List of top Mathematics Questions asked in JEE Main

Two parabolas with a common vertex and with axes along x-axis and y-axis, respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is :

Two sets $A$ and $B$ are as under: $A = \{(a, b) \in R \times R : |a - 5| < 1$ and $|b - 5| < 1\} $; $B = \{(a, b) \in R \times R : 4(a - 6)2 + 9(b - 5)^2 \leq 36\}$. Then

The set of all $\alpha \epsilon R$, for which $w = \frac{1 + (1 - 8 \alpha)z}{1 - z}$ is a purely imaginary number, for all $z \neq 1$, is :

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

A box contains $15$ green and $10$ yellow balls. If $10$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :

The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the y-axis passes through the point :

For any three positive real numbers a, b and c, $9(25a^2 + b^2) + 25 (c^2 - 3ac) = 15b (3a + c)$. Then :

Let $a, b, c \, \in \, R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f (x + y) = f (x) + f (y) + xy, \forall \, x, y \, \in \, R,$ then $\displaystyle\sum^{10}_{n = 1} f(n)$ is equal to :

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{\left(\pi - 2x\right)^{3}} $ equals :

If for $x \epsilon \left(0, \frac{1}{4}\right) ,$ the derivative of $ \tan^{-1} \left(\frac{6x \sqrt{x}}{1-9x^{3}}\right) $ is $\sqrt{x} . g(x)$, then $g(x)$ equals :

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in $s m$) of the flower-bed, is :

Let $l_n = \int \tan^{n} x \, dx , (n > 1) . l_4 + l_6 = a \, \, \tan^5 \, x + bx^5 + C$, where $C$ is a constant of integration, then the ordered pair $(a, b)$ is equal to :

The integral $\int\limits^{\frac{3\, \pi}{4}}_{\frac{\pi}{4}} \frac{dx}{ 1 + \cos \, x}$ is equal to :

The area (in s units) of the region $\{ (x , y) : x \geq 0 , x + y \leq 3, x^2 \leq 4 y$ and $y \leq 1 + \sqrt{x} \}$ is

If $(2 + \sin \, x ) \frac{dy}{dx} + (y + 1) \cos \, x = 0$ and $y(0) = 1,$ then $y \left( \frac{\pi}{2} \right)$ is equal to :

If $(27)^{999}$ is divided by $7$, then the remainder is :

If, for a positive integer n, the quadratic equation, $x(x+1)+(x+1)(x+2)+....+(x + \overline{ n - 1}) (x+ n)=10n$ has two consecutive integral solutions, then $n$ is equal to :

If two different numbers are taken from the set $\{0,1,2,3, \ldots \ldots, 10\}$then the probability that their sum as well as absolute difference are both multiple of $4$, is :

Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP = 2AB$. If $\angle BPC = \beta $, then tan $\beta$ is equal to :

Let $S_{n} = \frac{1}{1^{3}} + \frac{1+2}{1^{3} + 2^{3}} + \frac{1+2+3}{1^{3} + 2^{3} + 3^{3}} + ...... + \frac{1+2+...+n}{1^{3} + 2^{3} +.... +n^{3}} . $ . If $100 \, S_n = n , $ then $n$ is equal to :

Let $z \in C$, the set of complex numbers. Then the equation, $2 | z + 3i| - | z - i| = 0 $ represents :

The value of $\tan^{-1} \left[\frac{\sqrt{1+x^{2}} + \sqrt{1-x^{2}}}{\sqrt{1+x^{2}} - \sqrt{1-x^{2}}}\right] , \left|x\right| < \frac{1}{2}, x \ne0, $ is equal to :

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt{-3}$ ,If $\begin{vmatrix}1&1&1\\ 1&-\omega^{2} - 1 &\omega^{2}\\ 1&\omega^{2}& \omega^{7}\end{vmatrix} = 3 k , $ then $k$ is equal to :

The integral $\int \sqrt{ 1 + 2 \cot \, x (cosec \, x + \cot \, x) } dx \, \left( 0 < x < \frac{\pi}{2} \right)$ is equal to : (where $C$ is a constant of integration)

The value of $(^{21}C_{1} - ^{10}C_{1}) + (^{21}C_{2} - ^{10}C_{2}) + (^{21}C_{3} - ^{10}C_{3}) +(^{21}C_{4} - ^{10}C_{4}) +....+(^{21}C_{10} - ^{10}C_{10})$ is :