List of top Questions asked in JEE Advanced

Consider the following reaction,
\(2H_2(g) + 2NO(g) \rightarrow N_2(g) + 2H_2O(g)\)
which follows the mechanism given below:
\(2NO(g)\underset{k_{-1}}{\stackrel{k_1}{\rightleftharpoons}} N_2O_2(g)\) (fast equilibrium)
\(N_2O_2(g)+H_2(g) \xrightarrow[]{K_2}N_2O(g)+H_2O\)  (slow reaction)
\(N_2O(g)+H_2(g) \xrightarrow[]{K_3}N_2(g)+H_2O\)  (fast reaction)
The order of the reaction is________

Let \(\overrightarrow{OP}=\frac{\alpha-1}{\alpha}\hat{i}+\hat{j}+\hat{k},\overrightarrow{OQ}=\hat{i}+\frac{\beta-1}{\beta}\hat{j}+\hat{k}\) and \(\overrightarrow{OR}=\hat{i}+\hat{j}+\frac{1}{2}\hat{k}\) be three vector where α, β ∈ R - {0} and 0 denotes the origin. If \((\overrightarrow{OP}\times\overrightarrow{OQ}).\overrightarrow{OR}=0\) and the point (α, β, 2) lies on the plane 3x + 3y - z + l = 0, then the value of l is _______.

An organic compound P having molecular formula C₆H₆O₃ gives ferric chloride test and does not have intramolecular hydrogen bond. The compound P reacts with 3 equivalents of NH₂OH to produce oxime Q. Treatment of P with excess methyl iodide in the presence of KOH produces compound R as the major product. Reaction of R with excess iso-butylmagnesium bromide followed by treatment with H₃O⁺ gives compound S as the major product.
The total number of methyl (−CH₃) group(s) in compound S is ____.

A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into Pb-206 while the rest of it remains undisintegrated.
When the age of the sample is P x10⁸ years, the ratio of mass of Pb-206 to that of U-238 in the sample is found to be 7. The value of P is _____.
[Given: Half-life of U-238 is 4.5 x10⁹ years; log_e2 = 0.693]

For a double strand DNA, one strand is given below:

The amount of energy required to split the double strand DNA into two single strands is _____ kcal mol⁻¹.
[Given: Average energy per H-bond for A-T base pair = 1.0 kcal mol⁻¹, G-C base pair = 1.5 kcal mol⁻¹, and A-U base pair = 1.25 kcal mol⁻¹. Ignore electrostatic repulsion between the phosphate groups.]

Vessel-1 contains w₂ g of a non-volatile solute X dissolved in w₁ g of water. Vessel-2 contains w₂ g of another non-volatile solute Y dissolved in w₁ g of water. Both the vessels are at the same temperature and pressure. The molar mass of X is 80% of that of Y. The van’t Hoff factor for X is 1.2 times of that of Y for their respective concentrations.
The elevation of boiling point for solution in Vessel-1 is _____ % of the solution in Vessel-2.

To form a complete monolayer of acetic acid on 1g of charcoal, 100 mL of 0.5M acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 mL of 1M NaOH solution was required. If each molecule of acetic acid occupies P x 10⁻²³ m² surface area on charcoal, the value of P is _____.
[Use given data: Surface area of charcoal = 1.5 x 10² m²g⁻¹ ; Avogadro’s number (N_A) = 6.0 x 10²³ mol⁻¹ ]

A spherical soap bubble inside an air chamber at pressure \(𝑃_0 = 10^5 \)Pa has a certain radius so that the excess pressure inside the bubble is Δ𝑃 = 144 Pa. Now, the chamber pressure is reduced to \(8𝑃_0/27\) so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure Δ𝑃 in both the cases to be much smaller than the chamber pressure. The new excess pressure Δ𝑃 in Pa is

An infinitely long thin wire, having a uniform charge density per unit length of \(5 nC/m,\) is passing through a spherical shell of radius \(1 m\), as shown in the figure. A \(10 nC\) charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points P and R, in Volt, is ______. [Given: In SI units \(\frac{1}{ 4πϵ0} = 9 × 10^9 , ln \ 2 = 0.7\). Ignore the area pierced by the wire.]

Two equilateral-triangular prisms \(P_1 \)and \(P_2\) are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism \(P_1\) at an angle of incidence 𝜃 such that the outgoing ray undergoes minimum deviation in prism \(P_2\). If the respective refractive indices of \(P_1\) and\( P_2\) are \(√ 3 /2\) and \(√3\), then \(\theta  = sin{−1}[\sqrt \frac{ 3}{ 2} sin ( \frac{\pi}{B} )],\) where the value of \(\beta\) is ______.

A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle \(\theta\) at P, as shown in the figure. When \(\theta = 30\) , then the electric flux through the curved surface of the cylinder is \(Φ\). If \(\theta= 60\degree\) , then the electric flux through the curved surface becomes \(Φ/√𝑛\), where the value of n is______.

 

A ball is thrown from the location \((x_0, y_0 ) = (0,0)\) of a horizontal playground with an initial speed \(𝑣_0\) at an angle \(\theta_0\)\(\theta_0\) from the +𝑥-direction. The ball is to be hit by a stone, which is thrown at the same time from the location \((𝑥_1, 𝑦_1 ) = (𝐿, 0).\) The stone is thrown at an angle \((180 − \theta_1 )\) from the +𝑥-direction with a suitable initial speed. For a fixed \(𝑣_0\) , when \((\theta_0 , \theta_1 ) = (45° , 45° ),\) the stone hits the ball after time \(𝑇_1\) , and when \((\theta_0 , \theta_1 ) = (60° , 30° )\), it hits the ball after time \(𝑇_2\) . In such a case,\( (\frac{𝑇1 }{𝑇2} )^2\) is ______.

The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in thedetermination of the volume is ______.

Let the function \(f:[1,\infin)→\R\) be defined by
\(f(t) = \begin{cases}     (-1)^{n+1}2, & \text{if } t=2n-1,n\in\N, \\     \frac{(2n+1-t)}{2}f(2n-1)+\frac{(t-(2n-1))}{2}f(2n+1) & \text{if } 2n-1<t<2n+1,n\in\N. \end{cases}\)
Define \(g(x)=\int\limits_{1}^{x}f(t)dt,x\in(1,\infin).\) Let α denote the number of solutions of the equation g(x) = 0 in the interval (1, 8] and \(β=\lim\limits_{x→1+}\frac{g(x)}{x-1}\). Then the value of α + β is equal to _____.

A normal with slope \(\frac{1}{\sqrt6}\) is drawn from the point (0, -α) to the parabola x² = -4αy, where a > 0. Let L be the line passing through (0, -α) and parallel to the directrix of the parabola. Suppose that L intersects the parabola at two points A and B. Let r denote the length of the latus rectum and s denote the square of the length of the line segment AB. If r : s = 1 : 16 then the value of 24a is __________.

Let \(\vec{p}=2\hat{i}+\hat{j}+3\hat{k}\) and \(\vec{q}=\hat{i}-\hat{j}+\hat{k}\). If for some real numbers α, β and γ we have
\(15\hat{i}+10\hat{j}+6\hat{k}=α(2\vec{p}+\vec{q})+β(\vec{p}-2\vec{q})+γ(\vec{p}\times\vec{q})\),
then the value of γ is ________.

Let the function \(f:\R→\R\) be defined by
\(f(x)=\frac{\sin x}{e^{\pi x}}\frac{(x)^{2023}+2024x+2025}{(x^2-x+3)}+\frac{2}{e^{\pi x}}\frac{(x^{2023}+2024x+2025)}{(x^2-x+3)}\)
Then the number of solutions of f (x) = 0 in \(\R\) is __.

A bag contains N balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For i = 1, 2, 3, let W_i, G_i and B_i denote the events that the ball drawn in the i^th draw is a white ball, green ball, and blue ball, respectively. If the probability \(P(W_1∩G_2∩B_3)=\frac{2}{5N}\) and the conditional probability \(P(B_3|W_1∩G_2)=\frac{2}{9}\), then N equals ________.

Let \(f:\R→\R\) be a function such that f(x + y) = f(x) + f(y) for all x, y ∈ \(\R\), and \(g:\R→(0,\infin)\) be a function such that g(x + y) = g(x)g(y) for all x, y ∈ \(\R\). If \(f(\frac{-3}{5})=12\) and \(g(\frac{-1}{3})=2\), then the value of \((f(\frac{1}{4})+g(-2)-8)g(0)\) is ______.

Among the following complexes, the total number of diamagnetic species is ______.
[Mn(NH₃)₆]³⁺, [MnCl₆]³⁻, [FeF₆]³⁻, [CoF₆]³⁻, [Fe(NH₃)₆]³⁺, and [Co(en)₃]³⁺
[Given, atomic number: Mn = 25, Fe = 26, Co = 27;
en = H₂NCH₂CH₂NH₂]

In the following reaction sequence, the major product P is formed.

Glycerol reacts completely with excess P in the presence of an acid catalyst to form Q. Reaction of Q with excess NaOH followed by the treatment with CaCl₂ yields Ca-soap R, quantitatively. Starting with one mole of Q, the amount of R produced in gram is ______.
[Given, atomic weight: H = 1, C = 12, N = 14, O = 16, Na = 23, Cl = 35, Ca = 40]

Among V(CO)₆, Cr(CO)₅, Cu(CO)₃, Mn(CO)₅, Fe(CO)₅, [Co(CO)₃]^3-, [Cr(CO)₄]^4-, and Ir(CO)₃, the total number of species isoelectronic with Ni(CO)₄ is _________.
[Given, atomic number: V = 23, Cr=24, Mn 25, Fe 26, Co 27, Ni 28, Cu = 29, Ir = 77]

Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. NaOH solution, gives P and Q. Compound P does not give Tollens' test, whereas Q on acidification gives positive Tollens' test. Treatment of P with excess cyclohexanone in the presence of catalytic amount of p-toluenesulfonic acid (PTSA) gives product R.
Sum of the number of methylene groups (-CH2-) and oxygen atoms in R is _______

Consider the following volume−temperature (V−T) diagram for the expansion of 5 moles of an ideal monoatomic gas.

Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence X→Y→Z is ______.
[Use the given data: Molar heat capacity of the gas for the given temperature range, C_V,_m = 12 J K⁻¹mol⁻¹ and gas constant, R=8.3 JK⁻¹ mol⁻¹]

Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height ℎ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t1 and t2, respectively. If \(H = ( \frac{16}{ 9} ) ℎ\), then the ratio t1/t2 is ___