List of top Questions asked in JEE Advanced

For \(x ∈ R\), let \(y(x)\) be the solution of the differential equation \((x^2 -5)\)\(\frac{dy}{dx}\)\(-2xy = - 2x\)\((x^2-5)^2\) such that \(y(2) =7\). Then the maximum value of the function \(y(x)\) is

Consider the given data with frequency distribution

x_i	3	8	11	10	5	4
f_i	5	2	3	2	4	4

Match each entry in List-I to the correct entries in List-II.

	List-I		List-II
(P)	The mean of the above data is	(1)	2.5
(Q)	The median of the above data is	(2)	5
(R)	The mean deviation from the mean of the above data is	(3)	6
(S)	The mean deviation from the median of the above data is	(4)	2.7
		(5)	2.4

The correct option 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?

Let n ≥ 2 be a natural number and f:[0,1)]\(\rightarrow\) R be the function defined by

If n is such that the area of the region bounded by the curves x = 0, x = 1, y = 0 and y = f(x) is 4, then the maximum value of the function f is

Let Q be the cube with the set of vertices {(x₁, x₂, x₃) ∈ R³: x₁, x₂, x₃ ∈ {0,1}}. Let F be the set of all twelve lines containing the diagonals of the six faces of cube Q. Let S be the set of all four lines containing the main diagonals of the cube Q; for instance, the line passing through the vertices (0,0,0) and (1,1,1) is in S. For lines l₁ and l₂, let d(l₁,l₂) denote the shortest distance between them. Then the maximum value of d(l₁,l₂) as l₁ varies over f and l₂ varies over S, is

Consider an obtuse-angled triangle ABC in which the difference between the largest and the smallest angle is \(\frac{\pi}{2}\) and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.Then the inradius of the triangle ABC is

Let A = {\(\frac{1967+1686 i\,sin\theta}{7-3i\,cos\theta}:\theta\in R\) }. If A contains exactly one positive integer n, then the value of n is ______

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is 60 cm s^−1, the speed of the tip of the person’s shadow on the ground with respect to the person is _______ cm s^−1.

A hydrogen-like atom of atomic number Z transits from n=4 to n=3. The photon emitted from this transition is incident on a metal surface of threshold wavelength λ_th = 310nm. If the maximum kinetic energy of the emitted electron is 1.95ev, find the value of Z.

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 A = {\(\frac{1967+1686 i\,sin\theta}{7-3i\,cos\theta}:\theta\in R\) }. If A contains exactly one positive integer n, then the value of n is ______

In a radioactive decay process, the activity is defined as A = - \(\frac {dN}{dt}\), where 𝑁(𝑡) is the number of radioactive nuclei at time 𝑡. Two radioactive sources, 𝑆₁ and 𝑆₂ have same activity at time 𝑡 = 0. At a later time, the activities of 𝑆₁ and 𝑆₂ are 𝐴₁ and 𝐴₂, respectively. When 𝑆₁ and 𝑆₂ have just completed their 3^rd and 7^th half-lives, respectively, the ratio \(\frac{A_1}{A_2}\) is _________.

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)

On decreasing the 𝑝H from 7 to 2, the solubility of a sparingly soluble salt (MX) of a weak acid (HX) increased from 10⁻⁴ mol L⁻¹ to 10⁻³mol L⁻¹. The 𝑝Ka of HX 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

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

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?

H₂S (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of water produced is x, and the number of moles of electrons involved is y. The value of (x + y) 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

denote the (r + 2) digit number where the first and the last digits are 7 and the remaining r digits are 5. Consider the sum S = 77 + 757 + 7557 + …+

. If S =

, where m and n are natural numbers less than 3000, then the value of m + n is ______.

Find the α, β, γ in the Y = \(C^\alpha h^\beta G^\gamma,\,\,\)
\(\gamma\) = Young's Modulus
\(c\) = speed of Light
\(h\) = Plank's Constant
\(G\) = gravitational Constant

Consider an obtuse-angled triangle ABC in which the difference between the largest and the smallest angle is \(\frac{\pi}{2}\) and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.Let a be the area of the triangle ABC. Then the value of (64a)² is

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

A gas has a compressibility factor of 0.5 and a molar volume of 0.4 dm³ mol⁻¹ at a temperature of 800K and pressure x atm. If it shows ideal gas behavior at the same temperature and pressure, the molar volume will be y dm³ mol⁻¹. The value of \(\frac{x}{y}\) is ___. [Use: Gas constant, R = 8 × 10⁻² L atm K⁻¹ mol⁻¹]

A trinitro compound, 1,3,5-tris-(4-nitrophenyl)benzene, on complete reaction with an excess of Sn/HCl gives a major product, which on treatment with an excess of NaNO₂/HCl at 0°C provides P as the product. P, upon treatment with excess of H₂O at room temperature, gives the product Q. Bromination of Q in aqueous medium furnishes the product R. The compound P upon treatment with an excess of phenol under basic conditions gives the product S. The molar mass difference between compounds Q and R is 474 g mol^–1and between compounds P and S is 172.5 g mol^–1. The number of heteroatoms present in one molecule of R is ______ .
[Use: Molar mass (in g mol^–1): H = 1, C = 12, N = 14, O = 16, Br = 80, Cl = 35.5 Atoms other than C and H are considered as heteroatoms]

	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

List of top Questions asked in JEE Advanced

SUBSCRIBE TO OUR NEWS LETTER