List of top Questions asked in JEE Main

if $2x^y+3y^x=20$ then $\frac{dy}{dx}$ at (2,2) is equal to:

As shown in figure, a cuboid lies in a region with electric field $E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} N / C$. The magnitude of charge within the cuboid is $n \epsilon_0 C$. The value of $n$ is _____. (if dimension of cuboid is $1 \times 2 \times 3 m ^3$ )

A point source of $100 \,W$ emits light with $5 \%$ efficiency At a distance of $5\, m$ from the source, the intensity produced by the electric field component is:

For $z \in C$ if the minimum value of $(| z -3 \sqrt{2}|+| z - p \sqrt{2} i |)$ is $5 \sqrt{2}$, then a value of $p$ is ______

Let the point $P(\alpha, \beta)$ be at a unit distance from each of the two lines $L _1: 3 x -4 y +12=0$, and $L _2: 8 x +6 y +11=0$ If $P$ lies below $L _1$ and above $L _2$, then $100(\alpha+\beta)$ is equal to

Let $y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)$ Then, at $x=1$

In a Young’s double slit experiment, two slits are illuminated with light of wavelength $800 \, \text{nm}$. The first minimum is detected at $P$. The value of slit separation $a$ is:

Let A be a $n \times n$ matrix such that $| A |=2$ If the determinant of the matrix$\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 A ^{-1}\right)\right) \cdot$ is $2^{84}$, then $n$ is equal to ____

Height of tower AB is 30 m where B is foot of tower. Angle of elevation from a point C on level ground to top of tower is 60° and angle of elevation of A from a point D x m above C is 15° then find the area of quadrilateral ABCD.

Two charges each of magnitude 0.01 C and separated by a distance of 0.4 mm constitute an electric dipole. If the dipole is placed in an uniform electric field of 10 dyne/C making 30º angle with $\overrightarrow E$, the magnitude of torque acting on dipole is:

Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If an electric dipole of dipole moment 30 x 10-5 Cm is enclosed by a closed surface, the net flux coming out of the surface will by zero.
Reason R : Electric dipole consists of two equal and opposite charges.
In the light of above, statements, choose the correct answer from the options given below:

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

For a nucleus AAX having mass number A and atomic number Z
A. The surface energy per nucleon $(b_s)=−a_1A^{\frac{2}{3}} $
B. The Coulomb contribution to the binding energy $b_c=−a_2\frac{Z(Z−1)}{A^{\frac{4}{3}}} $
C. The volume energy b_v=a₃A
D. Decrease in the binding energy is proportional to surface area.
E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( a₁,a₂ and a₃ are constants)
Choose the most appropriate answer from the options given below:

A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0, the top most point on the disc is A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is

Let $x=\sin \left(2 \tan ^{-1} \alpha\right)$ and $y=\sin \left(\frac{1}{2} \tan ^{-1} \frac{4}{3}\right)$ If $S =\left\{\alpha \in R : y ^2=1- x \right\}$, then $\displaystyle\sum_{\alpha \in S } 16 \alpha^3$ is equal to ______

If the area of the region $ S={(x,y) : 2y-y^2 ≤ x^2 ≤ 2y, x ≥ y}$ is equal to $\frac{ n+2}{n+1}−\frac{π}{n−1}$, then the natural number n is equal to _____.

' $A$' and ' $B$ ' formed in the following set of reactions are:

A bullet strikes a stationary ball kept at a height as shown. After collision, range of bullet is 120 m and that of ball is 30 m. Find initial speed of bullet. Collision is along horizontal direction.
(Take g = 10 m/s²)

The trajectory of projectile, projected from the ground is given by y=x-x²/20. Where x and y are measured in meter. The maximum height attained by the projectile will be

Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is :

Two particles of equal mass ‘m’ move in a circle of radius ‘r’ under the action of their mutual gravitational attraction. The speed of each particle will be :

Given below are two statement:
statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g).
statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.
In the light of the above statements , choose the correct answer from the options given below

Let $f(x)=\frac{sinx+cosx-\sqrt2}{sinx-cosx},x∈[0.\pi]-\left[\frac{\pi}{4}\right]. Then f\left(\frac{7\pi}{12}\right)f^n\left(\frac{7\pi}{12}\right)$is equal to

Given below are two statements :
Statement I : The decrease in first ionization enthalpy from B to Al is much larger than that from Al to Ga.
Statement II : The d orbitals in Ga are completely filled. In the light of the above statements,
choose the most appropriate answer from the options given below

Let the lines l₁: $\frac{x+5}{3} =\frac{y+4}{1}=\frac{z−α}{−2}$ and l₂:3x+2y+z–2=0=x–3y+2z-13 be coplanar. If the point P(a, b, c) on l₁ is nearest to the point Q(-4,-3, 2), then |a| + |b|+|c| is equal to