List of top Questions asked in JEE Main

Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is : 

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 : 

The displacement of a particle executing simple harmonic motion with time period \(T\) is expressed as \[ x(t)=A\sin\omega t, \] where \(A\) is the amplitude of oscillation. If the maximum value of the potential energy of the oscillator is found at \[ t=\frac{T}{2\beta}, \] then the value of \(\beta\) is ________.
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.}
In hydrogen atom spectrum, (R → Rydberg's constant)
A. the maximum wavelength of the radiation of Lyman series is 4/3R
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is 9/R
D. the minimum wavelength of Lyman series is 5/4R
Choose the correct answer from the options given below :

Two short dipoles \( (A, B) \), \( A \) having charges \( \pm 2\,\mu\text{C} \) and length \( 1\,\text{cm} \) and \( B \) having charges \( \pm 4\,\mu\text{C} \) and length \( 1\,\text{cm} \) are placed with their centres \( 80\,\text{cm} \) apart as shown in the figure. The electric field at a point \( P \), equidistant from the centres of both dipoles is \underline{\hspace{2cm}} N/C.

The de Broglie wavelength of an oxygen molecule at 27°C is x × $10^{-12}$ m. The value of x is (take Planck's constant=6.63 × $10^{-34}$ J/s, Boltzmann constant=1.38 × $10^{-23}$ J/K, mass of oxygen molecule = 5.31 × $10^{-26}$ kg)
Which one of the following is not a measurable quantity?
A uniform bar of length \(12\,\text{cm}\) and mass \(20m\) lies on a smooth horizontal table. Two point masses \(m\) and \(2m\) are moving in opposite directions with the same speed \(v\) and in the same plane as the bar, as shown in the figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency \(\omega\). The ratio of \(v\) and \(\omega\) is
Let \( |A| = 6 \), where A is a \( 3 \times 3 \) matrix. If \( |\text{adj}(\text{adj}(A^2 \cdot \text{adj}(2A)))| = 2^{m \cdot 3^{n} \), then \( m + n \) is equal to :}
From the first 100 natural numbers, two numbers first \( a \) and then \( b \) are selected randomly without replacement. If the probability that \( a - b \ge 10 \) is \( m/n \), \( \text{gcd}(m, n) = 1 \), then \( m + n \) is equal to :
Let f be a twice differentiable non-negative function such that \((f(x))^2 = 25 + \int_0^x ( f(t)^2 + (f'(t))^2 ) dt\). Then the mean of \(f(\log_2(1)), f(\log_2(2)), \dots, f(\log_2(625))\) is equal to :
The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPRSTUVP, is :
Let the area of the region bounded by the curve \( y = \max \{ \sin x, \cos x \} \), lines \( x = 0 \), \( x = 3\pi/2 \), and the x-axis be A. Then, \( A + A^2 \) is equal to :
The value of \( \frac{100 C_{50}}{51} + \frac{100 C_{51}}{52} + \dots + \frac{100 C_{100}}{101} \) is :
The sum of all possible values of \( n \in \mathbb{N} \), so that the coefficients of \(x, x^2\) and \(x^3\) in the expansion of \((1+x^2)^2(1+x)^n\) are in arithmetic progression is :
Let \( S = \{z : 3 \le |2z - 3(1+i)| \le 7\ \) be a set of complex numbers. Then \( \min_{z \in S} \left| z + \frac{1}{2}(5+3i) \right| \) is equal to :}
Let \( \vec{a} = -\hat{i} + \hat{j} + 2\hat{k} \), \( \vec{b} = \hat{i} - \hat{j} - 3\hat{k} \), \( \vec{c} = \vec{a} \times \vec{b} \) and \( \vec{d} = \vec{c} \times \vec{a} \). Then \( (|\vec{a}|^2 - |\vec{b}|^2) \cdot \vec{d \) is equal to:}
Let A = \{-2, -1, 0, 1, 2, 3, 4\. Let R be a relation on A defined by xRy if and only if \(2x + y \le 2\). Let \(l\) be the number of elements in R. Let \(m\) and \(n\) be the minimum number of elements required to be added in R to make it reflexive and symmetric relations respectively. Then \(l + m + n\) is equal to :}
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 rectangle is formed by the lines \( x = 0 \), \( y = 0 \), \( x = 3 \) and \( y = 4 \). Let the line \( L \) be perpendicular to \( 3x + y + 6 = 0 \) and divide the area of the rectangle into two equal parts. Then the distance of the point \( \left(\frac{1}{2}, -5\right) \) from the line \( L \) is equal to :
Let \( y = y(x) \) be the solution of the differential equation \( x^2 dy + (4x^2 y + 2\sin x)dx = 0 \), \( x>0 \), \( y\left(\frac{\pi}{2}\right) = 0 \). Then \( \pi^4 y\left(\frac{\pi}{3}\right) \) is equal to :
A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in :
Let \( f(x) = \int \frac{(2 - x^2) \cdot e^x{(\sqrt{1 + x})(1 - x)^{3/2}} dx \). If \( f(0) = 0 \), then \( f\left(\frac{1}{2}\right) \) is equal to :}
Let the domain of \( f(x) = \log_3 \log_3 \log_7 (9x - x^2 - 13) \) be (m, n). Let the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) have eccentricity \( \frac{n}{3} \) and latus rectum \( \frac{8m}{3} \). Then \( b^2 - a^2 \) is equal to :