List of top Questions asked in JEE Main- 2024

The number of ions from the following that are expected to behave as oxidising agent is: $\text{Sn}^{4+}, \, \text{Sn}^{2+}, \, \text{Pb}^{2+}, \, \text{Tl}^{3+}, \, \text{Pb}^{4+}, \, \text{Tl}^{+}$

Given below are two statements: Statement I: $\text{PF}_5$ and $\text{BrF}_5$ both exhibit $\text{sp}^3\text{d}$ hybridisation.Statement II: Both $\text{SF}_6$ and $[\text{Co}(\text{NH}_3)_6]^{3+}$ exhibit $\text{sp}^3\text{d}^2$ hybridisation. In the light of the above statements,choose the correct answer from the options given below:

The incorrect statements regarding enzymes are
(A) Enzymes are biocatalysts.
(B) Enzymes are non-specific and can catalyse different kinds of reactions.
(C) Most Enzymes are globular proteins.
(D) Enzyme - oxidase catalyses the hydrolysis of maltose into glucose.
Choose the correct answer from the option given below:

Two open organ pipes of length $60 \, \text{cm}$ and $90 \, \text{cm}$ resonate at $6^\text{th}$ and $5^\text{th}$ harmonics respectively. The difference of frequencies for the given modes is ____ $\text{Hz}$.
(Velocity of sound in air $= 333 \, \text{m/s}$)

Two coherent monochromatic light beams of intensities I and 4I are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is x I. The value of x is______.

A wire of cross-sectional area $A$, modulus of elasticity $2 \times 10^{11} \, \text{Nm}^{-2}$, and length $2 \, \text{m}$ is stretched between two vertical rigid supports.
When a mass of $2 \, \text{kg}$ is suspended at the middle, it sags lower from its original position making angle $\theta = \frac{1}{100}$ radian on the points of support.  
The value of $A$ is ____ $\times 10^{-4} \, \text{m}^2$ (consider $x \ll l$).  
(Given: $g = 10 \, \text{m/s}^2$)

Three balls of masses $2 \, \text{kg}$, $4 \, \text{kg}$, and $6 \, \text{kg}$ respectively are arranged at the centre of the edges of an equilateral triangle of side $2 \, \text{m}$.The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of the triangle, will be ____ $\text{kg} \, \text{m}^2$

A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2 = 1 + t^2$.
Its acceleration at any time $t$ is $x^{-n}$ where $n =$ ____.

For a given series LCR circuit, it is found that maximum current is drawn when value of variable capacitance is $2.5 \, \text{nF}$. If resistance of $2000 \, \Omega$ and $100 \, \text{mH}$ inductor is being used in the given circuit. The frequency of AC source is ____ $\times \, 10^3 \, \text{Hz}$. (Given $\pi^2 = 10$)

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at 10.2 V. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is _____ nm.
(Given $hc = 1245 \, \text{eV nm}, \, e = 1.6 \times 10^{-19} \, \text{C}$).

Pressure inside a soap bubble is greater than the pressure outside by an amount;(given : R = Radius of bubble, S = Surface tension of bubble)

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be

The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is: (Given $e = 1.6 \times 10^{-19}$ C)

When UV light of wavelength 300 nm is incident on the metal surface having work function 2.13 eV, electron emission takes place. The stopping potential is : (Given hc = 1240 eV nm)

Energy of 10 non rigid diatomic molecules at temperature T is :

A car of 800 kg is taking a turn on a banked road of radius 300 m and angle of banking 30°. If the coefficient of static friction is 0.2, then the maximum speed with which the car can negotiate the turn safely: (Given $g = 10 \, \text{m/s}^2$, $\sqrt{3} = 1.73$).

The longest wavelength associated with Paschen series is: (Given $R_H = 1.097 \times 10^7$ SI unit)

If the system of equations \[2x + 7y + \lambda z = 3,\]\[3x + 2y + 5z = 4,\]\[x + \mu y + 32z = -1\]has infinitely many solutions, then $(\lambda - \mu)$ is equal to ________.

Let $\alpha, \beta$ be roots of $x^2 + \sqrt{2}x - 8 = 0$. If $U_n = \alpha^n + \beta^n$, then \[ \frac{U_{10} + \sqrt{12} U_9}{2 U_8} \] is equal to ________.

If the shortest distance between the lines \[ \frac{x - \lambda}{3} = \frac{y - 2}{-1} = \frac{z - 1}{1} \] and \[ \frac{x + 2}{-3} = \frac{y + 5}{2} = \frac{z - 4}{4} \] is \[ \frac{44}{\sqrt{30}}, \] then the largest possible value of $|\lambda|$ is equal to ________.

Let $[t]$ denote the largest integer less than or equal to $t$. If \[ \int_0^1 \left(\left[x^2\right] + \left\lfloor \frac{x^2}{2} \right\rfloor\right) dx = a + b\sqrt{2} - \sqrt{3} - \sqrt{5} + c\sqrt{6} - \sqrt{7}, \] where $a, b, c \in \mathbb{Z}$, then $a + b + c$ is equal to ________.

The length of the latus rectum and directrices of a hyperbola with eccentricity $e$ are 9 and $x = \pm \frac{4}{\sqrt{3}}$, respectively. Let the line $y - \sqrt{3}x + \sqrt{3} = 0$ touch this hyperbola at $(x_0, y_0)$. If $m$ is the product of the focal distances of the point $(x_0, y_0)$, then $4e^2 + m$ is equal to ________.

If P(6, 1) be the orthocentre of the triangle whose vertices are A(5, –2), B(8, 3) and C(h, k), then the point C lies on the circle.

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of m is equal to :

Considering acetic acid dissociates in water, its dissociation constant is $6.25 \times 10^{-5}$. If 5 mL of acetic acid is dissolved in 1 litre water, the solution will freeze at $-x \times 10^{-1}$ °C, provided pure water freezes at 0 °C. $x = $ _____ (Nearest integer)
Given: $(K_f)_{water} = 1.86$ K kg mol$^{-1}$
density of acetic acid is 1.2 g mol$^{-1}$
molar mass of water = 18 g mol$^{-1}$
molar mass of acetic acid = 60 g mol$^{-1}$
density of water = 1 g cm$^{-3}$
Acetic acid dissociates as CH$_3$COOH $\rightleftharpoons$ CH$_3$COO$^-$ + H$^+$