List of top Questions asked in JEE Advanced

An electric dipole is formed by two charges +q and -q located in the x-y plane at (0,2) mm and (0,-2) mm as shown in the figure. The electric potential at point P(100, 100) mm due to dipole is V₀. Now the charges +q and -q are moved to (-1,2)mm and (1,-2)mm respectively. What is the value of the electric potential at point P due to this new dipole?

A particle of mass m is moving such that its velocity at a point (x,y) is given by v = α (y\(\hat{i}\) + 2x\(\hat{j}\)), where α is a non-zero constant. What is the resultant force acting on the particle?

Let R=\(\begin{pmatrix}a&3&b\\c&2&d\\0&5&0\end{pmatrix}\): a,b,c,d ∈ {0,3,5,7,11,13,17,19}. Then the number of invertible matrices in R is

For He⁺, a transition takes place from the orbit of radius 105.8 pm to the orbit of radius 26.45 pm. The wavelength (in nm) of the emitted photon during the transition is ___.
[Use: Bohr radius, a = 52.9 pm, Rydberg constant, 𝑅H = 2.2 × 10⁻¹⁸ J, Planck’s constant, h = 6.6 × 10⁻³⁴ J s, Speed of light, c = 3 × 10⁸ m s⁻¹]

Let S = (0,1) ∪ (1,2) ∪ (3,4) and T = {0,1, 2,3} . Then which of the following statements is(are) true?

Let P be a point on the parabola y² = 4ax, where a > 0. The normal to the parabola at P meets the x -axis at a point Q. The area of the triangle PFQ where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive integers, then the pair (a, m) 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 \( \alpha, \beta, \) and \( \gamma \) be real numbers. Consider the following system of linear equations:
\( x + 2y + z = 7 \)
\( x + \alpha z = 11 \)
\( 2x - 3y + \beta z = \gamma \)
Match each entry in List I to the correct entries in List II

List I		List II
(P)	If \( \beta = \frac{1}{2}(7\alpha - 3) \) and \( \gamma = 28 \), then the system has	(1)	a unique solution
(Q)	If \( \beta = \frac{1}{2}(7\alpha - 3) \) and \( \gamma \neq 28 \), then the system has	(2)	no solution
(R)	If \( \beta \neq \frac{1}{2}(7\alpha - 3) \) where \( \alpha = 1 \) and \( \gamma \neq 28 \), then the system has	(3)	infinitely many solutions
(S)	If \( \beta \neq \frac{1}{2}(7\alpha - 3) \) where \( \alpha = 1 \) and \( \gamma = 28 \), then the system has	(4)	\( x = 11, y = -2 \) and \( z = 0 \) as a solution
		(5)	\( x = -15, y = 4 \) and \( z = 0 \) as a solution

50 mL of 0.2 molal urea solution (density = 1.012 g mL⁻¹ at 300 K) is mixed with 250 mL of a solution containing 0.06 g of urea. Both solutions were prepared in the same solvent. The osmotic pressure (in Torr) of the resulting solution at 300 K is ___.
[Use: Molar mass of urea = 60 g mol⁻¹ ; gas constant, R = 62 L Torr K⁻¹ mol⁻¹; Assume, Δ_mixH = 0, Δ_mixV = 0]

In the given reaction scheme, P is a phenyl alkyl ether, Q is an aromatic compound; R and S are the major products.

The correct statement about S is

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.

	List-I		List-II
(P)	\(^{238}_{92}U → ^{234}_{91}Pa\)	(1)	one 𝛼 particle and one 𝛽+ particle
(Q)	\(^{214}_{82}Pb → ^{210}_{82}Pb\)	(2)	three 𝛽− particles and one 𝛼 particle
(R)	\(^{210}_{81}Tl → ^{206}_{82}Pb\)	(3)	two 𝛽− particles and one 𝛼 particle
(S)	\(^{228}_{91}Pa → ^{224}_{88}Ra\)	(4)	one 𝛼 particle and one 𝛽− particle
		(5)	one 𝛼 particle and two 𝛽+ particles

Let f : (0,1) → R be the function defined as f(x) = √n if x ∈ [\(\frac{1}{n+1},\frac{1}{n}\)] where n ∈ N. Let g : (0,1) → R be a function such that \(\int_{x^2}^{x}\sqrt{\frac{1-t}{t}}dt<g(x)<2\sqrt x\) for all x ∈ (0,1).
Then \(\lim_{x\rightarrow0}f(x)g(x)\)

The correct molecular orbital diagram for F₂ molecule in the ground state is

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

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]

For \(x ∈ R\), let \(tan^{-1} (x) ∈ \) (\(-\frac{\pi}{2},\frac{\pi}{2}\)). Then the minimum value of function \(f: R \rightarrow R\) defined by \(f(x) =\) \(\int_{0}^{x\,tan^{-1}x}\frac{e^{(t-cos\,t)}}{1+t^{2023}}dt\) is

Let f:[1,∞) \(\rightarrow\) R be a differentiable function such that f(1) = \(\frac{1}{3}\) and 3\(\int_{1}^{x}\)f(t)dt=xf(x)-\(\frac{x^3}{3}\),x∈[1,∞). Let e denote the base of the natural logarithm. Then the value of f(e) is

A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3ℎ from the ground, as shown in the figure. A spherical ball of mass 𝑚 is released on the slide from rest at a height ℎ from the top of the terrace. The ball leaves the slide with a velocity \(\hat{u}_0=u_0\hat{x}\) and falls on the ground at a distance 𝑑 from the building making an angle θ with the horizontal. It bounces off with a velocity of v and reaches a maximum height of ℎ₁. The acceleration due to gravity is 𝑔 and the coefficient of restitution of the ground is \(\frac{1}{\sqrt3}\). Which of the following statement(s) is(are) correct?

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by \(\vec{E}\)=30(2𝑥̂ + 𝑦̂)sin [2𝜋 (5×10¹⁴𝑡 −\(\frac{10^7}{3}z\))] Vm⁻¹. Which of the following option(s) is(are) correct? [Given: The speed of light in vacuum, 𝑐 = 3 × 10⁸ ms⁻¹]

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.

The complex(es), which can exhibit the type of isomerism shown by [Pt(NH₃)₂Br₂], is(are) [en = H₂NCH₂CH₂NH₂]

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

Match the reactions in List-I with the features of their products in List-II and choose the correct option

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

Monochromatic light wave

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

	List-I		List-II
(P)	(-)-1-Bromo-2-ethylpentane (single enantiomer)	(1)	Inversion of configuration
(Q)	(-)-2-Bromopentane (single enantiomer)	(2)	Retention of configuration
(R)	(-)-3- Bromo-3-methylhexane (single enantiometer)	(3)	Mixture of enantiomers
(S)	(single enantiometer)	(4)	Mixture of structural isomers
		(5)	Mixture of diastereomers