List of top Questions asked in JEE Main

Let a circle passing through (2, 0) have its centre at the point \( (h, k) \). Let \( (x_c, y_c) \) be the point of intersection of the lines \( 3x + 5y = 1 \) and \( (2 + c)x + 5c^2y = 1 \). If \( h = \lim_{c \to 1} x_c \) and \( k = \lim_{c \to 1} y_c \), then the equation of the circle is:
Let \( f(x) = ax^3 + bx^2 + ex + 41 \) be such that \( f(1) = 40 \), \( f'(1) = 2 \) and \( f''(1) = 4 \). Then \( a^2 + b^2 + c^2 \) is equal to:
If the domain of the function \(f(x) = \sin^{-1}\left( \frac{x - 1}{2x + 3} \right)\) is \(\mathbb{R} - (\alpha, \beta)\), then \(12 \alpha \beta\) is equal to:
If the sum of the series $$ \frac{1}{1 \cdot (1 + d)} + \frac{1}{(1 + d)(1 + 2d)} + \cdots + \frac{1}{(1 + 9d)(1 + 10d)} $$ is equal to 5, then \(50d\) is equal to: 
Let \(\overrightarrow{OA} = 2\vec{a}\), \(\overrightarrow{OB} = 6\vec{a} + 5\vec{b}\), and \(\overrightarrow{OC} = 3\vec{b}\), where \(O\) is the origin. If the area of the parallelogram with adjacent sides \(\overrightarrow{OA}\) and \(\overrightarrow{OC}\) is 15 sq. units, then the area (in sq. units) of the quadrilateral \(OABC\) is equal to:
Let \[ \left| \cos \theta \cos (60^\circ - \theta) \cos (60^\circ - \theta) \right| \leq \frac{1}{8}, \quad \theta \in [0, 2\pi] \] Then, the sum of all \( \theta \in [0, 2\pi] \), where \( \cos 3\theta \) attains its maximum value, is:
Let \( \int \frac{2 - \tan x}{3 + \tan x} \, dx = \frac{1}{2} \left( \alpha x + \log_e \lvert \beta \sin x + \gamma \cos x \rvert \right) + C \), where \( C \) is the constant of integration.
Given below are two statements:
Statement I : Picric acid is 2, 4, 6-trinitrotoluene.
Statement II : Phenol-2, 4-disulphuric acid is treated with conc. HNO3 to get picric acid.
In the light of the above statement, choose the most appropriate answer from the options given below:
Let \( \lambda, \mu \in \mathbb{R} \). If the system of equations
\( 3x + 5y + \lambda z = 3 \) 
\( 7x + 11y - 9z = 2 \) 
\( 97x + 155y - 189z = \mu \) 
has infinitely many solutions, then \( \mu + 2\lambda \) is equal to:
Match List-I with the List-II
List-I
(Molecule / Species)		List-II
(Property / Shape)
(A) \(SO_2Cl_2\)(I) Paramagnetic
(B) NO(II) Diamagnetic
(C) \(NO^{-}_{2}\)(III) Tetrahedral
(D) \(I^{-}_{3}\)(IV) Linear
Choose the correct answer from the options given below:
Functional group present in sulphonic acid is :
For three vectors \( \vec{A} = (-xi - 6j - 2k), \) \( \vec{B} = (-i + 4j + 3k) \) and \( \vec{C} = (-8i - j + 3k), \) if \( \vec{A} \cdot (\vec{B} \times \vec{C}) = 0, \) then value of x is ___________.
A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is _______ cm/s.
A circular coil having 200 turns, $2.5 \times 10^{-4} \text{ m}^2$ area and carrying 100 $\mu$A current is placed in a uniform magnetic field of 1 T. Initially the magnetic dipole moment ($\vec{M}$) was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^\circ$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is ________ $\mu$J.
Radius of a certain orbit of hydrogen atom is 8.48 Å. If energy of electron in this orbit is E/x, then x = ______.
(Given a0 = 0.529Å, E = energy of electron in ground state)
A wire of resistance R and radius r is stretched till its radius became r/2. If new resistance of the stretched wire is x R, then value of x is _________.
The refractive index of prism is µ = √3 and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is ______o.
When a DC voltage of 100 V is applied to an inductor, a DC current of 5 A flows through it. When an AC voltage of 200 V peak value is connected to the inductor, its inductive reactance is found to be \( 20\sqrt{3} \, \Omega \). The power dissipated in the circuit is _________ W.
Three infinitely long charged thin sheets are placed as shown in the figure. The magnitude of the electric field at the point \( P \) is \(\frac{x \sigma}{\epsilon_0}\). The value of \( x \) is _________.
(All quantities are measured in SI units).
A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of the big drop is \( \frac{10}{x} \).The value of x is _________.
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be ______ hours 30 minutes.
In photoelectric experiment energy of 2.48 eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5 V. Work function of the photo sensitive material is :
The solution curve, of the differential equation \( 2y \frac{dy}{dx} + 3 = 5 \frac{dy}{dx} \), passing through the point \( (0, 1) \), is a conic, whose vertex lies on the line:
A ray of light coming from the point \( P(1, 2) \) gets reflected from the point \( Q \) on the x-axis and then passes through the point \( R(4, 3) \). If the point \( S(h, k) \) is such that \( PQRS \) is a parallelogram, then \( hk^2 \) is equal to:
A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After some time, the ball falls with constant velocity. The viscous force on the ball is: