2.82\mathrm{B}.\mathrm{M}$. is

Q2.The species having pyramidal shape is

Q3.In the reaction

(1) $\mathrm{NaOH}/{\mathrm{Br}}_2$

Product T is

Q4.The compounds P, Q and S

Q

s

were separately subjected to nitration using ${\mathrm{HNO}}_3/{\mathrm{H}}_2{\mathrm{SO}}_4$ mixture. The major product formed in each case respectively, is

Q5.The packing efficiency of the two-dimensional square unit cell shown below is

Q6.Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule ${\mathrm{B}}_2$ is

Q7.The total number of diprotic acids among the following is
${\mathrm{H}}_3{\mathrm{PO}}_4$
${\mathrm{H}}_2{\mathrm{SO}}_4$
${\mathrm{H}}_3{\mathrm{PO}}_3$
${\mathrm{H}}_2{\mathrm{CO}}_3$
${\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_7$ …

Q8.Total number of geometrical isomers for the complex $\left[\mathrm{RhCl}(\mathrm{CO})({\mathrm{PPh}}_3)({\mathrm{NH}}_3)\right]$ is

Q9.Among the following, the number of elements showing only one non-zero oxidation state is
O,
C1,
F ,
N,
P,
Sn,
Tl,
Na,
Ti

Q10.Silver (atomic weight $=108\mathrm{g}{\mathrm{mol}}^{-1}$ ) has a density of $10.5\mathrm{g}{\mathrm{cm}}^{-3}$. The number of silver atoms on a surface of area $10^{-12}{\mathrm{m}}^2$ can be expressed in scientific notation as $\mathrm{y}\times 10^{\mathrm{x}}$. …

Q11.One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is ${\mathrm{w}}_{\mathrm{s}}$ and that along the dotted line path is ${\mathrm{w}}_{\mathrm{d}}$, then …

Q12.Two aliphatic aldehydes P and Q react in the presence of aqueous ${\mathrm{K}}_2{\mathrm{CO}}_3$ to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below :

The compounds P and Q respectively are

Q13.Two aliphatic aldehydes P and Q react in the presence of aqueous ${\mathrm{K}}_2{\mathrm{CO}}_3$ to give compound R, which upon treatment with HCN provides compound S. On acidification and heating, S gives the product shown below :

The compound R is

Q15.The hydrogen-like species ${\mathrm{Li}}^{2+}$ is in a spherically symmetric state ${\mathrm{S}}_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state ${\mathrm{S}}_2$. The state ${\mathrm{S}}_2$ has one radial node and its energy is equal to …

Q16.The hydrogen-like species ${\mathrm{Li}}^{2+}$ is in a spherically symmetric state ${\mathrm{S}}_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state ${\mathrm{S}}_2$. The state ${\mathrm{S}}_2$ has one radial node and its energy is equal to …

Q17.The hydrogen-like species ${\mathrm{Li}}^{2+}$ is in a spherically symmetric state ${\mathrm{S}}_1$ with one radial node. Upon absorbing light the ion undergoes transition to a state ${\mathrm{S}}_2$. The state ${\mathrm{S}}_2$ has one radial node and its energy is equal to …

Q18.Match the reactions in Column I with appropriate options in Column II.
| D) (see structure) | s) Cou …

Q1.For $\mathrm{r}=0,1,\dots ,10$, let ${\mathrm{A}}_{\mathrm{r}},{\mathrm{B}}_{\mathrm{r}}$ and ${\mathrm{C}}_{\mathrm{r}}$ denote, respectively, the coefficient of ${\mathrm{x}}^{\mathrm{r}}$ in the expansions of $(1+\mathrm{x}{)}^{10},(1+\mathrm{x}{)}^{20}$ and …

Q2.Let $\mathrm{S}=\{1,2,3,4\}$. The total number of unordered pairs of disjoint subsets of S is equal to

Q3.Let $f$ be a real-valued function defined on the interval $(-1,1)$ such that ${\mathrm{e}}^{-\mathrm{x}}\mathrm{f}(\mathrm{x})=2+{\int }_0^{\mathrm{x}}\sqrt{{\mathrm{t}}^4+1}\mathrm{dt}$, for all $\mathrm{x}\in (-1,1)$, and let ${\mathrm{f}}^{-1}$ be the inverse function …

Q4.If the distance of the point $\mathrm{P}(1,-2,1)$ from the plane $\mathrm{x}+2\mathrm{y}-2\mathrm{z}=\alpha$, where $\alpha >0$, is 5 , then the foot of the perpendicular from $P$ to the plane is

Q6.A signal which can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac{3}{4}$. If the signal received at station …

Q7.Two parallel chords of a circle of radius 2 are at a distance $\sqrt{3}+1$ apart. If the chords subtend at the center, angles of $\frac{\pi }{\mathrm{k}}$ and $\frac{2\pi }{\mathrm{k}}$, where $\mathrm{k}>0$, then the value of $[\mathrm{k}]$ is

[Note : [k] denotes the l …

Q8.Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose $\mathrm{a}=6,\mathrm{b}=10$ and the area of the triangle is $15\sqrt{3}$. If $\angle \mathrm{ACB}$ is obtuse and if r denotes the radius of t …

Q9.Let f be a function defined on $\mathbf{R}$ (the set of all real numbers) such that ${\mathrm{f}}^{\prime }(\mathrm{x})=2010(\mathrm{x}-2009)(\mathrm{x}-2010{)}^2(\mathrm{x}-2011{)}^3(\mathrm{x}-2012{)}^4$, for all $\mathrm{x}\in \mathbf{R}$. If $g$ is a function defined on …

Q10.Let ${\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3,\dots ,{\mathrm{a}}_{11}$ be real numbers satisfying …

Q11.Let k be a positive real number and let …

Q12.Consider the polynomial

Let s be the sum of all distinct real roots of $\mathrm{f}(\mathrm{x})$ and let $\mathrm{t}=|\mathrm{s}|$.

The real number s lies in the interval

Q13.Consider the polynomial

Let s be the sum of all distinct real roots of $\mathrm{f}(\mathrm{x})$ and let $\mathrm{t}=|\mathrm{s}|$.

The area bounded by the curve $\mathrm{y}=\mathrm{f}(\mathrm{x})$ and the lines …

Q14.Consider the polynomial

Let s be the sum of all distinct real roots of $\mathrm{f}(\mathrm{x})$ and let $\mathrm{t}=|\mathrm{s}|$.

The function $f^{\prime }(x)$ is

Q15.Tangents are drawn from the point P(3, 4) to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points A and B.

The coordinates of A and B are

Q16.Tangents are drawn from the point P(3, 4) to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points A and B.

The orthocenter of the triangle PAB is

Q17.Tangents are drawn from the point P(3, 4) to the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ touching the ellipse at points A and B.

The equation of the locus of the point whose distances from the point P and the line AB are equal, is

Q18.Match the statements in Column-I with those in Column-II.

[Note: Here $z$ takes values in the complex plane and $\mathrm{Im}z$ and $\mathrm{Re}z$ denote, respectively, the imaginary part and the real part of z.]
| A) | The set of …