List of top Questions asked in IIT JAM PH- 2024

The roots of the polynomial, 𝑓(𝑧)=𝑧 ⁴-8𝑧 ³+27𝑧 ²-38𝑧+26, are 𝑧₁, 𝑧₂, 𝑧₃,& 𝑧₄, where 𝑧 is a complex variable. Which of the following statements is correct?

Consider the following logic circuit.

The output Y is LOW when:

The number of atoms in the basis of a primitive cell of hexagonal closed packed structure is:

A crystal plane of a lattice intercepts the principal axes \(\overrightarrow𝑎_1, \overrightarrow𝑎_2,\) and  \(\overrightarrow{a_3}\) at 3𝑎₁, 4𝑎₂, and 2𝑎₃, respectively. The Miller indices of the plane are:

Which of the following types of motion may be represented by the trajectory,
𝑦(𝑥)=𝑎𝑥 ²+𝑏𝑥+𝑐 ? 
(Here a, b, and c are constants; x, y are the position coordinates)

A particle moving along the x-axis approaches 𝑥=0 from 𝑥 =−∞ with a total energy E. It is subjected to a potential 𝑉(𝑥). For time 𝑡→∞, the probability density P(x) of the particle is schematically shown in the figure.

The correct option for the potential 𝑉(𝑥) is:

The magnitudes of spin magnetic moments of electron, proton and neutron are μ_e, μ_p and μ_n, respectively. Then

The sum of three binary numbers, 10110.10, 11010.01, and 10101.11, in decimal system is:

The total number of Na and Cl ions per unit cell of the NaCl crystal is:

The co-ordinate system (x,y,z) is transformed to the system (u,v,w), as given by:
𝑢 = 2𝑥 + 3𝑦 − 𝑧 
𝑣 = 𝑥 − 4𝑦 + 𝑧 
𝑤 = 𝑥 + 𝑦 
The Jacobian of the above transformation is ________.