List of top Questions asked in JEE Main

A hall has a square floor of dimension 10 m $\times$ 10 m (see the figure) and vertical walls. If the angle GPH between the diagonals AG and BH is $\cos^{-1}\frac{1}{5}$, then the height of the hall (in meters) is :

If the area of the bounded region $R = \left\{(x, y) : \max\{0, \log_e x\} \le y \le 2^x, \frac{1}{2} \le x \le 2\right\}$ is, $\alpha(\log_e 2)^{-1} + \beta(\log_e 2) + \gamma$, then the value of $(\alpha + \beta - 2\gamma)^2$ is equal to :

A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of an ellipse with eccentricity $\frac{1}{3}$ and the distance of the nearer focus from this directrix is $\frac{8}{\sqrt{53}}$, then the equation of the other directrix can be :

Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} = 2(y + 2\sin x - 5)x - 2\cos x$ such that $y(0) = 7$. Then $y(\pi)$ is equal to :

Let a and b be two non-zero vectors perpendicular to each other and |a| = |b|. If |a × b| = |a|, then the angle between the vectors (a + b + (a × b)) and a is equal to :

The value of the integral ∫ sinθ sin2θ (sin⁶θ + sin⁴θ + sin²θ) / √(2sin⁴θ + 3sin²θ + 6) dθ is: (where c is a constant of integration)

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :

The real valued function f(x) = csc⁻¹x / √(x - [x]), where [x] denotes the greatest integer less than or equal to x, is defined for all x belonging to :

If the value of the integral $\int_{0}^{5} \frac{x+[x]}{e^{x-[x]}} dx = \alpha e^{-1} + \beta$, where $\alpha, \beta \in R, 5\alpha+6\beta=0$, and $[x]$ denotes the greatest integer less than or equal to x; then the value of $(\alpha + \beta)^2$ is equal to :

Let $f:R \rightarrow R$ be a function such that $f(2)=4$ and $f'(2)=1$. Then, the value of $\lim_{x\to 2}\frac{x^2f(2) - 4f(x)}{x-2}$ is equal to :

A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is the distance of the point (2, -3) form the line 3x + 4y = 5, is given by :

If the solution curve of the differential equation $(2x - 10y^3)dy + y dx = 0$, passes through the points (0, 1) and (2, $\beta$), then $\beta$ is a root of the equation :

Let $f:(-\frac{\pi}{4}, \frac{\pi}{4}) \rightarrow R$ be defined as

If f is continuous at $x=0$, then the value of $6a+b^2$ is equal to :

Two poles, AB of length a metres and CD of length a + b (b $\neq$ a) metres are erected at the same horizontal level with bases at B and D. If BD = x and $\tan(\angle ACB) = \frac{1}{2}$, then :

If for $x, y \in \mathbb{R}, x>0, y = \log_{10} x + \log_{10} x^{1/3} + \log_{10} x^{1/9} + \dots$ upto $\infty$ terms and $\frac{2 + 4 + 6 + \dots + 2y}{3 + 6 + 9 + \dots + 3y} = \frac{4}{\log_{10} x}$, then the ordered pair $(x, y)$ is equal to :

The domain of the function $f(x) = \sin^{-1} \left( \frac{3x^2 + x - 1}{(x - 1)^2} \right) + \cos^{-1} \left( \frac{x - 1}{x + 1} \right)$ is :

$ \lim_{x \to 0} \frac{\sin^2(\pi \cos^4 x)}{x^4} $ is equal to :

The major product of the following reaction is :

The correct sequential addition of reagents in the preparation of 3-nitrobenzoic acid from benzene is :

Match List - I with List - II :
List - I (a) Antifertility drug (b) Antibiotic (c) Tranquilizer (d) Artificial Sweetener
List - II (i) Meprobamate (ii) Alitame (iii) Norethindrone (iv) Salvarsan Choose the most appropriate match :

Hydrolysis of sucrose gives :

Consider the following reaction, the major product 'P' is:

The correct structures of A and B formed in the following reactions are :