List of top Questions asked in JEE Main

Let the function f(x) = 2x² – log_ex, x> 0, be decreasing in (0, a) and increasing in (a, 4). A tangent to the parabola y² = 4ax at a point P on it passes through the point (8a, 8a –1) but does not pass through the point (-1/a, 0). If the equation of the normal at P is
\(\frac{x}{α}+\frac{y}{β}=1\)
 then α + β is equal to _______ .

If 
\(\lim_{{x \to 1}} \frac{{\sin(3x^2 - 4x + 1) - x^2 + 1}}{{2x^3 - 7x^2 + ax + b}} = -2\)
, then the value of (a – b) is equal to_______.

If 
\(\sum\limits_{k=1}^{31}\) \((^{31}C_k) (^{31}C_{k-1})\) \(-\sum\limits_{k=1}^{30}\) \((^{30}C_k) (^{30}C_{k-1})\) \(= \frac{α (60!)} {(30!) (31!)}\)
where \(α ∈ R\), then the value of 16α is equal to

A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time t = T/√2, is _________.
[Take g = 10m/s²]

Let \(S=\left\{(x,y)∈\N×\N:9(x−3)^2+16(y−4)^2≤144\right\}\)
and \(T=\left\{(x,y)∈\R×\R:(x−7)^2+(y−4)^2≤36\right\}.\)
Then n(S ⋂ T) is equal to ____ .

Let a function ƒ : N →N be defined by
 \(f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 &  n = 3,7,11,15,\ldots \\ \frac{n+1}{2} &  n = 1,5,9,13 \end{array} \right.\)
then, ƒ is