List of top Mathematics Questions asked in JEE Main

If $x = \sqrt{2^{cosec^{-1} } t}$ and $y = \sqrt{2^{\sec^{-1}} t} (|t | \geq 1)$, then $\frac{dy}{dx}$ is equal to :

Let N denote the set of all natural numbers. Define two binary relations on N as $R_1 = \{(x, y) \epsilon N \times N : 2x + y = 10 \}$ and $R_2 = \{(x, y) \epsilon N \times N : x + 2y = 10 \}$. Then :

For a positive integer $n$, if the mean of the binomial coefficients in the expansion of $(a + b)^{2n - 3}$ is 16, then $n$ is equal to :

Fill in the blanks. (i) If $x > y$ and $z < 0$, then $-xz$ $-yz$. (ii) If $p > 0$ and $q < 0$, then $p - q$ $p$. (iii) If $-2x + 1 \ge 9$, then $x$ $-4$.

The least positive integer n for which $\left( \frac{1 + i \sqrt{3}}{1 - i \sqrt{3}} \right)^n = 1 $, is :

A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min. for the angle of depression of the car to change from $30^{\circ}$ to $45^{\circ}$ ; then after this, the time taken (in min.) by the car to reach the foot of the tower, is :

If the tangent at $(1, 7)$ to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ then the value of c is:

Consider the following two statements : The value of $\sin \, 120^{\circ}$ can be derived by taking $\theta =240^{\circ}$ in the equation $2 \sin \, \frac{\theta}{2} = \sqrt{1 + \sin \, \theta} - \sqrt{1 - \sin \, \theta}$. The angles A, B, C and D of any quadrilateral ABCD satisfy the equation $\cos \left( \frac{1}{2} (A + C) \right) + \cos \left( \frac{1}{2} (B + D) \right) = 0 $ Then the truth values of p and q are respectively :

If the length of the latus rectum of an ellipse is $4$ units and the distance between a focus and its nearest vertex on the major axis is $\frac{3}{2}$ units, then its eccentricity 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 :

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

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 :

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 :

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

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

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 :

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

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 :

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)

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 :

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 :

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 :