JEE Advanced 2010 · 11 Apr 2010 · Paper 1

Q1.Consider a thin square sheet of side L and thickness t, made of a material of resistivity $\rho$. The resistance between two opposite faces, shown by the shaded areas in the figure is

Q2.A real gas behaves like an ideal gas if its

Q3.Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, $100\mathrm{W},60\mathrm{W}$ and 40 W bulbs have filament resistances ${\mathrm{R}}_{100},{\mathrm{R}}_{60}$ and …

Q4.To verify Ohm's law, a student is provided with a test resistor ${\mathrm{R}}_{\mathrm{T}}$, a high resistance ${\mathrm{R}}_1$, a small resistance ${\mathrm{R}}_2$, two identical galvanometers ${\mathrm{G}}_1$ and ${\mathrm{G}}_2$, and a variable voltage source V. The co …

Q5.An AC voltage source of variable angular frequency $\omega$ and fixed amplitude ${\mathrm{V}}_{\mathrm{o}}$ is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $\omega$ is increased

Q6.A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a …

Q7.A block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta >\mu$. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plan …

Q10.A student uses a simple pendulum of exactly 1m length to determine $g$, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) tr …

Q11.A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of $2{\mathrm{ms}}^{-1}$. Which of the following statement(s) is (are) correct for the system of these two masses ?

Q12.A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of $60^{\circ }$ (see figure). If the refractive index of the material of the prism is $\sqrt{3}$, which of the following is (are) correct ?

Q13.One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is $P_0$. Choose the correct option(s) from the following

Q15.When a particle of mass m moves on the x-axis in a potential of the form $V(x)=k{x}^2$, it performs simple harmonic motion. The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be seen easily using dimensional analysis. However, the motion of a particle c …

Q16.When a particle of mass m moves on the x-axis in a potential of the form $V(x)=k{x}^2$, it performs simple harmonic motion. The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be seen easily using dimensional analysis. However, the motion of a particle c …

Q17.Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature $T_c(0)$. An interesting property of superconductors is that their critical temperature becomes small …

Q19.The focal length of a thin biconvex lens is 20cm. When an object is moved from a distance of 25cm in front of it to 50cm, the magnification of its image changes from $m_{25}$ to $m_{50}$. The ratio $\frac{m_{25}}{m_{50}}$ is

Q20.An $\alpha$-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are ${\lambda }_{\alpha }$ and ${\lambda }_p$ respectively. The ratio $\frac{{\lambda }_p}{{\lambda }_{\alpha }}$, to the nearest integer, is

Q21.When two identical batteries of internal resistance $1\Omega$ each are connected in series across a resistor R, the rate of heat produced in R is $J_1$. When the same batteries are connected in parallel across R, the rate is $J_2$. If $J_1=2.25J_2$ then the value of R i …

Q22.Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures $T_1$ and $T_2$, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rat …

Q23.When two progressive waves $y_1=4\sin (2x-6t)$ and $y_2=3\sin \left(2x-6t-\frac{\pi }{2}\right)$ are superimposed, the amplitude of the resultant wave is

Q24.A 0.1 kg mass is suspended from a wire of negligible mass. The length of the wire is 1 m and its cross-sectional area is $4.9\times 10^{-7}{m}^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular fre …

Q25.A binary star consists of two stars A (mass $2.2{\mathrm{M}}_{\mathrm{s}}$) and B (mass $11{\mathrm{M}}_{\mathrm{s}}$), where ${\mathrm{M}}_{\mathrm{s}}$ is the mass of the sun. They are separated by distance $d$ and are rotating about their centre of mass, which is stationary. The r …

Q26.Gravitational acceleration on the surface of a planet is $\frac{\sqrt{6}}{11}\mathrm{g}$, where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is $\frac{2}{3}$ times that of the earth. If the escape speed on the surface o …

Q27.A piece of ice (heat capacity $=2100\mathrm{J}{\mathrm{kg}}^{-1}{}^{\circ }{\mathrm{C}}^{-1}$ and latent heat $=3.36\times 10^5\mathrm{J}{\mathrm{kg}}^{-1}$) of mass m grams is at -5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finall …

Q28.A stationary source is emitting sound at a fixed frequency ${\mathrm{f}}_0$, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of ${\mathrm{f}}_0$. What is the difference in the speeds of the car …

Q1.The correct structure of ethylenediaminetetraacetic acid (EDTA) is

Q2.The ionization isomer of $\left[\mathrm{Cr}{\left({\mathrm{H}}_2\mathrm{O}\right)}_4\mathrm{Cl}\left({\mathrm{NO}}_2\right)\right]\mathrm{Cl}$ is

Q3.The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are

Q4.The correct statement about the following disaccharide is

Q5.In the reaction

the products are

Q6.Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation is

Q7.The species which by definition has ZERO standard molar enthalpy of formation at 298 K is

Q8.The bond energy (in $\mathbf{kcal}{\mathbf{mol}}^{-1}$) of a C-C single bond is approximately

Q10.In the reaction

Q11.In the Newman projection for 2,2-dimethylbutane

$\mathbf{X}$ and $\mathbf{Y}$ can respectively be

Q12.Among the following, the intensive property is (properties are)

Q13.Aqueous solutions of ${\mathrm{HNO}}_3,\mathrm{KOH},{\mathrm{CH}}_3\mathrm{COOH}$, and ${\mathrm{CH}}_3\mathrm{COONa}$ of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)

Q14.Copper is the most noble of the first row transition metals and occurs in small deposits in several countries. Ores of copper include chalcanthite $\left({\mathrm{CuSO}}_4\cdot 5{\mathrm{H}}_2\mathrm{O}\right)$, atacamite …

