List of top Questions asked in JEE Advanced

A planet of radius $R=\frac{1}{10}$ x (radius of earth) has the same mass density as earth. Scientists dig a well of depth $\frac{R}{5}$ on it and lower a wire of the same length and of linear mass density $10^{-3}$ $kgm^{-1}$ into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of earth = $6 \times 10^6$ m and the acceleration due to gravity of earth is $10 \,ms^{-2}$)

A transparent thin film of uniform thickness and refractive index $n _{1}=1.4$ is coated on the convex spherical surface of radius $R$ at one end of a long solid glass cylinder of refractive index $n_{2}=1.5$, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance $f _{1}$ from the film, while rays of light traversing from glass to air get focused at distance $f _{2}$ from the film. Then

One end of a taut string of length $3 \,m$ along the $x$ axis is fixed at $x =0$. The speed of the waves in the string is $100 \,ms ^{-1}$. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

In the quadratic equation $p(x) = 0$ with real coefficients has purely imaginary roots. Then, the equation $p[p(x)] = 0 $ has

Three boys and two girls stand in a queue. The probability that the number of boys a head of every girl is atleast one more that the number of girls ahead of her, is

Let $M$ and $N$ be two $3 \times 3$ matrices such that $MN = NM$. Further, if $M \neq N ^{2}$ and $M ^{2}= N ^{4}$, then

From a point $P (\lambda, \lambda, \lambda)$, perpendiculars $PQ$ and $PR$ are drawn respectively on the lines $y=x, z=1$ and $y=$ $-x, z=-1$. If $P$ is such that $\angle QPR$ is a right angle, then the possible value(s) of $\lambda$ is(are)

The locus of the foot of perpendicular drawn from the centre of the ellipse $ x^2 + 3y^2 = 6$ on any tangent to it is

If the temperature of the body is increased by $ 10\%, $ the percentage increase in the emitted indication will be

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is (are)

If the value of mode and mean is $60$ and $66$ respectively, then the value of median is

Let $w = \frac{\sqrt 3 + i }{2}$ and $P = \{W^n:n=1,2,3,....\}$ Further $H_1 = \bigg \{z \in C: Re \, z >\frac{1}{2}\bigg \}$ and $H_2=\bigg[ z\in C: Re \,z

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the smaller loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the bigger loop, then the flux linked with smaller loop is

Perpendicular are drawn from points on the line $ \frac{x+2}{2}=\frac{y+1}{-1}= \frac{z}{3}$ to the plane $x+ y + z = 3$. The feet of perpendiculars lie on the line

The correct statement(s) about $O_3$ is/are

For $3 \times 3$ matrices $M$ and $N$ , which of the following statement(s) is/are not correct ?

The thermal dissociation of equilibrium of $CaCO_3 $ (s) is studied under different conditions $ CaCO_3 \, ( g) \rightleftharpoons CaCO ( g ) + CO_2 ( g)$ For this equilibrium, the correct statement(s) is/are

The $ K_{sp} \, of \, Ag_2CrO_4 $ is $ 1.1 \times 10^{ - 12 } $ at 298 K. The solubility (in mol/L) of $Ag_2 CrO_4 $ in $ a 0.1 M \, AgNO_3 $ solution is

How many litres of water must be added to 1 L of an aqueous solution of HCL with a pH of 1 to create an aqueous solution with pH of 2?

One end of a horizontal thick copper wire of length $2\, L$ and radius $2 \,R$ is welded to an end of another horizontal thin copper wire of length $L$ and radius $R$. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at $25^\circ $C. For this process, the correct statement is

If $ 3^x = 4^{ x - 1} $ then x is equal to

Two non-conducting solid spheres of radii $R$ and $2R$ , having uniform volume charge densities $\rho _1 $ and $ \rho _2 $ respectively, touch each other. The net electric field at a distance $2R$ from the centre of the smaller sphere, along the line joining the centre of the spheres, is zero. The ratio $\rho _1 \, / \, \rho _2 $ can be

The work done on a particle of mass $m$ by a force $K \left[\frac{ x }{\left( x ^{2}+ y ^{2}\right)^{3 / 2}} \hat{ i }+\frac{ y }{\left( x ^{2}+ y ^{2}\right)^{3 / 2}} \hat{ j }\right]$ ( $K$ being a constant of appropriate dimensions, when the particle is taken from the point $( a , 0)$ to the point $(0, a )$ along a circular path of radius a about the origin in the $x$-y plane is

The initial rate of hydrolysis of methyl acetate $(1 M)$ by a weak acid $(HA, 1M) $ is 1/100th of that of a strong acid $(HX, 1M)$, at $ 25^{\circ} C.$ The $ K_a ( H A ) $ is