List of top Questions asked in JEE Advanced

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 Wi, Gi and Bi denote the events that the ball drawn in the ith 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.
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, CV,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 ___
A source (S) of sound has frequency\( 240 Hz\). When the observer (O) and the source move towards each other at a speed \(v\) with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be \(288 Hz\). However, when the observer and the source move away from each other at the same speed v with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be \(n\) Hz. The value of \(n\) is _____.
Alternative_text
A disc of mass \(M\) and radius \(R\) is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass \(M\) and radius \(R/2\) is fixed to the motor’s thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed \(\omega\). If the angular speed at which the large disc rotates is \(\omega/n\), then the value of \(n\) is _____
Alternative_Text
The specific heat capacity of a substance is temperature dependent and is given by the formula C = kT, where k is a constant of suitable dimensions in SI units, and T is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance from −73 ° C to 27 ° C is nk, the value of n is ___[Given: 0 K = −273 °C.]
Let X be a random variable, and let P(X = x) denote the probability that X takes the value x. Suppose that the points (x, P(X = x)), x = 0,1,2,3,4, lie on a fixed straight line in the xy -plane, and P(X = x) = 0 for all x ∈ R - {0,1,2,3,4}. If the mean of X is \(\frac{5}{2}\) , and the variance of X is α, then the value of 24α is ______.
Let \(S=\left\{\begin{pmatrix} 0 & 1 & c \\ 1 & a & d\\ 1 & b & e \end{pmatrix}:a,b,c,d,e\in\left\{0,1\right\}\ \text{and} |A|\in \left\{-1,1\right\}\right\}\), where |A| denotes the determinant of A. Then the number of elements in S is _______.
The compound(s) having peroxide linkage is(are)
The option(s) with correct sequence of reagents for the conversion of P to Q is(are)
The option(s) with correct sequence of reagents for the conversion of P to Q is
An aqueous solution of hydrazine (N2H4) is electrochemically oxidized by O2, thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is N2(g).
Choose the correct statement(s) about the above process
The species formed on fluorination of phosphorus pentachloride in a polar organic solvent are
In the following reaction sequence, the major product Q is
\(\text{L-Glucose}\xrightarrow[ii)Cr_2,775K,10-20 \text{atm}]{i)HI, \Delta}P\xrightarrow[UV]{Cl_2(excess)}Q\)
In a metal deficient oxide sample, MXY2O4(M and Y are metals), M is present in both +2 and +3 oxidation states and Y is in +3 oxidation state. If the fraction of M2+ ions present in M is \(\frac{1}{3}\), the value of X is______.
According to Bohr’s model, the highest kinetic energy is associated with the electron in the
A positive, singly ionized atom of mass number \(A_M\) is accelerated from rest by the voltage \(192 V\). Thereafter, it enters a rectangular region of width 𝑤 with magnetic field \(\bar{B_0} = 0.1𝑘̂\)Tesla, as shown in the figure. The ion finally hits a detector at the distance 𝑥 below its starting trajectory. [Given: Mass of neutron/proton =\((5/3) × 10^{−27}\) kg, charge of the electron \(= 1.6 × 10^{−19} C.\)]
Alternative_Text
Which of the following option(s) is(are) correct?
A table tennis ball has radius \((3/2) × 10^{−2} \)m and mass \((22/7) × 10^{−3} \)kg. It is slowly pushed down into a swimming pool to a depth of 𝑑 = 0.7 m below the water surface and then released from rest. It emerges from the water surface at speed 𝑣, without getting wet, and rises up to a height 𝐻. Which of the following option(s) is(are) correct?[Given: \(\pi = 22/7, g = 10 m s ^{−2} \), density of water = \(1 × 10^3 kg\ m^{−3}\) , viscosity of water = \(1 × 10^{−3}\) Pa-s.]