List of top Questions asked in JEE Advanced

Consider the following complex ions, $P, Q$ and $R$. $P=[FeF_6]^{3-},Q=[V(H_2O)_6]^{2+} and \, R=[Fe(H_2O)_6]^{2+} $ The correct order of the complex ions, according to their spin-only magnetic moment values (in $B.M.$) is

The compound that does not liberate $CO_2$, on treatment with aqueous sodium bicarbonate solution, is

The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

The carbon-based reduction method is not used for the extraction of

Upon treatment with ammoniacal $H_2 S$, the metal ion that precipitates as a sulphide is

Among $P, Q, R$ and $S$, the aromatic compounds(s) is/are

A steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement(s) is (are)

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $8 : 15$ is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is $100$, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are

A particle of mass $m$ is projected from the ground with an initial speed $u _{0}$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed $u_{0}$. The angle that the composite system makes with the horizontal immediately after the collision is

A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $u _{1}=4 \hat{i}ms ^{-1}$, enters a region of uniform static magnetic field normal to the $x$-y plane. The region of the magnetic field extends from $x =$ 0 to $x = L$ for all values of $y$. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity $\vec{ u }_{2}=2(\sqrt{3} i +\hat{ j }) m / s ^{-1}$. The correct statement(s) is (are)

Let $\omega$ be a complex cube root of unity with $\omega \ne 0$ and $P = [P_{ii}] $ be an $n \times \, n$ matrix with $p_{ij} = \omega^{i+j}$ Then, $P^2 \ne 0$ when $n$ =

A line $l$ passing through the origin is perpendicular to the lines $ L_1 : (3+t) \widehat {i} +(1-2t) \widehat {j}+(4+2t)\widehat {k}, - \infty < t < \infty$ $ L_2 : (3+2s) \widehat {i} +(3+2s) \widehat {j}+(2+s)\widehat {k}, - \infty < s < \infty$ Then, the coordinate(s) of the point(s) on $l_2$ at a distance of $\sqrt 17$ from the point of intersection of l and $l_1$ is (are)

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}$ Then,the probability that the problem is solved correctly by at least one of them, is

Two lines $L_1:x = 5\, \frac{y}{3-\alpha} = \frac{z}{-2}$ and $L_1:x = \alpha \, \frac{y}{-1} =\frac{z}{2-\alpha}$ are coplaner. Then, $\alpha$ can take value(s)

A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is

The image of an object, formed by a plano-convex lens at a distance of $8\,m$ behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is

A ray of light travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3} j)$. The angle of incidence is

In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$ the path difference (in terms of an integer $n$) corresponding to any point having half the peak intensity is

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2 : 3$. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is $4 : 3$. The ratio of their densities is

Using the expression 2d sin $\theta =\lambda,$ one calculates the values of d by measuring the corresponding angles $\theta$ in the range 0 to 90$^{\circ}$. The wavelength X is exactly known and the error in $\theta$ is constant for all values of $\theta$. As $\theta$ increases from 0$^{\circ}$

Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity $\kappa$ and the other $2 \,\kappa .$ The temperature difference between the ends along the $x$-axis is the same in both the configurations. It takes $9\, s$ to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is

Circle(s) touching X-axis at a distance 3 from the origin and having an intercept of length $2 \sqrt7$ on Y-axis is/are

Consider a disc rotating in the horizontal plane with a constant angular speed to about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) \(\omega\) remains constant throughout. Then

Consider a thin spherical shell of radius $R$ with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field and the electric potential $V (r)$ with the distance $r$ from the centre, is best represented by which graph?

If $S$ be the area of the region enclosed by $ y = e^{-x^2} $, $y = 0,x = 0$ and $x = 1$ . Then,