List of top Questions asked in JEE Main

A screw gauge has a least count of $0.01$ mm. Using this screw gauge a measurement was done. When nothing was present in the jaw, zero of circular scale was above reference line by $3$ units. When a sphere was kept between the jaws, main scale reads $1$ mm and $51^{\text{st}$ division of circular scale coincides with reference line. Find the actual diameter of the ball:}
Consider the following statements about group 13 elements of the periodic table. (A) Electronegativity decreases down the group.
(B) Size increases down the group.
(C) Ionization energy decreases down the group.
(D) Boiling point of Boron is maximum.
(E) Melting point of Boron is maximum.

Masses $m$ and $2m$ are connected by a massless rod of length $d$. If angular momentum about an axis passing through centre of mass and perpendicular to the rod is $L$, then the angular speed $(\omega)$ of the system is:

The RMS speeds of \( \mathrm{H_2} \) and \( \mathrm{O_2} \) gases are the same. If the temperature of \( \mathrm{O_2} \) gas is \(23^\circ\mathrm{C}\), find the temperature of \( \mathrm{H_2} \) gas.
If the area of the region \[ \{(x,y): x^2+1 \le y \le 3-x\} \] is divided by the line \(x=-1\) in the ratio \(m:n\) (where \(m\) and \(n\) are coprime natural numbers), then find the value of \(m+n\).
The largest value of \( n \in \mathbb{N} \) such that \( 7^{n} \) divides \( (101)! \) is _____.
A block of mass \(m\) is at rest with respect to a hollow cylinder which is rotating with angular speed \( \omega \). The radius of the cylinder is \(R\). Find the minimum coefficient of friction between the block and the cylinder.
Two balls of mass \(2m\) and \(m\) collide with a rod of mass \(m\) and length \(L\) as shown. The balls stick to the rod after collision. Find \( \dfrac{v}{\omega} \) if the rod is hinged at its centre. (Given: \( L = 8\,\text{m} \))
Which of the following is a basic buffer?
In the binomial expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26}, \] the coefficients of \(x, x^2, x^3\) are \(-56, 0\) and \(0\) respectively. Then the value of \( (a + b + c) \) is:
If the domain of the function \[ \cos^{-1}\!\left(\frac{2x-5}{11x-7}\right) + \sin^{-1}\!\left(2x^2 - 3x + 1\right) \] is \[ [0,a] \cup \left[\frac{12}{13},\, b\right], \] then the value of \( \dfrac{1}{ab} \) is:
If \( f(3)=18,\; f'(3)=0 \) and \( f''(3)=4 \), then the value of \[ \lim_{x\to 1}\ln\left(\frac{f(x+2)}{f(3)}\right)^{\frac{18}{(x-1)^2}} is: \]
The value of \[ \int_{\frac{\pi}{6}}^{\pi} \frac{\pi + 4x^{11}}{1 - \sin\left(|x| + \frac{\pi}{6}\right)}\,dx is: \]

Given below are two statements: 
Statement I: All the pairs of molecules \((\mathrm{PbO}, \mathrm{PbO_2}); (\mathrm{SnO}, \mathrm{SnO_2})\) and \((\mathrm{GeO}, \mathrm{GeO_2})\) contain amphoteric oxides. 
Statement II: \(\mathrm{AlCl_3}, \mathrm{BH_3}, \mathrm{BeH_2}\) and \(\mathrm{NO_2}\) all have incomplete octet. 
In the light of the above statements, choose the correct option.

Find the volume flow rate in the Venturi meter shown below in which water is flowing. Given that the cross-sectional areas at \(A\) and \(B\) are \(A\) and \(a\) respectively, \[ \frac{A}{a} = 2, A = \sqrt{3}\,\text{m}^2, \] the difference in water levels is \(5\,\text{cm}\) and \(\rho = 1000\,\text{kg m}^{-3}\).
If the mean and variance of observations \( x, y, 12, 14, 4, 10, 2 \) is \(8\) and \(16\) respectively, where \( x>y \), then the value of \( 3x - y \) is:
If the electric field of an EM wave is given by \[ 60\,[\sin(3\times10^{14}t) + \sin(12\times10^{14}t)] \] at \( x = 0 \) and it falls on a photosensitive material having work function \( 2.8\,\text{eV} \), find the maximum kinetic energy (in eV) of the ejected electrons.
Find the moment of inertia of the system formed using two identical rods about the given axis of rotation as shown in the figure. Each rod has mass \( M \) and length \( L \). v
If \( x^2 + x + 1 = 0 \), then evaluate \[ \left(x + \frac{1}{x}\right)^4 + \left(x^2 + \frac{1}{x^2}\right)^4 + \left(x^3 + \frac{1}{x^3}\right)^4 + \cdots + \left(x^{25} + \frac{1}{x^{25}}\right)^4. \]
If \( O \) is the vertex of the parabola \( x^2 = 4y \), \( Q \) is a point on the parabola. If \( C \) is the locus of a point which divides \( OQ \) in the ratio \( 2:3 \), then the equation of the chord of \( C \) which is bisected at the point \( (1,2) \) is:
If \( a_1, a_2, a_3, \ldots \) are in increasing geometric progression such that \[ a_1 + a_3 + a_5 = 21, a_1 a_3 a_5 = 64, \] then \( a_1 + a_2 + a_3 \) is:
The locus of the point of intersection of tangents drawn to the circle \[ (x - 2)^2 + (y - 3)^2 = 16, \] which subtends an angle of \(120^\circ\), is:
The sum of roots of the equation \[ |x - 1|^2 - 5|x - 1| + 6 = 0 \] is:
Correct order of ionisation enthalpy is:
Area enclosed by \( 4x^2 + y^2 \le 8 \) and \( y^2 \le 4x \) (in square unit) is: