List of top Mathematics Questions asked in AIEEE

The normal at $\left(2,\frac{3}{2}\right)$ to the ellipse, $\frac{x^{2}}{16}+\frac{y^{2}}{3} = 1$ touches a parabola, whose equation is

If the point $(1, a)$ lies between the straight lines $x + y = 1$ and $2(x+y) = 3$ then a lies in interval

The parabola $y^2=x$ divides the circle $x^2 +y^2 = 2$ into two parts whose areas are in the ratio

If $\frac{d}{dx}G\left(x\right) = \frac{e^{tan\,x}}{x},x\in\left(0, \pi/2\right),$ then $\int\limits^{1/2}_{1/4} \frac{2}{x}. e^{tan\left(\pi\,x^2\right)}dx $ is equal to

Let $a_{n}$ denote the number of all $n$ -digit positive integers formed by the digits 0,1 or both such that no consecutive digits in them are $0 .$ Let $b_{n}=$ the number of such $n$ -digit integers ending with digit 1 and $c_{n}=$ the number of such $n$ -digit integers ending with digit $0 .$ Which of the following is correct?

Let $f : \left(-\infty, \infty\right) \to \left(-\infty , \infty \right)$ be defined by $f(x) = x^3 + 1$. The function f has a local extremum at $x = 0$ The function f is continuous and differentiable on (-??,oo) and/'(0) = 0

If the sum of the series $1^{2} + 2.2^{2} + 3^{2} + 2.4^{2} + 5^{2}+ ... 2.6^{2} +...$ upto n terms, when n is even, is $\frac{n\left(n+1\right)^{2}}{2}$, then the sum of the series, when n is odd, is

A spherical balloon is filled with $4500\,\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\,\pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases $49$ minutes after the leakage began is

The value of cos $255^{\circ}$ + sin $195^{\circ}$ is

Let A and B be real matrices of the form $\begin{bmatrix}\alpha&0\\ 0&\beta\end{bmatrix}$ and $\begin{bmatrix}0&\gamma\\ \delta&0\end{bmatrix}$, respectively. AB - BA is always an invertible matrix. AB-BA is never an identity matrix.

The weight $W$ of a certain stock of fish is given by $W= nw,$ where n is the size of stock and w is the average weight of a fish. If $n$ and $w$ change with time $t$ as $n=2t^{2}+3$ and $w=t^{2}-t+2,$ then the rate of change of $W$ with respect to $t$ at $t = 1$ is

The range of the function $f \left(x\right)=\frac{x}{1+\left|x\right|}, x\,\in\,R,$ is

The general solution of the differential equation $\frac{dy}{dx}+\frac{2}{x}y=x^{2}$ is

The equation of the circle passing through the point (1,2) and through the points of intersection of $x^2+y^2-4x-6y-21 = 0$ and $3x+4y+5 = 0$ is given by

The equation of a plane containing the line $\frac{x+1}{-3} = \frac{y-3}{2} = \frac{z+2}{1}$ and the point (0,7, - 7) is

$\int \limits \frac {sec^2x}{(secx+tan \, x)^{9/2}}dx $ equals to (for some arbitrary constant K)

Three numbers are chosen at random without replacement from $\{1, 2, 3, ..., 8\}$. The probability that their minimum is $3$, given that their maximum is $6$ is :

The value of k for which the equation $(K - 2)x^2 + 8x + K + 4 = 0$ has both roots real, distinct and negative is

The sum of the series $1+\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+.... $ upto $n $ terms is

The population $p(t)$ at time $t$ of a certain mouse species satisfies the differential equation $\frac{dp\left(t\right)}{dt} = 0.5 p\left(t\right) - 450.$ If $p\left(0\right) = 850$, then the time at which the population becomes zero is :

The number of common tangents of the circles given by $x^2+y^2-8x-2y +1 = 0$ and $x^2+y^2 + 6x+8y = 0$ is

The integral of $\frac{x^{2}-x}{x^{3}-x^{2}+x-1}$ w.r.t. x is

The area of the triangle whose vertices are complex numbers z, iz, z + iz in the Argand diagram is

The variance of first n odd natural numbers is $\frac{n^{2}-1}{3}$ : The sum of first n odd natural number is $n^2$ and the sum of square of first n odd natural numbers is $\frac{n\left(4n^{2}-1\right)}{3}.$

An equation of a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} + y^{2} = 4$ is $y = 2x + 2\sqrt{3}$ If the line $y = mx + \frac{4\sqrt{3}}{m}, \left(m\ne0\right)$ is a common tangent to the parabola $y^{2} = 16\sqrt{3}x$ and the ellipse $2x^{2} + y^{2} = 4$, then m satisfies $m^{4} + 2m^{2} = 24.$