List of top Questions asked in JEE Main

An object is projected with kinetic energy K from point A at an angle 60° with the horizontal. The ratio of the difference in kinetic energies at points B and C to that at point A (see figure), in the absence of air friction is :

Let $ \overrightarrow{AB} = 2\hat{i} + 4\hat{j} - 5\hat{k} $ and $ \overrightarrow{AD} = \hat{i} + 2\hat{j} + \lambda \hat{k} $, $ \lambda \in \mathbb{R} $. Let the projection of the vector $ \vec{v} = \hat{i} + \hat{j} + \hat{k} $ on the diagonal $ \overrightarrow{AC} $ of the parallelogram $ ABCD $ be of length one unit. If $ \alpha, \beta $, where $ \alpha>\beta $, be the roots of the equation $ \lambda^2 x^2 - 6\lambda x + 5 = 0 $, then $ 2\alpha - \beta $ is equal to

Let the direction cosines of two lines satisfy the equations : $ 4l + m - n = 0 $ and $ 2mn + 5nl + 3lm = 0 $. Then the cosine of the acute angle between these lines is :

Let the line $ y - x = 1 $ intersect the ellipse $ \frac{x^2}{2} + \frac{y^2}{1} = 1 $ at the points A and B. Then the angle made by the line segment AB at the center of the ellipse is:

The final product [B] is:

Two cars $A$ and $B$ each of mass $10^3$ kg are moving on parallel tracks separated by a distance of $10$ m, in same direction with speeds $72$ km/h and $36$ km/h. The magnitude of angular momentum of car $A$ with respect to car $B$ is _________ J.s.

The pH and conductance of a weak acid (HX) was found to be 5 and $4\times10^{-5}$ S, respectively. The conductance was measured under standard condition using a cell where the electrode plates having a surface area of 1 cm$^2$ were at a distance of 15 cm apart. The value of the limiting molar conductivity ($\Lambda_m^\circ$) is___ S cm$^2$ mol$^{-1}$ (nearest integer) (Given: degree of dissociation $\alpha \ll 1$)

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface. If refractive index of the material of prism is $\sqrt{2}$, the angle $\theta$ of prism is :

As compared with chlorocyclohexane, which of the following statements correctly apply to chlorobenzene?
The magnitude of negative charge is more on chlorine atom.
The C--Cl bond has partial double bond character.
C--Cl bond is less polar.
C--Cl bond is longer due to repulsion between delocalised electrons of the aromatic ring and lone pairs of electrons of chlorine.
The C--Cl bond is formed using $sp^2$ hybridised orbital of carbon.
Choose the correct answer from the options given below:

Electric field in a region is given by \[ \vec{E} = A x\,\hat{i} + B y\,\hat{j}, \] where $ A = 10 \,\text{V/m}^2 $ and $ B = 5 \,\text{V/m}^2 $. If the electric potential at a point $ (10, 20) $ is $500\ \text{V}$, then the electric potential at origin is __________ V.

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Let the mean and variance of 8 numbers -10, -7, -1, x, y, 9, 2, 16 be $ 2 $ and $ \frac{293}{4} $, respectively. Then the mean of 4 numbers x, y, x+y+1, |x-y| is:

A $7.9\ \text{MeV}$ $\alpha$-particle scatters from a target material of atomic number $79$. From the given data, the estimated diameter of the nuclei of the target material is (approximately) _________ m. \[ \left[\frac{1}{4\pi\varepsilon_0}=9\times10^9\ \text{Nm}^2\text{/C}^2 \text{ and electron charge }=1.6\times10^{-19}\ \text{C}\right] \]

A point charge of $10^{-8}$ C is placed at origin. The work done in moving a point charge 2 $\mu$C from point A(4, 4, 2) m to B(2, 2, 1) m is_______ J. ($\frac{1}{4\pi\epsilon_0} = 9 \times 10^9$ in SI units)

Let $ f : [1,\infty) \to \mathbb{R} $ be a differentiable function. If
\[ 6\int_{1}^{x} f(t)\,dt = 3x f(x) + x^3 - 4 \] for all $ x \ge 1 $, then the value of $ f(2) - f(3) $ is

Consider a modified Bernoulli equation. \[ P + \frac{A}{Bt^2} + \rho g(h + Bt) + \frac{1}{2} \rho v^2 = \text{constant} \] If t has the dimension of time then the dimensions of A and B are_________ respectively.

A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity (g = 10 m/s²) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travels a vertical distance of 200 m is_______ mV.}

Let a circle of radius $4$ pass through the origin $O$, the points $A(-\sqrt{3}a,0)$ and $B(0,-\sqrt{2}b)$, where $a$ and $b$ are real parameters and $ab\neq0$. Then the locus of the centroid of $\triangle OAB$ is a circle of radius

Let \[ f(x)=\int \frac{dx}{2\left(\frac{3}{2}\right)^x+2x\left(\frac12\right)^x} \] such that $f(0)=-26+24\log_e(2)$. If $f(1)=a+b\log_e(3)$, where $a,b\in\mathbb{Z}$, then $a+b$ is equal to:

Let
\[ A=\begin{pmatrix} 3 & -4 \\ 1 & -1 \end{pmatrix} \] and $ B $ be two matrices such that
\[ A^{100}-100B+I=0. \]
Then the sum of all the elements of $ B^{100} $ is _______.

Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

From the given following (A to D) cyclic structures, those which will not react with Tollen's reagent are :

Let \[ A = \{x : |x^2 - 10| \le 6\} \quad \text{and} \quad B = \{x : |x - 2| > 1\}. \] Then

$6 \int_{0}^{\pi} (\sin 3x + \sin 2x + \sin x)dx$ is equal to:

Let \[ f(x)=x^{2025}-x^{2000},\quad x\in[0,1] \] and the minimum value of the function $f(x)$ in the interval $[0,1]$ be \[ (80)^{80}(n)^{-81}. \] Then $n$ is equal to