List of top Questions asked in JEE Main

Let i = √-1. If $\frac{(-1 + i\sqrt{3})^{21}}{(1 - i)^{24}} + \frac{(1 + i\sqrt{3})^{21}}{(1 + i)^{24}} = k$, and $n = \lfloor |k| \rfloor$. Then $\sum_{j=0}^{n+5} (j + 5)^2 - \sum_{j=0}^{n+5} (j + 5)$ is equal to __________.

The students S1, S2, ......., S10 are to be divided into 3 groups A, B and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is _________

The maximum value of k for which the sum $\sum_{i=0}^k \binom{10}{i} \binom{15}{k-i} + \sum_{i=0}^{k+1} \binom{12}{i} \binom{13}{k+1-i}$ exists, is equal to __________.

If a + α = 1, b + β = 2 and a f(x) + α f(1/x) = b x + β / x, then [f(x) + f(1/x)] / [x + 1/x] is ________

If the shortest distance between x - λ = 2y - 1 = -2z and x = y + 2λ = z - λ is √7 / 2√2, then |λ| is _______

If $n \geq 2$ is a positive integer, then the sum of the series ${ }^{n+1} C_{2}+2\left({ }^{2} C_{2}+{ }^{3} C_{2}+{ }^{4} C_{2}+\ldots .+{ }^{n} C_{2}\right)$ is:

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is \(0.9\) and that of the second unit is \(0.8\). The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is \(p\), then \(98p\) is equal to \dots\dots.

In the given figure, a mass \(M\) is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is \(k\). The mass oscillates on a frictionless surface with the time period \(T\) and amplitude \(A\). When the mass is in an equilibrium position, as shown in the figure, another mass \(m\) is gently fixed upon it. The new amplitude of oscillation will be : 

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ______ Hz. [Velocity of sound in air is 340 m/s.]

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90 W. How long it would take to increase the internal energy by $2.5 \times 10^3$ J ?

The sum of first 4 terms of a G.P. is 65/12 and sum of their reciprocals is 65/18. If product of first 3 terms is 1 and the 3rd term is α, then 2α is _________

A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

A body of mass 2 kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10}$ m/s. Then the value of $x$ is ________.

The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom at each lattice point. The calculated density of copper in kg/m³ is ________ . [Molar mass of Cu: 63.54 g; Avogadro Number=6.022$\times$10²³]

Water does not produce CO on reacting with:

A free electron of 2.6 eV energy collides with a \(H^+\) ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon. (\(h = 6.6 \times 10^{-34}\) J s)

The major product (A) formed in the reaction given below is :
\includegraphics[width=0.6\linewidth]{image43.png}

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be _________ Hz.

Two fair dice are thrown. The numbers on them are taken as \(\lambda\) and \(\mu\), and a system of linear equations
\(x+y+z=5\)
\(x+2y+3z=\mu\)
\(x+3y+\lambda z=1\)
is constructed. If p is the probability that the system has a unique solution and q is the probability that the system has no solution, then :

A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 \(\times\) 10\(^{14}\) Hz. The velocity of ejected electron is ___________ \(\times\) 10\(^{5}\) ms\(^{-1}\). (Nearest integer)
[Use: h = 6.63\(\times\)10\(^{-34}\) Js, m\(_e\) = 9.0\(\times\)10\(^{-31}\) kg]

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is __________ N.
(take g=10 ms\(^{-2}\))
\includegraphics[width=0.5\linewidth]{21.png}

According to Bohr's atomic theory :- (A) Kinetic energy of electron is $\propto \frac{ Z ^{2}}{ n ^{2}}$. (B) The product of velocity (v) of electron and principal quantum number (n), 'vn' $\propto Z ^{2}$. (C) Frequency of revolution of electron in an orbit is $\propto \frac{ Z ^{3}}{ n ^{3}}$. (D) Coulombic force of attraction on the electron is $\propto \frac{ Z ^{3}}{ n ^{4}}$. Choose the most appropriate answer from the options given below:

Complete combustion of $1.80 g$ of an oxygen containing compound $\left( C _{ x } H _{ y } O _{2}\right)$ gave $2.64 g$ of $CO _{2}$ and $1.08 g$ of $H _{2} O$. The percentage of oxygen in the organic compound is:

(A) $HOCl + H _{2} O _{2} \rightarrow H _{3} O ^{+}+ Cl ^{-}+ O _{2}$
(B) $I _{2}+ H _{2} O _{2}+2 OH ^{-} \rightarrow 2 I ^{-}+2 H _{2} O + O _{2}$
Choose the correct option.