JEE Advanced 2017 · 21 May 2017 · Paper 1

Q1.A flat plate is moving normal to its plane through a gas under the action of a constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

Q2.A block of mass $M$ has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $x=0$, in a co-ordinate system fixed to the table. A point mass $m$ is released …

Q3.A block $M$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. A transverse wave pulse (Pulse 1) of wavelength ${\lambda }_0$ is produced at point $O$ on the rope. The …

Q4.A human body has a surface area of approximately $1{\mathrm{m}}^2$. The normal body temperature is 10 K above the surrounding room temperature $T_0$. Take the room temperature to be $T_0=300\mathrm{K}$. For $T_0=300\mathrm{K}$, the value of …

Q5.A circular insulated copper wire loop is twisted to form two loops of area $A$ and $2A$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field …

Q6.In the circuit shown, $L=1\mu \mathrm{H},C=1\mu \mathrm{F}$ and $R=1k\Omega$. They are connected in series with an a.c. source $V=V_0\sin \omega t$ as shown. Which of the following options is/are correct?

Q7.For an isosceles prism of angle $A$ and refractive index $\mu$, it is found that the angle of minimum deviation ${\delta }_m=A$. Which of the following options is/are correct?

Q8.A drop of liquid of radius $\mathrm{R}=10^{-2}\mathrm{m}$ having surface tension $\mathrm{S}=\frac{0.1}{4\pi }{\mathrm{Nm}}^{-1}$ divides itself into $K$ identical drops. In this process the total change in the surface energy $\Delta U=10^{-3}\mathrm{J}$. If …

Q9.An electron in a hydrogen atom undergoes a transition from an orbit with quantum number $n_i$ to another with quantum number $n_f.V_i$ and $V_f$ are respectively the initial and final potential energies of the electron. If $\frac{V_i}{V_f}=6.25$, then the sm …

Q10.A monochromatic light is travelling in a medium of refractive index $n=1.6$. It enters a stack of glass layers from the bottom side at an angle $\theta =30^{\circ }$. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers …

Q11.A stationary source emits sound of frequency $f_0=492\mathrm{Hz}$. The sound is reflected by a large car approaching the source with a speed of $2{\mathrm{ms}}^{-1}$. The reflected signal is received by the source and superposed with the original. What will be the beat fr …

Q12.${}^{131}$ I is an isotope of Iodine that $\beta$ decays to an isotope of Xenon with a half-life of 8 days. A small amount of a serum labelled with ${}^{131}\mathrm{I}$ is injected into the blood of a person. The activity of the amount of ${}^{131}\mathrm{I}$ injected was …

Q13.A charged particle (electron or proton) is introduced at the origin $(x=0,y=0,z=0)$ with a given initial velocity $\vec{v}$. A uniform electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ exist everywhere. The velocity $\vec{v}$, electric field $\vec{E}$ …

Q14.A charged particle (electron or proton) is introduced at the origin $(x=0,y=0,z=0)$ with a given initial velocity $\vec{v}$. A uniform electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ exist everywhere. The velocity $\vec{v}$, electric field $\vec{E}$ …

Q15.A charged particle (electron or proton) is introduced at the origin $(x=0,y=0,z=0)$ with a given initial velocity $\vec{v}$. A uniform electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ exist everywhere. The velocity $\vec{v}$, electric field $\vec{E}$ …

Q16.An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V$ diagrams in column 3 of the table. Consider only the path from state 1 to state 2. $W$ denotes the corresponding work done on the system. The equations and plots in …

Q17.An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V$ diagrams in column 3 of the table. Consider only the path from state 1 to state 2. $W$ denotes the corresponding work done on the system. The equations and plots in …

Q18.An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $P-V$ diagrams in column 3 of the table. Consider only the path from state 1 to state 2. $W$ denotes the corresponding work done on the system. The equations and plots in …

Q1.An ideal gas is expanded from $(p_1,V_1,T_1)$ to $(p_2,V_2,T_2)$ under different conditions. The correct statement(s) among the following is(are)

Q2.For a solution formed by mixing liquids L and M, the vapour pressure of L plotted against the mole fraction of M in solution is shown in the following figure. Here $x_L$ and $x_M$ represent mole fractions of L and M, respectively, in the solution. The corr …

Q3.The correct statement(s) about the oxoacids, ${\mathrm{HClO}}_4$ and HClO, is(are)

Q4.The colour of the ${\mathrm{X}}_2$ molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to

