List of top Questions asked in JEE Advanced

Let \(S=\left\{(x,y)\in\R\times\R:x\ge0,y\ge0,y^2\le12-2x\ \text{and}\ 3y+\sqrt8\ x\le5\sqrt8\right\}\). If the area of the region S is \(\alpha\sqrt2\), then α is equal to

Considering only the principal values of the inverse trigonometric functions, the value of
\(\tan(\sin^{-1}(\frac{3}{5})-2\cos^{-1}(\frac{2}{\sqrt5}))\)
is

List-I contains various reaction sequences and List-II contains different phenolic compounds. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option.

List I		List II
(P)	XeF₂	(1)	Trigonal bipyramidal and two lone pair of electrons
(Q)	XeF₄	(2)	Tetrahedral and one lone pair of electrons
(R)	XeO₃	(3)	Octahedral and two lone pair of electrons
(S)	XeO₃F₂	(4)	Trigonal bipyramidal and no lone pair of electrons
		(5)	Trigonal bipyramidal and three lone pair of electrons

In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition.
The limiting ionic conductivity (Λ0) values (in mS m²mol⁻¹ ) for different ions in aqueous solutions are given below:

Ions	Ag⁺	K⁺	Na⁺	H⁺	\(\text{NO}_{3}^{-}\)	Cl^-	\(\text{SO}^{2-}_{4}\)	OH^-	CH₃COO^-
\(\Lambda_0\)	6.2	7.4	5.0	35.0	7.2	7.6	16.0	19.9	4.1

For different combinations of titrates and titrants given in List-I, the graphs of 'conductance' versus ‘volume of titrant’ are given in List-II.
Match each entry in List-I with the appropriate entry in List-II and choose the correct option.

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 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________

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]

The option(s) in which at least three molecules follow Octet Rule is(are)

Reaction of iso-propylbenzene with O₂ followed by the treatment with H₃O⁺ forms phenol and a by-product P. Reaction of P with 3 equivalents of Cl₂ gives compound Q. Treatment of Q with Ca(OH)₂ produces compound R and calcium salt S.
The correct statement(s) regarding P, Q, R and S is(are)

Among the following, the correct statement(s) for electrons in an atom is(are)

Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other.
[en = H₂NCH₂CH₂NH₂]

Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is

At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid (HNO₂) gives the species

A closed vessel contains 10 g of an ideal gas X at 300 K, which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm. The ratio of root mean square velocities of X and Y at 300 K is

The circuit shown in the figure contains an inductor L, a capacitor \(C_0\), a resistor\( R_0\) and an ideal battery. The circuit also contains two keys \(K_1\) and \(K_2\). Initially, both the keys are open and there is no charge on the capacitor. At an instant, key \(K_1\) is closed and immediately after this the current in \(R_0\) is found to be \(I_1\). After a long time, the current attains a steady state value \(I_2\). Thereafter,\( K_2\) is closed and simultaneously \(K_1\) is opened and the voltage across \(C_0\) oscillates with amplitude \(C_0\) and angular frequency \(\omega_0\).

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I		List-II
P	The value of \(I1\) in Ampere is	I	\(0\)
Q	The value of I2 in Ampere is	II	\(2\)
R	The value of \(\omega_0\) in kilo-radians/s is	III	\(4\)
S	The value of \(V_0\) in Volt is	IV	\(20\)
			200

A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence \(\theta_0\). The ray partially refracts into the sphere with angle of refraction \(\phi\) and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is \(a\). Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I		List-II
P	If \(n = 2\) and \(\alpha = 180°\), then all the possible values of \(\theta_0\) will be	I	\(30\degree\) or \(0\degree\)
Q	If \(n = √3\) and \(\alpha= 180°\), then all the possible values of \(\theta_0\) will be	II	\(60\degree\) or \(0\degree\)
R	If \(n = √3\) and \(\alpha= 180°\), then all the possible values of \(\phi_0\) will be	III	\(45\degree\) or \( 0\degree\)
S	If \(n = \sqrt2\) and \(\theta_0 = 45°\), then all the possible values of \(\alpha\) will be	IV	\(150\degree\)
			\[0\degree\]

Four identical thin, square metal sheets, S1, S2, S3 and S4, each of side a are kept parallel to each other with equal distance \(d (≪ a)\) between them, as shown in the figure. Let \(C_0 = \epsilon_0\frac{a^2}{d}, \)where \(\epsilon_0\) is the permittivity of free space.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

List-I		List-II
P	The capacitance between S1 and S4, with S2 and S3 not connected, is	I	\(3C_0\)
Q	The capacitance between S1 and S4, with S2 shorted to S3, is	II	\(\frac{C_0}{2}\)
R	The capacitance between S1 and S3, with S2 shorted to S4, is	III	\(\frac{C_0}{3}\)
S	The capacitance between S1 and S2, with S3 shorted to S1, and S2 shorted to S4, is	IV	\(2\frac{C_0}{3}\)
			\[2C_0\]

One mole of a monatomic ideal gas undergoes the cyclic process J→ K→ L→ M→ J, as shown in the P-T diagram.Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option. [ℛ is the gas constant.]

List-I		List-II
P	Work done in the complete cyclic process	I	\(ℛT_0 − 4ℛT_0 ln 2\)
Q	Change in the internal energy of the gas in the process JK	II	\(0\)
R	Heat given to the gas in the process KL	III	\(3ℛT_0\)
S	Change in the internal energy of the gas in the process MJ	IV	\(−2ℛT_0 ln 2\)
			\[−3ℛT_0 ln 2\]

A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x = L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is _____.

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 ___

List I		List II
(P)	Titrate: KCl Titrant: AgNO₃	(1)
(Q)	Titrate: AgNO₃ Titrant: KCl	(2)
(R)	Titrate: NaOH Titrant: HCl	(3)
(S)	Titrate: NaOH Titrant: CH₃COOH	(4)
		(5)