List of top Questions asked in JEE Advanced

Let $\alpha$, $\beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2},2\beta$ be the roots of the equation $x^2-qx+r=0.$ Then, the value of r is

$ lim_ { x \to \frac{\pi}{4}} \frac{ \int \limits_2^{sec^2 \, x} \, f \, (t) \, dt }{ x^2 - \frac{\pi^2}{ 16}} $ equals

A resistance of $2 \Omega$ is connected across one gap of a meter-bridge (the length of the wire is $100\, cm$) and an unknown resistance, greater than $2 \Omega$, is connected across the other gap. When these resistances are interchanged, the balance point shifts by $20\, cm$. Neglecting any corrections, the unknown resistance is

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

For inside points $(r \le R) $ $E = 0\, \, \Rightarrow\, \, V =constant = \frac{1}{4 \pi\varepsilon_0} \frac{q}{R}$ For inside points $(r \ge R) $ $\hspace18mm E = \frac{1}{4 \pi\varepsilon_0}.\frac{q}{r^2}$ or $E \propto \frac{1}{r^2}$ and $\hspace10mm V = \frac{1}{4 \pi\varepsilon_0}\frac{q}{r}$ or $V \propto \frac{1}{r}$ On the surface (r = R) $\hspace20mm V = \frac{1}{4 \pi\varepsilon_0}\frac{q}{R}$ $\Rightarrow\hspace15mm E = \frac{1}{4 \pi\varepsilon_0}.\frac{q}{R^2}=\frac{\sigma}{\varepsilon_0}$ where, $ \sigma = \frac{q}{4 \pi R^2}=$ surface charge density corresponding to above equations the correct graphs are shown in option (d).

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). 

Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2x $ is

In the following reaction, The produce X is

In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

The compound(s) formed upon combustion of sodium metal in excess air is (are)

Let $0(0, 0), P(3, 4)$ and $Q(6, 0)$ be the vertices of a $\Delta$ OP The point R inside the $\Delta OPQ$ is such th at the triangles $OPR, PQR$ and $OQR $ are of equal area. The coordinates of R are

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that Indian m an is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2\widehat{i}+\widehat{j}+\widehat{k}, \widehat{i}-\lambda^2\widehat{j}+\widehat{k}$ and $\widehat{i}+\widehat{j}-\lambda^2\widehat{k}$ are coplanar, is

Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be unit vectors such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}.$ Which one of the following is correct?

Let $E^c$ denotes the complement of an event $E$. If $E, F, G$ are pairwise independent events with $P (G) > 0$ and $P(E \cap F \cap G)=0$ then , $P(E^c \cap F^c|G) equals$

A man walks a distance of 3 units from the origin towards the North-East (N 45$^{\circ}$ E) direction. From there, he walks a distance of 4 units towards the North-West (N 45$^\circ$ W) direction to reach a point P. Then, the position of P in the Arg and plane is

Let $ABCD$ be a quadrilateral with area 18, with side AB parallel to the side $CD$ and $AB = 2 CD$. Let $AD$ be perpendicular to $AB$ and $CD$. If a circle is drawn inside the quadrilateral $ABCD$ touching all the sides, then its radius is

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN, is

Electrons with de-Broglie wavelength $ \lambda $ fall on the target in an $X-ray$ tube. The cut-off wavelength of the emitted $X-rays$ is

Among the following metal carbonyls, the $C-O$ bond order is lowest in

A solution of a metal ion when treated with $KI$ gives a red precipitate which dissolves in excess $KI$ to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt (II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is

The percentage of $p$-character in the orbitals forming $P-P$ bonds in $P_4$ is

Among the following, the least stable resonance structure is

A ray of light travelling in water is incident on its surface open to air. The angle of incidence is $\theta$, which is less than the critical angle. Then there will be

A magnetic field $B=B_0 \widehat{j}$ exists in the region a < x < 2 a and $B=-B_0 \widehat{j}$ in the region 2a < x < 3a, where $B_0$ is a positive constant. A positive point charge moving with a velocity$v-v_0 \widehat{i} $ where $v_0$ is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like

A particle moves in the X-Y plane under the influence of a force such that its linear momentum is $p(t) =A[\widehat{i}cos\, (kt) -\widehat{j}sin\, (kt)]$ where, A and k are constants. The angle between the force and the momentum is