Q5.Addition of excess aqueous ammonia to a pink coloured aqueous solution of ${\mathrm{MCl}}_2\cdot 6{\mathrm{H}}_2\mathrm{O}$ (X) and ${\mathrm{NH}}_4\mathrm{Cl}$ gives an octahedral complex Y in the presence of air. In aqueous solution, complex Y behaves as 1:3 electrolyte. …

Q6.The IUPAC name(s) of the following compound is(are)

Q7.The correct statement(s) for the following addition reactions is(are)

(i)

(ii)

Q8.A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is $8{\mathrm{g}\mathrm{cm}}^{-3}$, then the number of atoms present in 256 g of the crystal is $N\times 10^{24}$. The value of $N$ …

Q9.The conductance of a 0.0015 M aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized Pt electrodes. The distance between the electrodes is 120 cm with an area of cross section of $1{\mathrm{cm}}^2$. The conductance of this …

Q10.The sum of the number of lone pairs of electrons on each central atom in the following species is

(Atomic numbers: …

Q11.Among ${\mathrm{H}}_2,{\mathrm{He}}_2^{+},{\mathrm{Li}}_2,{\mathrm{Be}}_2,{\mathrm{B}}_2,{\mathrm{C}}_2,{\mathrm{N}}_2,{\mathrm{O}}_2^{-}$, and ${\mathrm{F}}_2$, the number of diamagnetic species is (Atomic numbers: …

Q12.Among the following, the number of aromatic compound(s) is

Q13.| (II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus …

Q14.| (II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus …

Q15.| (II) 2s orbital | (ii) One radial node | (Q) Probability density at nucleus …

Q16.| (III) Benzaldehyde | (iii) …

Q17.| (III) Benzaldehyde | (iii) …

Q18.| (III) Benzaldehyde | (iii) …

Q1.If $2x-y+1=0$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{16}=1$, then which of the following CANNOT be sides of a right angled triangle?

Q2.If a chord, which is not a tangent, of the parabola $y^2=16x$ has the equation $2x+y=p$, and midpoint $(h,k)$, then which of the following is(are) possible value(s) of $p,h$ and $k$?

Q3.Let $[x]$ be the greatest integer less than or equals to $x$. Then, at which of the following point(s) the function $f(x)=x\cos (\pi (x+[x]))$ is discontinuous?

Q4.Let $f:\mathbb{R}\to (0,1)$ be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the interval (0, 1)?

Q5.Which of the following is(are) NOT the square of a $3\times 3$ matrix with real entries?

Q6.Let $a,b,x$ and $y$ be real numbers such that $a-b=1$ and $y\ne 0$. If the complex number $z=x+iy$ satisfies $\mathrm{Im}\left(\frac{az+b}{z+1}\right)=\mathrm{y}$, then which of the following is(are) possible value(s) of $x$?

Q7.Let $X$ and $Y$ be two events such that $P(X)=\frac{1}{3},P(X\mid Y)=\frac{1}{2}$ and $P(Y\mid X)=\frac{2}{5}$. Then

Q8.For how many values of $p$, the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points?

Q9.Let $f:\mathbb{R}\to \mathbb{R}$ be a differentiable function such that $f(0)=0,f\left(\frac{\pi }{2}\right)=3$ and $f^{\prime }(0)=1$. If

for …

Q10.For a real number $\alpha$, if the system

of lin …

Q11.Words of length 10 are formed using the letters A, B, C, D, E, F, G, H, I, J. Let $x$ be the number of such words where no letter is repeated; and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, …

Q12.The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?

Q13.| (II) $x^2+a^2{y}^2=a^2$ | (ii) $y=mx+a\sqrt{m^2+1}$ | (Q) …

Q14.| (II) $x^2+a^2{y}^2=a^2$ | (ii) $y=mx+a\sqrt{m^2+1}$ | (Q) …

Q15.| (II) $x^2+a^2{y}^2=a^2$ | (ii) $y=mx+a\sqrt{m^2+1}$ | (Q) …

Q16.Let $f(x)=x+{\log }_{\mathrm{e}}x-x{\log }_{\mathrm{e}}x,x\in (0,\infty )$.

• Column 1 contains information about zeros of $f(x),f^{\prime }(x)$ and $f^{\prime \prime }(x)$.
• Column 2 contains information about the limiting behavior of $f(x),f^{\prime }(x)$ and …

Q18.Let $f(x)=x+{\log }_{\mathrm{e}}x-x{\log }_{\mathrm{e}}x,x\in (0,\infty )$.

• Column 1 contains information about zeros of $f(x),f^{\prime }(x)$ and $f^{\prime \prime }(x)$.
• Column 2 contains information about the limiting behavior of $f(x),f^{\prime }(x)$ and …