List of top Questions asked in JEE Main

The boolean expression (~(p ∧q)) ∨q is equivalent to:

The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is

A pressure-pump has a horizontal tube of cross sectional area \(10  cm^2 \) for the outflow of water at a speed of \(20 m/s\). The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is 
[given: density of water = \(1000  kg/m^3\)].
Let \([t]\) denote the greatest integer less than or equal to \(t\). Then, the value of the integral \(∫_0^1 [ -8x^2 + 6x - 1] dx\) is equal to 

In the following nuclear reaction,
\(D \stackrel{α}{⟶} D1 \stackrel{β^-}{⟶} D2 \stackrel{α}{⟶} D3 \stackrel{γ}{⟶} D4\)
Mass number of D is 182 and atomic number is 74. Mass number and atomic number
of D4, respectively, will be _____.

The positive value of the determinant of the matrix A, whose 
\(\text{Adj}(\text{Adj}(A)) = \begin{bmatrix} 14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14 \end{bmatrix}\)
 is ___.

A rectangle R with end points of one of its sides as (1, 2) and (3, 6) is inscribed in a circle. If the equation of a diameter of the circle is 2x – y + 4 = 0, then the area of R is ________.
We do not transmit low frequency signal to long distance because-
(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength
(b) Effective power radiated by a long wavelength baseband signal would be high
(c) We want to avoid mixing up signals transmitted by different transmitter simultaneously
(d) Low frequency signal can be sent to long distances by superimposing with a high frequency wave as well
Therefore, the most suitable option will be
A rolling wheel of \(12\) kg is on an inclined plane at position P and connected to a mass of \(3\) kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface.
The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be \(\frac{1}{2}\sqrt{ xgh}\) \(m/s\). The value of x is _________.
The integral \(∫_0^ 1 \frac{ 1}{7^{[\frac{1}{z}}]}dx\) where [⋅] denotes the greatest integer function, is equal to
Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers: \(Mn = 25; Fe = 26\))
(1) \([FeF_6]^{3–}\)
(2) \([Fe(CN)_6]^{3–}\)
(3) \([MnCl_6]^{3–}\) (high spin)
(4) \([Mn(CN)_6]^{3–}\)
17.0 g of NH3 completely vapourises at – 33.42°C and 1 bar pressure and the enthalpy change in the process is 23.4 kJ mol–1 . The enthalpy change for the vapourisation of 85 g of NH3 under the same conditions is ____ kJ.
Let the plane ax + by + cz = d pass through (2, 3, –5) and is perpendicular to the planes 2x + y – 5z = 10 and 3x + 5y – 7z = 12. If a, b, c, d are integers d > 0 and gcd (|a|, |b|, |c|, d) = 1, then the value of a + 7b + c + 20d is equal to :

\(\tan⁡(2\tan^{−1}\frac{⁡1}{5}+\sec^{−1}⁡\frac{\sqrt5}{2}+2\tan^{−1}⁡\frac{1}{8})\)
is equal to :

Vulcanization of rubber is carried out by heating a mixture of
The spin-only magnetic moment value of the compound with strongest oxidizing ability among MnF4, MnF3 and MnF2 is____ B.M. [nearest integer]

The number of q∈ (0, 4π) for which the system of linear equations
3(sin 3θ) x – y + z = 2
3(cos 2θ) x + 4y + 3z = 3
6x + 7y + 7z = 9
has no solution, is

Let \(x, y > 0\). If \(x^3y^2 = 2^{15}\), then the least value of \(3x + 2y\) is

Choose the correct answer :

1. Production of iron in blast furnace follows the following equation

Fe3O4(s)+4CO(g)→3Fe(I)+4CO22(g)

when 4.640 kg of Fe3O4 and 2.520 kg of CO are allowed to react then the amount of iron (in g) produced is

[Given : Molar Atomic mass (g mol–1) : Fe = 56

Molar Atomic mass (g mol–1) : O = 16

Molar Atomic mass (g mol–1) : C = 12]

Match List-I with List-II.

List-I (Metal)List-II (Application)
(A) Cs (I) High temperature thermometer
(B) Ga (II) Water repellent sprays
(C) B (III) Photoelectric cells
(D) Si (IV) Bullet proof vest

Choose the most appropriate answer from the options given below:

Two projectiles thrown at 30° and 45° with the horizontal, respectively, reach the maximum height in same time. The ratio of their initial velocities is :
A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350 N. If monkey initially climbs down with an acceleration of 4 m/s2 and then climbs up with an acceleration of 5 m/s2. Choose the correct option (g = 10 m/s2).
Reaction of \(BeCl_2\) with \(LiAlH_4\) gives :
  1. \(AlCl_3\)
  2. \(BeH_2\)
  3. \(LiH\)
  4. \(LiCl\)
  5. \(BeAlH_4\)
Choose the correct answer from the options given below :
An expression for a dimensionless quantity P is given by \(P=\frac{α}{β} log_e(\frac{kt}{βx})\); where α and β are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of α will be
Which of the following compounds is not aromatic?