List of top Questions asked in JEE Main

The number of points, where the curve \(f(x) = e^{8x} - e^{6x} - 3e^{4x} - e^{2x} + 1\), \(x ∈ R\) cuts x-axis, is equal to

For \(k ∈ N\), if the sum of the series \(1 + \frac{4}{k}+\frac{8}{k^2}+\frac{13}{k^3}+\frac{19}{k^4}+..\)..  is 10, then the value of k is___

If A is the area in the first quadrant enclosed by the curve \(C: 2x^2 – y + 1 = 0\), the tangent to C at the point (1, 3) and the line x + y = 1, then the value of 60A is ________

Let A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6). Then the number of functions f: A→B satisfying f(1) + f(2) = f(4)-1 is equal to _________ .

Let S = \(\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}\) if \(\alpha-\frac{13}{11}i\in S, a \in R-{0}\), then  \(242\alpha^2\) is equal to ____.

Let the line / : x = \(\frac{1-y}{2}=\frac{z-3}{\lambda}, \lambda \in R\) meet the plane P : x+2y +3z = 4 at the point \((\alpha, \beta, \lambda)\). If the angle between the line I and the plane P is \(cos^{-1}\bigg(\sqrt{\frac{5}{14}}\bigg)\) then \(\alpha+2\beta+6\lambda\) is equal to______.

Let the probability of getting head for a biased coin be \(\frac{1}{4}\) . It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation \(64x² + 5Nx + 1 = 0\) has no real root is \(\frac{p}{q}\) , where p and q are co-prime, then q – p is equal to _______.

Let \(\overrightarrow a=\overrightarrow i+2\overrightarrow j+3 \overrightarrow k\) and \(\overrightarrow b= \overrightarrow i+ \overrightarrow j - \overrightarrow k\) . If \(\overrightarrow c\) is a vector such that \(\overrightarrow a. \overrightarrow c=11,\overrightarrow b.(\overrightarrow a.\overrightarrow c)=27\) and \(\overrightarrow b. \overrightarrow c=-\sqrt{3}|b|,\)  then \(|\overrightarrow a \times \overrightarrow c|^2\) is equal to _______ .

If the line \(l_1 : 3y - 2x = 3\) is the angular bisector of the lines \(l_2 : x - y + 1 = 0\) and \(l_3\) : \(αx + βy + 17 = 0\), then \(α^2 + β^2  - α - β\) is equal to__

A car P travelling at 20 \(ms^{–1}\) sounds its horn at a frequency of 400 Hz. Another car Q is travelling being the first car in the same direction with a velocity 40 \(ms^{–1}\) . The frequency heard by the passenger of the car Q is approximately [Take, velocity of sound = 360 \(ms^{–1}\) ]

A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :

A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time, \(\overrightarrow E =6.6 \;\hat jV/m  .\)What is \(\overrightarrow B\) at this point ?

The energy of \(He^+\) ion in its first excited state is, (The ground state energy for the Hydrogen atom is – 13.6 eV) :

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
A. The electron will experience magnetic force along the axis of the solenoid. 
B. The electron will not experience magnetic force. 
C. The electron will continue to move along the axis of the solenoid. 
D. The electron will be accelerated along the axis of the solenoid. 
E. The electron will follow parabolic path-inside the solenoid. 
Choose the correct answer from the options given below :

The root mean square speed of molecules of nitrogen gas at 27°C is approximately : (Given mass of a nitrogen molecule = \(4.6 × 10^{–26}\) kg and take Boltzmann constant KB = \(1.4 × 10^{–23}\) JK–1 )

The current flowing through \(R_2\) is

In satellite communication, the uplink frequency band used is :

A body of mass 500 g moves along x-axis such that it's velocity varies with displacements x according to the relation \(v  =10 \sqrt x\) m/s the force acting on the body is :

Eight equal drops of water are falling through air with a steady speed of 10 cm/s. If the drops coalesce, the new velocity is :

When one light ray is reflected from a plane mirror with 30° angle of reflection, the angle of deviation of the ray after reflection is :

A space ship of mass 2 × 10⁴ kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if g = 10 m/s² and radius of earth = 6400 km)

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A): A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass. 
Reason (R) : For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. 
In the light of the above statement, choose the correct answer from the options given below : 

When vector \(\overrightarrow A = 2\hat i+3\hat J+2\hat k\) is subtracted from vector \(\overrightarrow B\)  , it gives a vector equal to \(2\hat j\) . Then the magnitude of vector \(\overrightarrow B\) will be :

A coil has an inductance of 2H and resistance of 4W, A 10V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ____ × 10^{–2} J.