List of top Questions asked in JEE Advanced

A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index n up to the level QPR. If the image of a point object O at a height of ℎ (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct?

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.]

A particle of mass 𝑚 is under the influence of the gravitational field of a body of mass 𝑀 (≫ 𝑚). The particle is moving in a circular orbit of radius \(𝑟_0\) with time period \(𝑇_0\) around the mass 𝑀. Then, the particle is subjected to an additional central force, corresponding to the potential energy 𝑉c(𝑟) = 𝑚𝛼/𝑟 3 , where 𝛼 is a positive constant of suitable dimensions and 𝑟 is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius\( 𝑟_0\) in the combined gravitational potential due to 𝑀 and 𝑉c(𝑟), but with a new time period \(𝑇_1\), then\( (𝑇_1^2  − 𝑇_0^ 2 )/𝑇_1^ 2\) is given by [𝐺 is the gravitational constant.]

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 _______.

Let \(\frac{\pi}{2}<x<\pi\) be such that \(\cot x=\frac{-5}{\sqrt{11}}\). Then
\((\sin\frac{11x}{2})(\sin 6x-\cos6x)+(\cos\frac{11x}{2})(\sin 6x+\cos 6x)\)
is equal to

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)

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		List II
(P)		(1)
(Q)		(2)
(R)		(3)
(S)		(4)
		(5)

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]

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 _____.

A dimensionless quantity is constructed in terms of electronic charge \(e\), permittivity of free space \(\epsilon_0\) , Planck’s constant ℎ, and speed of light c. If the dimensionless quantity is written as \(e^\alpha\epsilon_0^\beta h^\gamma c^\delta\)and n is a non-zero integer, then\((\alpha, \beta,\gamma,\delta)\) is given by

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 _______.

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 _____

Match the transport infrastructure described in Column I, with their names and locations in Column II.

Consider a 3D hollow geometry with six faces and nine equal edges, as indicated in Figure D. Which of the given shapes will generate the described 3D geometry when folded along the dotted lines?

Five identical pillars, having equal height of 10 units and equal cross section, are inserted into the ground. Figure C shows only the portions of the pillars visible above ground. Which of the options given below indicates the ratio of the total volume of the pillars above and below the ground?

Which of the following materials, used in construction, is an industrial waste product?

The mighty weight of a tree, supported through its trunk, is transferred to the ground by its roots. In the same way, the weight of a building is transferred to the ground through different components, i.e., beams, columns, etc. Identify the correct sequence of the components through which the weight of a building is transferred to the ground.

Four circular cutouts have been made in the text in Figure B. Identify the option with the group of those four cutouts.

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 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]

A dinner plate was broken into six pieces. Five of the pieces are indicated in Figure A. Find out the missing piece from the options given below.

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 remains undisintegrated. When the age of the sample is \( P \times 10^8 \) years, the ratio of the mass of Pb-206 to that of U-238 in the sample is found to be 7. The value of \( P \) is: \[ \text{[Given: Half-life of U-238 = \(4.5 \times 10^9\) years; \(\log_e2 = 0.693\)]} \]

Re-using waste material is an accepted principle of sustainability. Used tyres are one such waste material. You are required to design and sketch a utility object made of tyres, which could be of different sizes and types (e.g. bicycle, car, two-wheeler tyres, etc.).

An impressive entrance gateway has to be designed for a college. Make a pencil drawing of the elevation of the gateway, adding appropriate elements of your choice. Also, add shade, patterns, and textures. Some indicative outlines of part of the gateway, and a line of symmetry, are given below.