Q17.The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple mod …

Q18.The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple mod …

Q19.The total number of basic groups in the following form of lysine is

(see structure)

Q20.The total number of cyclic isomers possible for a hydrocarbon with the molecular formula ${\mathrm{C}}_4{\mathrm{H}}_6$ is

Q22.Amongst the following, the total number of compounds soluble in aqueous NaOH is

(see structure)

Q23.Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is
| KCN | ${\mathrm{K}}_2{\mathrm{SO}}_4$ | ${\left({\mathrm{NH}}_4\right)}_2{\mathrm{C}}_2{\mathrm{O}}_4$ | NaCl | $\mathrm{Zn}{\left({\mathrm{NO}}_3\right)}_2$ || …

Q25.The value of n in the molecular formula ${\mathrm{Be}}_{\mathrm{n}}{\mathrm{Al}}_2{\mathrm{Si}}_6{\mathrm{O}}_{18}$ is

Q26.A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average titre value is

Q27.The concentration of $R$ in the reaction $R\to P$ was measured as a function of time and the following data is obtained:

The order of the reaction is

Q1.If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression $\frac{a}{c}\sin 2C+\frac{c}{a}\sin 2A$ is

Q2.Equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}$ and perpendicular to the plane containing the straight lines $\frac{x}{3}=\frac{y}{4}=\frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}=\frac{z}{3}$ is

Q3.Let $\omega$ be a complex cube root of unity with $\omega \ne 1$. A fair die is thrown three times. If $r_1,r_2$ and $r_3$ are the numbers obtained on the die, then the probability that ${\omega }^{r_1}+{\omega }^{r_2}+{\omega }^{r_3}=0$ is

Q4.Let P, Q, R and S be the points on the plane with position vectors $-2\hat{i}-\hat{j},4\hat{i},3\hat{i}+3\hat{j}$ and $-3\hat{i}+2\hat{j}$ respectively. The quadrilateral PQRS must be a

Q5.The number of 3×3 matrices A whose entries are either 0 or 1 and for which the system $A\left[\begin{array}{l}x\\ y\\ z\end{array}\right]=\left[\begin{array}{l}1\\ 0\\ 0\end{array}\right]$ has exactly two distinct solutions, is

Q6.The value of ${\lim }_{x\to 0}\frac{1}{x^3}{\int }_0^x\frac{t\ln (1+t)}{t^4+4}dt$ is

Q7.Let $p$ and $q$ be real numbers such that $p\ne 0,p^3\ne q$ and $p^3\ne -q$. If $\alpha$ and $\beta$ are nonzero complex numbers satisfying $\alpha +\beta =-p$ and ${\alpha }^3+{\beta }^3=q$, then a quadratic equation having $\frac{\alpha }{\beta }$ and …

Q8.Let $f,g$ and $h$ be real-valued functions defined on the interval $[0,1]$ by $f(x)=e^{x^2}+e^{-x^2},g(x)=x{e}^{x^2}+e^{-x^2}$ and $h(x)=x^2{e}^{x^2}+e^{-x^2}$. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then

Q13.The value(s) of ${\int }_0^1\frac{x^4(1-x{)}^4}{1+x^2}dx$ is (are)

Q14.Let p be an odd prime number and $T_p$ be the following set of $2\times 2$ matrices:


The number of A in $T_p$ such that A is either symmetric or skew-symm …

Q16.Let p be an odd prime number and $T_p$ be the following set of $2\times 2$ matrices:


The number of A in $T_p$ such that $\det (A)$ is not divisible by p is

Q17.The circle $x^2+y^2-8x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points A and B.

Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

Q18.The circle $x^2+y^2-8x=0$ and hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$ intersect at the points A and B.

Equation of the circle with AB as its diameter is

Q19.The number of values of $\theta$ in the interval $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ such that $\theta \ne \frac{n\pi }{5}$ for $n=0,\pm 1,\pm 2$ and $\tan \theta =\cot 5\theta$ as well as $\sin 2\theta =\cos 4\theta$ is

Q20.The maximum value of the expression $\frac{1}{{\sin }^2\theta +3\sin \theta \cos \theta +5{\cos }^2\theta }$ is

Q21.If $\vec{a}$ and $\vec{b}$ are vectors in space given by $\vec{a}=\frac{\hat{i}-2\hat{j}}{\sqrt{5}}$ and $\vec{b}=\frac{2\hat{i}+\hat{j}+3\hat{k}}{\sqrt{14}}$, then the value of $(2\vec{a}+\vec{b})\cdot [(\vec{a}\times \vec{b})\times (\vec{a}-2\vec{b})]$ is

Q22.The line $2x+y=1$ is tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is

Q23.If the distance between the plane $Ax-2y+z=d$ and the plane containing the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ is $\sqrt{6}$, then $|d|$ is

Q24.For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by

Then the value …

Q25.Let $\omega$ be the complex number $\cos \frac{2\pi }{3}+\mathrm{i}\sin \frac{2\pi }{3}$. Then the number of distinct complex numbers $z$ satisfying …

Q26.Let ${\mathrm{S}}_{\mathrm{k}},\mathrm{k}=1,2,\dots ,100$, denote the sum of the infinite geometric series whose first term is $\frac{\mathrm{k}-1}{\mathrm{k}!}$ and the common ratio is $\frac{1}{\mathrm{k}}$. Then the value of …

Q27.The number of all possible values of $\theta$, where $0<\theta <\pi$, for which the system of equations …

Q28.Let f be a real-valued differentiable function on R (the set of all real numbers) such that $\mathrm{f}(1)=1$. If the y-intercept of the tangent at any point $\mathrm{P}(\mathrm{x},\mathrm{y})$ on the curve $\mathrm{y}=\mathrm{f}(\mathrm{x})$ is equal to the cube of the ab …