List of top Mathematics Questions asked in JEE Main

The foci of a hyperbola coincide with the foci of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1 $ If the eccentricity of the hyperbola is 2, then the equation of the tangent to this hyperbola passing through the point (4, 6) is :

A hyperbola, having the transverse axis of length $2 \, \sin \, \theta$ is confocal with the ellipse $3x^2 + 4y^2 = 12$. Its equation is

The locus of the point of intersection of the lines, $\sqrt{2} x-y + 4 \sqrt{2} \, k=0$ and $\sqrt{2} k x+k \, y-4 \sqrt{2} = 0$ (k is any non-zero real parameter), is :

A ball is dropped from a platform $19.6\,m$ high. Its position function is -

$PQR$ is a triangular park with $PQ = PR = 200 \,m. A \,T.V$. tower stands at the mid-point of $QR$. If the angles of elevation of the top of the tower at $P, Q $ and $R$ are respectively $45^{\circ}, 30^{\circ}$ and $30^{\circ}$, then the height of the tower (in m) is :

If $\tan \, A$ and $\tan \, B$ are the roots of the quadratic equation, $3x^2 - 10x - 25 = 0$, then the value of $3 \, \sin^2(A + B) -10 \, \sin ( A + B)?\cos(A + B)-25 \cos^2(A+B) $ is :

A bag contains $4$ red and $6$ black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :

Let $A$ be the sum of the first $20$ terms and $B$ be the sum of the first $40$ terms of the series $1^2 + 2.2^2 + 3^2 + 2.4^2 + 5^2 + 2.6^2 + ?.$ If $B - 2A = 100\lambda$, then $\lambda$ is equal to :

If b is the first term of an infinite $G.P$. whose sum is five, then b lies in the interval :

Let $\frac{1}{x_1} , \frac{1}{x^2} ,...., \frac{1}{x_n} (x_1 \neq 0$ for $i = 1 , 2 , ... , n)$ be in A.P. such that $x_1 = 4$ and $x_{21} = 20$. If n is the least positive integer for which $x_n > 50$, then $\displaystyle\sum^n_{i = 1} \left( \frac{1}{x_i}\right)$ is equal to

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

A box contains 5 black and 4 white balls. A ball is drawn at random and its colour is noted. The ball is then put back in the box along with two additional balls of its opposite colour. If a ball is drawn again from the box, then the probability? that the ball drawn now is black, 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

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 $x$ $-4$.

An aeroplane flying at a constant speed, parallel to the horizontal ground, $\sqrt{3} \, km$ above it, is observed at an elevation of $60^{\circ}$ from a point on the ground. If, after five seconds, its elevation from the same point, is $30^{\circ}$, then the speed (in km/hr) of the aeroplane, is :

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 :

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 :