List of top Questions asked in JEE Main

Let y = y(x), x > 1, be the solution of the differential equation
\((x-1)\frac{dy}{dx} + 2xy = \frac{1}{x-1}\)with \(y(2) = \frac{1+e^4}{2e^4}\). If \(y(3) = \frac{e^α + 1}{βe^α}\) , 
then the value of α + β is equal to ____.

Let
\(M = \begin{bmatrix}   0 & -\alpha \\   \alpha & 0 \\ \end{bmatrix}\)
where α is a non-zero real number an
\(N =   \sum\limits_{k=1}^{49} M^{2k}. \) If \((I - M^2)N = -2I\)
then the positive integral value of α is ____ .

Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x² – 2x and g(f(x)) = 4x² + 6x + 1, then the value of f(2) + g(2) is ____________ .

Let
\(f(x) = \begin{vmatrix} a & -1 & 0\\ ax & a & -1\\ ax^2 & ax & a \end{vmatrix}\)
a ∈ R. Then the sum of the square of all the values of a, for which 2f′(10) –f′(5) + 100 = 0, is

Match List-I with List-II :
 

Choose the correct answer from the options given below:

Among the following structures, which will show the most stable enamine formation? 
(Where Me is –CH₃)

In the following reaction,
the % yield for reaction I is 60% and that of reaction II is 50%. The overall yield of the complete reaction is _______%. [Nearest integer].

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