List of top Questions asked in JEE Main

The largest value of a, for which the perpendicular distance of the plane containing the lines
$ \vec{r} (\hat{i}+\hat{j})+λ(\hat{i}+a\hat{j}−\hat{k})\ and\ \vec{r}=(\hat{i}+\hat{j})+μ(−\hat{i}+\hat{j}−a\hat{k}) $
from the point (2, 1, 4) is √3, is _____________.

In neutral or alkaline solution, MnO₄^– oxidises thiosulphateto :

Two tangent lines l₁ and l₂ are drawn from the point (2, 0) to the parabola 2y² = – x. If the lines l₁ and l₂ are also tangent to the circle (x – 5)² + y² = r, then 17r is equal to _________.

Let $\vec{a}=\alpha \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0$. If the projection of $\vec{a} \times \vec{b}$ on the vector $-\hat{ i }+2 \hat{ j }-2 \hat{ k }$ is $30$, then $\alpha$ is equal to

The plane passing through the line L :lx – y + 3(1 – l) z = 1, x + 2y – z = 2 and perpendicular to the plane 3x + 2y + z = 6 is 3x – 8y + 7z = 4. If θ is the acute angle between the line L and the y-axis, then 415 cos²θ is equal to ________.

Ka₁, Ka₂ and Ka₃ are the respective ionization constants for the following reactions (a),(b), and (c).
(a) H₂C₂O₄⇌H⁺+HC₂O₄⁻
(b) HC₂O₄⁻⇌H⁺+HC₂O₄²⁻
(c) H₂C₂O₄⇌2H⁺+_C2O₄²⁻
The relationship between Ka₁,Ka₂ and Ka₃ is given as

If $\begin{array}{l} \frac{6}{3^{12}}+\frac{10}{3^{11}}+\frac{20}{3^{10}}+\frac{40}{3^9}+\cdots +\frac{10240}{3}=2^n\cdot m, \end{array}$where m is odd, then m⋅n is equal to ________.

Number of electron deficient molecules among the following
$PH_3, B_2H_6, CCl_4, NH_3, LiH $ and $BCl_3$ is

Let f : R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x ∈ R where k > 0 and n is a positive integer. If
$l_1 = \int_{0}^{4nk} f(x) \, dx$ and $l_2 = \int_{-k}^{3k} f(x) \, dx$, then

Let for n = 1, 2, …, 50, S_n be the sum of the infinite geometric progression whose first term is n² and whose common ratio is
$\frac{1}{(n+1)^2}$ . Then the value of
$\frac{1}{26} + \sum_{n=1}^{50} \left(S_n+\frac{2}{n+1}-n-1 \right)$
is equal to ________.

A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping They start from rest The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :

Let R₁ = {(a, b) ∈ N × N : |a – b| ≤ 13} and R₂ = {(a, b) ∈ N × N : |a – b| ≠ 13}. Then on N:

The number of solutions of the equation $2\theta - \cos^2(\theta) + \sqrt{2} = 0$ in R is equal to ___________.

Let f : R → R be a differentiable function such that
$f(\frac{π}{4})=\sqrt2,f(\frac{π}{2})=0 $ and $f′(\frac{π}{2})=1$
and let
$g(x) = \int_{x}^{\frac{\pi}{4}} \left(f'(t)\sec(t) + \tan(t)\sec(t)f(t)\right) \, dt$
for$ x∈(\frac{π}{4},\frac{π}{2})$ Then $\lim_{{x \to \frac{\pi}{2}^-}} g(x)$is equal to