List of top Questions asked in JEE Advanced

In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10 ± 0.1 cm and the distance of its real image from the lens is 20 ± 0.2 cm. The error in the determination of focal length of the lens is 𝑛 %. The value of 𝑛 is ____ .

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.
[Given: Wien’s constant as $2.9 \times 10^{−3} m^{-K}$ and $\frac{hc}{e} = 1.24 \times 10^{−6} V^{-m}$]

List-I		List-II
(P)	2000 K	(1)	The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function 4 eV.
(Q)	3000 K	(2)	The radiation at peak wavelength is visible to human eye.
(R)	5000 K	(3)	The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction.
(S)	10000 K	(4)	The power emitted per unit area is $\frac{1}{16}$ of that emitted by a blackbody at temperature 6000 K.
		(5)	The radiation at peak emission wavelength can be used to image human bones.

The plot of log 𝑘_𝑓 versus $\frac{1}{T}$ for a reversible reaction, A (g) ⇌ P (g) is shown.

plot of log 𝑘𝑓 versus 1/T for a reversible reaction

Pre-exponential factors for the forward and backward reactions are 10¹⁵s^-1 and 10¹¹s^-1 respectively. If the value of log K for the reaction at 500 K is 6, the value of |log kb| at 250K is_________
[K = equilibrium constant of the reaction,
𝑘_𝑓 = rate constant of forward reaction,
𝑘_𝑏 = rate constant of backward reaction]

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight line on the horizontal ground. The lamp post and the person are always vertical. If the speed of the person is 60 cm/sec, then find the speed of tip point of its shadow with respect to the person in cm/sec.

Plotting $\frac{1}{Λ_{m}}$against $cΛ_{m}$ for aqueous solutions of a monobasic weak acid (HX) resulted in a straight line with y-axis intercept of P and slope of S. The ratio $\frac{P}{S}$ is
[$Λ_{m}$ = molar conductivity,
$Λ^{o}_{m}$= limiting molar conductivity,
$c$ = molar concentration,
$K_{a}$ = dissociation constant of HX]

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is un and the speed of sound in the gas is vn. At a fixed temperature and pressure, which of the following is the correct option?

One mole of an ideal gas expands adiabatically from an initial state(T_A, V₀) to a final state (T_f,5V₀). Another mole of the same gas expands isothermally from a different initial state (T_B, V₀) to the same final state (T_f,5V₀). The ratio of the specific heat of constant pressure and constant volume of the ideal gas is λ. What is the ratio of $\frac{T_A}{T_B}$?

In the following reactions, P, Q, R, and S are the major products.

The correct statement(s) about P, Q, R, and S is(are)

One mole of an ideal gas undergoes two different cyclic processes I and I, as shown in the P-V diagrams below. In cycle, I processes a, b, c and d are isobaric, isothermal, isobaric, and isochoric, respectively. In cycle II, processes a',b',c', and d' are isothermal, isochoric, isobaric, and isochoric, respectively. The total work done during cycle I is 𝑊_I and that during cycle II is 𝑊_II. The ratio W_I/W_II is

A disaccharide X cannot be oxidised by bromine water. The acid hydrolysis of X leads to a laevorotatory solution. The disaccharide X is

In a one-litre flask, 6 moles of A undergoes the reaction A (g) ⇌ P (g). The progress of product formation at two temperatures (in Kelvin), T₁ and T₂, is shown in the figure:

If T₁ = 2T₂ and (∆G₂^Θ − ∆G₁^Θ) = RT₂ ln x, then the value of x is ___ .
[∆G₁^Θ and ∆G₂^Θ are standard Gibb’s free energy change for the reaction at temperatures T₁ and T₂, respectively.]

A series LCR circuit is connected to a 45 sin(𝜔𝑡) Volt source. The resonant angular frequency of the circuit is $10^5$ rad s⁻¹ and current amplitude at resonance is I₀.

When the angular frequency of the source is 𝜔 =$8 ×$ $10^4$ rad s⁻¹, the current amplitude in the circuit is 0.05 I₀. If L=50 mH, match each entry in List-I with an appropriate value from List-II and choose the correct option.

List-I	List-II
(P) I₀ in mA	(1) 44.4
(Q) The quality factor of the circuit	(2) 18
(R) The bandwidth of the circuit in rad s⁻¹	(3) 400
(S) The peak power dissipated at resonance in Watt	(4) 2250
	(4) 2250

The total number of $sp^2$ hybridised carbon atoms in the major product P (a non-heterocyclic compound) of the following reaction is ___.

