List of top Mathematics Questions asked in AIEEE

If $f: R \rightarrow S $ defined by $ f(x)=\sin x-\sqrt{3} \,\cos\,x+\,$ 1, is onto, function then S = ?

The graph of the function $y = f(x) $is symmetrical about the line $x = 2$, then

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is $60^{\circ}$ and when he retires $40$ meter away from the tree the angle of elevation becomes $30^{\circ}$. The breadth of the river is

If $\left(\frac{1+i}{1-i}\right)^{x}=1,$ then

If $1,\omega,\omega^2$ are the cube roots of unity, then $\Delta=\begin{vmatrix} 1&\omega^n &\omega^{2n} \\[0.3em] \omega^n &\omega^{2n} & 1 \\[0.3em] \omega^{2n} &1& \omega^n \end{vmatrix}$ is equal to

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of side a, is

The number of real solutions of the equation $x^2 - 3 |x| + 2 = 0$ is

If $A = \begin{bmatrix}a&b\\ b&a\end{bmatrix}$ and $A^{2}\begin{bmatrix}\alpha&\beta \\ \beta&\alpha\end{bmatrix}$, then

If $f (a + b - x) = f (x)$, then $\int\limits^{b}_{{a}}x\, f\, (x) \,dx$ is equal to

If $f(x) = \begin{cases} xe^{-\left(\frac{1}{\left|x\right|}+\frac{1}{x}\right)}, & \text{$x \ne0$} \\[2ex] 0, & \text{$x=0$} \end{cases}$ then $f (x)$ is

If $f (x) = x^n$, then the value of $f \left(1\right)-\frac{f '\left(1\right)}{1!}+\frac{f ''\left(1\right)}{2!}-\frac{f "'\left(1\right)}{3!}+\dots+\frac{\left(-1\right)^{n}f ^{n}\left(1\right)}{n!}$ is

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ equal to

The trigonometric equation $sin^{-1} x = 2\, sin^{-1}$ a, has a solution for

Let f (x) be a polynomial function of second degree. If $f (1) = f (- 1)$ and $a, b, c$ are in $A. P.,$ then $f' (a), f' (b)$ and $f' (c)$ are in

The sum of the series $\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{3\cdot4}-...... $ upto $8$ is equal to

If $\begin{vmatrix}a&a^{2}&1+a^{3}\\ b&b^{2}&1+b^{3}\\ c&c^{2}&1+c^{3}\end{vmatrix}=0 $ and vectors $(1, a, a^2) (1, b, b^2)$ and $(1, c, c^2)$ are non-coplanar, then the product abc equals

A tetrahedron has vertices at $ O (0, 0, 0), A(1, 2, 1) B(2, 1, 3 )$ and $C(-1, 1, 2)$. Then the angle between the faces OAB and ABC will be

If $z$ and $?$ are two non-zero complex numbers such that $|z?| = 1$, and Arg $(z)$ - Arg $\left(\omega\right)=\frac{\pi}{2},$ then $\bar{z}\omega$ is equal to

If $a > 0$ and discriminant of $ax^2 + 2bx +c $ is -ve then $\begin{vmatrix}a&b&ax+b\\ b &c&bx+c\\ ax+b &bx+c&0\end{vmatrix} $ is equal to

The domain of $\sin^{-1}\left[\log_3\left(\frac{x}{3}\right)\right]$ is

If $(\omega\,\neq\,1)$ is a cube root of unity , then $ \begin{vmatrix} 1 &1+i+\omega^2 &\omega^2 \\[0.3em] 1-i&-1 & \omega^2-1 \\[0.3em] -i & -1+\omega-i& -1 \end{vmatrix}=$

If the vectors $\vec{ a }=x \hat{ i }+y \hat{ j }+z \hat{ k }$ and such that $\vec{ a }, \vec{ c }$ and $\vec{ b }$ form a right handed system, then $\vec{ c }$ is :

The direction ratios of a normal to the plane through $ (1, 0, 0), (0, 1, 0)$ which makes angles of $\frac{\pi}{4}$ with the plane $x + y = 3$ are

The positive integer just greater than $(1 + 0.0001)^{10000}$ is

If the sum of the coefficients in the expansion of $(a + b)^n$ is 4096, then the greatest coefficient in the expansion is