List of top Questions asked in JEE Advanced

The correct statement(s) related to the metal extraction processes is(are)

The smallest division on the main scale of a Vernier calipers is $01 \,cm$ Ten divisions of the Vernier scale correspond to nine divisions of the main scale The figure below on the left shows the reading of this calipers with no gap between its two jaws The figure on the right shows the reading with a solid sphere held between the jaws The correct diameter of the sphere is

The total number of possible isomers for $[ \text{Pt(NH}_3\text{)}_4\text{Cl}_2 ]\text{Br}_2$ is ___.

In order to measure the internal resistance r₁ of a cell of emf E, a meter bridge of wire resistance R₀ = 50 Ω, a resistance $\frac{R_0}{2}$, another cell of emf $\frac{E}{2}$ (internal resistance r) and a galvanometer G are used in a circuit, as shown in the figure. If the null point is found at l = 72 cm, then the value of r ₁ = ____

For the following reaction scheme, percentage yields are given along the arrow:

$X\, g$ and $y \,g$ are mass of $R$ and $U$, respectively (Use : Molar mass (in $g \,mol^{-1})$ of $H, C$ and $O$ as $1, 12$ and $16$, respectively) The value of $x$ is ______

Ozonolysis of $ClO_2$ produces oxide of chlorine. The average oxidation state of chlorine in this oxide is ____.

Let $O$ be the origin and $\overrightarrow{ OA }=2 \hat{ i }+2 \hat{ j }+\hat{ k }, \overrightarrow{ OB }=\hat{ i }-2 \hat{ j }+2 \hat{ k }$ and $\overrightarrow{ OC }=\frac{1}{2}(\overrightarrow{ OB }-\lambda \overrightarrow{ OA })$ for some $\lambda $>$ 0$. If $|\overrightarrow{ OB } \times \overrightarrow{ OC }|=\frac{9}{2}$, then which of the following statements is(are) TRUE?

The reaction sequence(s) that would lead to o-xylene as the major product is(are).

An ideal gas undergoes a four step cycle as shown in the $P-V$ diagram below During this cycle, heat is absorbed by the gas in

Let $E , F$ and $G$ be three events having probabilities
$P(E)=\frac{1}{8}, P(F)=\frac{1}{6}$ and $P(G)=\frac{1}{4}$, and let $P(E \cap F \cap G)=\frac{1}{10}$.
For any event $H$, if $H ^{ C }$ denotes its complement, then which of the following statements is(are) TRUE?

The reaction of Q with PhSNa yields an organic compound (major product) that gives a positive Carius test on treatment with Na₂O₂ followed by the addition of BaCl₂. The correct option(s) for Q is(are).

The correct statement(s) related to colloids is(are)

A wide slab consisting of two media of refractive indices $n_{1}$ and $n_{2}$ is placed in air as shown in the figure A ray of light is incident from medium $n _{1}$ to $n _{2}$ at an angle $\theta$, where $\sin \theta$ is slightly larger than $\frac1 { n _{1}}$ Take refractive index of air as $1$ Which of the following statement(s) is(are) correct?
$A wide slab consisting of two media of refractive indices 𝑛1 and 𝑛2 is placed in air$

A particle of mass $M =02 \,kg$ is initially at rest in the $xy$-plane at a point $( x =-\ell, y =- h )$, where $\ell=10 \,m$ and $h =1\, m$ The particle is accelerated at time $t =0$ with a constant acceleration $a =10\, m / s ^{2}$ along the positive $x$-direction Its angular momentum and torque with respect to the origin, in SI units, are represented by $\vec{ L }$ and $\vec{\tau}$ respectively $\hat{ i }, \hat{ j }$ and $\hat{ k }$ are unit vectors along the positive $x , y$ and $z$-directions, respectively If $\hat{k}=\hat{i} \times \hat{j}$ then which of the following statement(s) is(are) correct?

For any $3 \times 3$ matrix $M$, let $|M|$ denote the determinant of $M$. Let $I$ be the $3 \times 3$ identity matrix Let $E$ and $F$ be two $3 \times 3$ matrices such that $( I - EF )$ is invertible. If $G =( I - EF )^{-1}$, then which of the following statements is(are) TRUE?

Consider three sets E₁ = {1, 2, 3}, F₁ = {1, 3, 4} and G₁ = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E₁, and let S₁ denote the set of these chosen elements. Let E₂ = E₁ – S₁and F₂ = F₁ ⋃ S₁. Now two elements are chosen at random, without replacement, from the set F₂ and let S₂ denote the set of these chosen elements.
Let G₂ = G₁ ⋃ S₂. Finally, two elements are chosen at random, without replacement from the set G₂ and let S₃ denote the set of these chosen elements. Let E₃ = E₂ ⋃ S₃. Given that E₁ = E₃, let p be the conditional probability of the event S₁ = {1, 2}. Then the value of p is;

For the given close packed structure of a salt made of cation $X$ and anion $Y$ shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction $=\frac{\text { packing efficiency }}{100}$ )

An extended object is placed at point O, 10 cm in front of a convex lens L1 and a concave lens L2 is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is

A cylindrical tube, with its base as shown in the figure, is filled with water It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta=45^{\circ} P_{1}$ and $P_{2}$ are pressures at points $1$ and $2$, respectively located at the base of the tube Let $\beta=\left(P_{1}-P_{2}\right) /(\rho g d)$, where $\rho$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity Which of the following statement(s) is(are) correct?

For any complex number $w=c+$ id, let $\arg (w) \in(-\pi, \pi]$, where $i=\sqrt{-1}$ Let $\alpha$ and $\beta$ be real numbers such that for all complex numbers $z=x+$ iy satisfying $\arg \left(\frac{z+\alpha}{z+\beta}\right)=\frac{\pi}{4}$, then ordered pair $(x, y)$ lies on the circle
$x^{2}+y^{2}+5 x-3 y+4=0$
Then which of the following statements is(are) TRUE?

A mixture of two salts is used to prepare a solution S, which gives the following results:

$\text{White precipitate(s) only} \underset{\text{Room temperature}}{\overset{\text{Dilute NaOH(aq)}}{\longleftarrow}} \text{S (aq solution of the salts)}\underset{\text{Room temperature}}{\overset{\text{Dilute HCl(aq)}}{\longrightarrow}} \text{White precipitate(s) only}$
The correct option(s) for the salt mixture is(are)

Among the following, the conformation that corresponds to the most stable conformation of meso-butane-$2,3$-diol is

Consider a triangle $P Q R$ having sides of lengths $p, q$ and $r$ opposite to the angles $P, Q$ and $R$, respectively. Then which of the following statements is(are) TRUE?

A heavy nucleus $N$, at rest, undergoes fission $N \rightarrow P + Q$, where $P$ and $Q$ are two lighter nuclei. Let $\delta= M _{ N }$ - $M_{P}-M_{Q}$, where $M_{P}, M_{Q}$ and $M_{N}$ are the masses of $P, Q$ and $N$, respectively. $E _{P}$ and $E_{Q}$ are the kinetic energies of $P$ and $Q$, respectively. The speeds of $P$ and $Q$ are $v_{P}$ and $v_{Q}$, respectively. If $c$ is the speed of light, which of the following statement(s) is(are) correct?

Let $E$ denote the parabola $y ^{2}=8 x$ Let $P =(-2,4)$ and let $Q$ and $Q ^{\prime}$ be two distinct points on $E$ such that the lines $P Q$ and $P Q^{\prime}$ are tangents to $E$ Let $F$ be the focus of $E$. Then which of the following statements is(are) TRUE?