List of top Questions asked in JEE Main

The remainder when \(7^{2022}+3^{2022}\) is divided by \(5\) is:

Total number of relatively more stable isomer(s) possible for octahedral complex [Cu(en)2(SCN)2] wiil be ______.

Two identical charged particles each having a mass 10 g and charge \(2.0 × 10^{–7}\) C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is \(0.25\), find the value of L. [Use g = \(10\) \(ms^{–2}\)]

A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table as shown in the figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be
A system of two blocks of masses m = 2 kg and M = 8 kg is placed on a smooth table
A block of mass 2 kg moving on a horizontal surface with speed of 4 ms–1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm–1. The speed of the block as it just crosses the rough surface will be
One end of a massless spring of spring constant k and natural length \(l_0\) is fixed while the other end is connected to a small object of mass \(m\) lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity \(ω\) about an axis passing through fixed end, then the elongation of the spring will be :
Two masses \(M_1\) and \(M_2\) are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass \(M_2\) is twice that of \(M_1\), the acceleration of the system is \(a_1\). When the mass \(M_2\) is thrice that of \(M_1\), the acceleration of the system is \(a_2\). The ratio \(\frac{a_1}{a_2}\) will be
Two uniformly charged spherical conductors, A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at surface of the spheres A and B will be
Given below are two statements:
Statement I: A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.
Statement II: In a material medium, the EM wave travels with speed
\(V=\frac{1}{\sqrt{µ0ε0}}\) In the light of the above statements, choose the correct answer from the options given below.
A velocity selector consists of electric field \(\overrightarrow E=E\hat K\) and magnetic field \(\overrightarrow B=B\hat j\) with \(B = 12 \;mT\). The value of E required for an electron of energy \(728\) \(eV\) moving along the positive x-axis to pass undeflected is (Given, mass of electron = \(9.1 × 10^{–31}\) kg)
A spherically symmetric charge distribution is considered with charge density varying as
\(ρ(r) =   \begin{cases}     ρ_0(\frac 34−\frac rR)      &; \text{for} \ r≤R\\     Zero  &; \text{for}\ r>R    \end{cases}\)
Where, r(r<R) is the distance from the centre O (as shown in figure) The electric field at point P will be :
A spherically symmetric charge distribution
If the equation of the parabola, whose vertex is at \((5, 4)\) and the directrix is \(3x + y – 29 = 0\), is \(x^2 + ay^2 + bxy + cx + dy + k = 0\), then \(a + b + c + d + k\) is equal to
An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, g = 10 ms–2 and radius of earth = 6400 km]
The correct structure of C is
structure of C

Let ℝ → ℝ be function defined as
f(x) = αsin(\((\frac{π[x]}{2})\)+[2-x],α∈R
where [t] is the greatest integer less than or equal to t.
If lim x→1 f(x) exists, then the value of\(∫_0^4\) f(x)dx
is equal to

\(250\) \(g\) solution of \(D-glucose\) in water contains 10.8% of carbon by weight. The molality of the solution is nearest to (Given: Atomic Weights are, \(H, 1 u; C, 12 u; O, 16 u\))
The disproportionation of MnO42- in acidic medium resulted in the formation of two manganese compounds A and B. If the oxidation state of Mn in B is smaller than that of A, then the spin-only magnetic moment (μ) value of B in BM is _______. (Nearest integer)
Given below are two statements.
Statement I: \(O_2, Cu^{2+}, \;and\; Fe^{3+}\) are weakly attracted by magnetic field and are magnetized in the same direction as magnetic field.
Statement II: \(NaCl\) and \(H_2O\) are weakly magnetized in opposite directions to the magnetic field.
In the light of the above statements, choose the most appropriate answer from the options given below.
Which of the following methods are not used to refine any metal?
  1. Liquation
  2. Calcination
  3. Electrolysis
  4. Leaching
  5. Distillation
Choose the correct answer from the options given below :
Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium.
Reason R : Energies of the orbitals in the same subshell decrease with increase in the atomic number.
In the light of the above statements, choose the correct answer from the options given below.

Match List-I with List-II

Choose the correct answer from the options given below:
 

Given below are two statements.
Statement I : Hydrogen peroxide can act as an oxidizing agent in both acidic and basic conditions.
Statement II : Density of hydrogen peroxide at 298 K is lower than that of \(D_2O\).
In the light of the above statements, choose the correct answer from the options given below :
Given below are two statements.
Statement I : The chlorides of Be and Al have Cl-bridged structure. Both are soluble in organic solvents and act as Lewis bases.
Statement II : Hydroxides of Be and Al dissolve in excess alkali to give beryllate and aluminate ions.
In the light of the above statements, choose the correct answer from the options given below.
Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.
The value of the integral \(\begin{array}{l} \displaystyle\int\limits_0^{\frac{\pi}{2}}60\frac{\sin\left(6x\right)}{\sin x}dx \end{array}\) is equal to ______.