List of top Questions asked in JEE Advanced- 2017

A big water drop is formed by the combination of ?n? small water drops of equal radii. The ratio of the surface energy of ?n' drops to the surface energy of big drop is

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T =0.01$ seconds and he measures the depth of the well to be $L =20$ meters. Take the acceleration due to gravity $g =10\, ms ^{-2}$ and the velocity of sound is $300\, ms ^{-1}$. Then the fractional error in the measurement, $\delta L / L$, is closest to

The instantaneous voltages at three terminals marked $X , Y$ and $Z$ are given by $V _{ x }= V _{0} \sin \omega t$ $V _{ y }= V _{0} \sin \left(\omega t +\frac{2 \pi}{3}\right)$ and $V _{ z }= V _{0} \sin \left(\omega t +\frac{4 \pi}{3}\right)$ An ideal voltmeter is configured to read $rms$ value of the potential difference between its terminals. It is connected between points $X$ and $Y$ and then between $Y$ and $Z$. The reading(s) of the voltmeter will be

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 correct statement $(s)$ applicable to this system is (are)

Let $S=\{1,2,3, \ldots \ldots, 9\}$. For $k=1,2, \ldots \ldots, 5$, let $N_{k}$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=$

The colour of the $X_2$ molecules of group $17$ elements changes gradually from yellow to violet down the group. This is due to

A conducting circular loop of radius r carries a constant current z. It is placed in a uniform magnetic field $\vec{B}_{0}$ such that $\vec{B}_{0}$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is

A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3R having centre at the point C. The bead is attached to one of the ends of spring of spring constant k. Natural length of spring is R and the other end of the spring is fixed at point O as shown in figure. Bead is released from position A, what will be kinetic energy of the bead when it reaches at point B ?

One twirls a circular ring (of mass $M$ and radius $R$ ) near the tip of one's finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is $r$. The finger rotates with an angular velocity $\omega_{0}$. The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is $\mu$ and the acceleration due to gravity is $g$. The total kinetic energy of the ring is

An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding $ Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?

Which of the following combination will produce $H_2$ gas?

Pure water freezes at $273 \,K$ and $1$ bar. The addition of $34.5\, g$ of ethanol to $500\, g$ of water changes the freezing point of the solution. Use the freezing point depression constant of water as $2\,K\, kg\,mol^{-1}$. The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T). [molecular weight of ethanol is $46\, g\,mol^{-1}$] Among the following, the option representing change in the freezing point is

If '' > 0$for all$

If $f: R \rightarrow R$ is a differentiable function such that $f'(x)>2 f(x)$ for all $x \in R$, and $f(0)=1$, then

Three randomly chosen nonnegative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even, is

How many $3 \times 3$ matrices $M$ with entries from $\{0,1,2\}$ are there, for which the sum of the diagonal entries of $M^{T} M$ is $5$ ?

If $8\sqrt{x}\left(\sqrt{9+\sqrt{x}}\right)dy = \left(\sqrt{4+\sqrt{9+\sqrt{x}}}\right)^{-1}\,\,dx, \,\,\,\,x > 0$ and $

The equation of the plane passing through the point $(1, 1, 1)$ and perpendicular to the planes $2

Let $O$ be the origin and let $P Q R$ be an arbitrary triangle. The point $S$ is such that $\overrightarrow{O P} \cdot \overrightarrow{O Q}+\overrightarrow{O R} \cdot \overrightarrow{O S}=\overrightarrow{O R} \cdot \overrightarrow{O P}+\overrightarrow{O Q} \cdot \overrightarrow{O S}=\overrightarrow{O Q} \cdot \overrightarrow{O R}+\overrightarrow{O P} \cdot \overrightarrow{O S}$ Then the triangle $P Q R$ has $S$ as its

In a bimolecular reaction, the steric factor $P$ was experimentally determined to be $4.5.$ The correct option(s) among the following is(are)

Consider an expanding sphere of instantaneous radius

Addition of excess aqueous ammonia to a pink coloured aqueous solution of $MCl _{2} \cdot 6 H _{2} O (X)$ and $NH _{4} Cl$ gives an octahedral complex $Y$ in the presence of air. In aqueous solution, complex $Y$ behaves as $1: 3$ electrolyte. The reaction of $X$ with excess $HCl$ at room temperature results in the formation of a blue colured complex $Z$. The calculated spin only magnetic moment of $X$ and $Z$ is $3.87\, B.M$., whereas it is zero for complex $Y$. Among the following options, which statement(s) is(are) correct ?

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

The correct statement(s) about the oxoacids, $HClO_4$ and $HClO$, is(are)