List of top Questions asked in JEE Main

The total current supplied to the circuit as shown in figure by the 5 V battery is _______ A.
The total current supplied to the circuit
The current in a coil of self inductance \(2.0\ H\) is increasing according to \(I = 2\ sin(t^2)\ A\). The amount of energy spent during the period when current changes from 0 to \(2\ A\) is _______ \(J\).
A force on an object of mass \(100\ g\) is \((10\hat i+5\hat j)\ N\). The position of that object at \(t = 2s\) is \((a\hat i+b\hat j)\ m\) after starting from rest. The value of \(\frac ab\) will be _______ .
The number of N atoms in \(681\ g\) of \(C_7H_5N_3O_6\) is \(x × 10^{21}\). The value of \(x\) is ______ . (\(N_A\) = \(6.02 × 10^{23}\ mol^{–1}\)) (Nearest Integer)
The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is \(x × 10^{–8}\ m\). The value of \(x\) is ______. (Nearest Integer)
(Given : Energy of the electron in the first shell of the hydrogen atom is \(2.2 \times 10^{–18} J\);
\(h = 6.63 × 10^{–34}Js\) and \(c = 3 × 10^8 ms^{–1}\))
1L aqueous solution of \(H_2SO_4\) contains 0.02 m mol \(H_2SO_4\). 50% of this solution is diluted with deionized water to give 1L solution (A). In solution (A), 0.01 m mol of \(H_2SO_4\) are added. Total m mols of \(H_2SO_4\) in the final solution is ______ \(× 10^3\) m mols.
The distance between \(Na^+\) and \(Cl^–\) ions in solid \(NaCl\) of density \(43.1\ g\ cm^{–3}\) is ____ \(× 10^{–10}\ m\). (Nearest Integer)
(Given : \(N_A = 6.02 × 10^{23} mol^{–1}\))
The standard entropy change for the reaction \(4Fe(s) + 3O_2(g) → 2Fe_2O_3(s)\) is \(–550\ J K^{–1}\) at \(298\ K\). The temperature in K at which the reaction attains equilibrium is ______. (Nearest Integer)
[Given: The standard enthalpy change for the reaction is \(–165\ kJmol^{–1}\)].
A body is projected from the ground at an angle of 45° with the horizontal. Its velocity after \(2\) \(s\) is \(20\) \(ms^{–1}\). The maximum height reached by the body during its motion is ________ m. (use \(g\) = \(10\) \(ms^{–2}\))
An antenna is placed in a dielectric medium of dielectric constant \(6.25\). If the maximum size of that antenna is \(5.0\) \(mm\), it can radiate a signal of minimum frequency of __________GHz. (Given \(μr\) = \(1\) for dielectric medium)
The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :
The standard free energy change \((ΔG°)\) for \(50%\) dissociation of \(N_2O_4\) into \(NO_2\) at \(27°C\) and 1 atm pressure is \(x\ J mol^{–1}\). The value of \(x\) is _____. (Nearest Integer)
[Given : \(R = 8.31\ JK^{–1} mol^{–1}\), \(log\ 1.33 = 0.1239\), \(ln\ 10 = 2.3\)]

If the inverse trigonometric functions take principal values, then
\(cos^{-1} ( \frac{3}{10} cos (tan^{-1} (\frac{4}{3})) + \frac{2}{5} sin (tan^{-1} (\frac{4}{3})))\)
is equal to :

In a cell, the following reactions take place
\(Fe^{2+} → Fe^{3+} + e^-\)
\(E°_{Fe^{3+}/Fe^{2+}} = 0.77\ V\)
\(2I^- → I_2 + 2e^-\)
\(E_{I_2/I^-} = 0.54\ V\)
The standard electrode potential for the spontaneous reaction in the cell is \(x×10^{–2} V\) at \(208\ K\). The value of \(x\) is _______. (Nearest Integer)

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.
Reason R : Coefficient of viscosity
\(= \frac{Force}{Velocity ∼ gradient}\)

Choose the correct answer from the options given below.

For a given chemical reaction
\(γ_1A + γ_2B → γ_3C + γ_4D\)
Concentration of C changes from 10 mmol dm–3 to 20 mmol dm–3 in 10 seconds. Rate of appearance of D is 1.5 times the rate of disappearance of B which is twice the rate of disappearance A. The rate of appearance of D has been experimentally determined to be 9 mmol dm–3 s–1. Therefore, the rate of reaction is _____ mmol dm–3 s–1. (Nearest Integer)

If \([Cu(H_2O)_4]^{2+}\) absorbs a light of wavelength 600 nm for d-d transition, then the value of octahedral crystal field splitting energy for [\(Cu(H_2O)_6]^{2+}\) will be _______ \(×10^{–21} J\). [Nearest integer]
(Given : h = \(6.63 × 10^{–34} Js\) and \(c = 3.08×10^8 ms^{–1}\))

Number of grams of bromine that will completely react with 5.0 g of pent-1-ene is ______ × 10–2 g. (Atomic mass of Br = 80 g/mol) [Nearest integer]
A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k2rt2, where k is a constant. The power delivered to the particle by the force acting on it is given as

Motion of a particle in x–y plane is described by a set of following
\(x = 4sin (\frac{π}{2} - ωt )m\)
and y = 4sin(ωt) m. The path of the particle will be

Let \(y = y(x)\) be the solution of the differential equation \((x + 1)y' – y = e^{3x}(x + 1)^2\), with \(y(0)=\frac 13\). Then, the point \(x=−\frac 43\) for the curve \(y = y(x)\) is :

Match List-I with List-II.

 List - I List - II
  A.    Moment of inertia of solid sphere of Radius R about any tangent           i.\(\frac{5}{3}MR^2\)  
B.Moment of inertia of hollow sphere of radius (R) about any tangentii.\(\frac{7}{5}MR^2\)
C.Moment of inertia of circular ring of radius (R) about its diameteriii.\(\frac{1}{4}MR^2\)
D.Moment of inertia of circular disc of radius (R) about any diameteriv.\(\frac{1}{2}MR^2\)

Choose the correct answer from the options given below.

 

 

 

 



 

If \(y = m_1x + c_1 \)and \(y = m_2x + c_2\), \(m_1≠m_2\) are two common tangents of circle \(x_2 + y_2 = 2\) and parabola \(y^2 = x\), then the value of \(8|m_1m_2|\) is equal to :
Let \(Q\) be the mirror image of the point \(P(1, 0, 1)\) with respect to the plane \(S\): \(x + y + z = 5\). If a line L passing through \((1, –1, –1)\), parallel to the line \(PQ\) meets the plane \(S\) at \(R\), then \(QR_2\) is equal to :
Two planets A and B of equal mass are having their period of revolutions TA andTB such that TA= 2TB. These planets are revolving in the circular orbits of radii rA and rB respectively. Which out of the following would be the correct relationship of their orbits?