Let a and b be two nonzero real numbers. If the coefficient of x⁵ in the expansion of ($ax^2+(\frac{70}{27bx})^4$ is equal to the coefficient of x^-5 in the expansion of $(ax-\frac{1}{bx^2})^7$. then the value of 2b is

A closed container constrains a homogeneous mixture made of, 2 moles of an ideal monatomic gas($\gamma=\frac{5}{3}$) and one mole of an ideal diatomic gas($\gamma=\frac{7}{5}$). Here, γ is the ratio of the specific heat at content pressure and constant volume of an ideal gas. The gas mixture does a work of 66 joules when heated at constant pressure. The change in its internal energy is ____Joule.

One mole of an ideal monoatomic gas undergoes two reversible processes ($A → B$ and $B → C$) as shown in the given figure:

$A → B$ is an adiabatic process. If the total heat absorbed in the entire process ($A → B$ and $B → C$) is $R𝑇_2\ ln\ 10$, the value of $2 log\ 𝑉_3$ is ___ .
[Use, molar heat capacity of the gas at constant pressure, $𝐶_{p,m} = \frac 52R$]

Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 cm. This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is 1.2 × 10⁻⁸N m rad^−1. The angular frequency of the oscillations in 𝑛 × 10⁻³ rad s⁻¹. The value of 𝑛 is _____.

An optical arrangement consists of two concave mirrors M₁ and M₂, and a convex lens L with a common principal axis, as shown in the figure. The focal length of L is 10 cm. The radii of curvature of M₁ and M₂ are 20 cm and 24 cm, respectively. The distance between L and M₂ is 20 cm. A point object S is placed at the mid-point between L and M₂ on the axis. When the distance between L and M₁ is $\frac{n}{7}$ cm, one of the images coincides with S. The value of 𝑛 is _______.

Let A₁, A₂, A₃, A₄,........, A₈ be the vertices of the regular octagons that lie on the circle of radius 2. Let p be a point on the circle and let PA_i denote the distance between the point P and Ai for i = 1,2,3,....,8. If P varies over the circle, then the maximum value of the product is PA₁.Pa₂..........PA₈, is

Two spherical stars $A$ and $B$ have densities $\rho_A$ and $\rho_B$, respectively $A$ and $B$ have the same radius, and their masses $M_A$ and $M_B$ are related by $M_B=2 M_A$ Due to an interaction process, star $A$ loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains $\rho_A$ The entire mass lost by $A$ is deposited as a thick spherical shell on $B$ with the density of the shell being $\rho_A$ If $v_A$ and $v_B$ are the escape velocities from $A$ and $B$ after the interaction process, the ratio $\frac{v_B}{v_A}=\sqrt{\frac{10 n}{15^{\frac 13}}}$. The value of $n$ is ___ .

The stoichiometric reaction of 516 g of dimethyldichlorosilane with water results in a tetrameric cyclic product X in 75% yield. The weight (in g) of X obtained is___ .
[Use, molar mass (g mol⁻¹): H = 1, C = 12, O = 16, Si = 28, Cl = 35.5]

Let $X$ be the set of all five-digit numbers formed using $1,2,2,2,2,4,4,0$. for example $22240$ is in $X$ while $02244$ and $44422$ are not in $X$. Suppose that each element of $X$ has an equal chance of being chosen. Let $p$ be the conditional probability that a component chosen at random is a multiple of $20 $ given that it is a multiple of $5$. Then the numerous of $38p$ is equal to

A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from n1 to n2 over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

Match the temperature of a black body given in L-I with an appropriate statement in L-II and choose the correct option. (given: wien is constant as $2.9\times10^{-3}$ m.k. $\frac{hc}{e}=1.24\times10^{-6}\,v.m$

	List-I		List-II
(P)	2000 K	(1)	The radiation at peek wavelength can lead to the emission of photo e$^-$ from a metal of work function 4 eV
(Q)	3000 K	(2)	The radiation at peek wavelength is visible to the human eye
(R)	5000K	(3)	The radiation at peek emission wavelength will result in the widest central maximum of a single slit diffraction
(S)	10000K	(4)	The power emitted per unit area is $\frac{1}{16}$ of that emitted by a black body at a temperature of 6000K.
		(5)	The radiation at peak emission wavelength can be used to image human bone.

Consider the 6 x 6 square in the figure. Let A₁, A₂, ........, A₄₉ be the points of intersections (dots in the picture) in some order. We say that A_i and A_j are friends if they are adjacent along a row or a column. Assume that each point Ai has an equal chance of being chosen. Two distinct points are chosen randomly out of the points A₁, A₂, ........, A₄₉. Let p be the probability that they are friends. Then the value of 7p is