List of top Mathematics Questions asked in AIEEE

The system of equations $\alpha \, x + y + z = \alpha - 1$ $x + \alpha y + z = \alpha - 1$ $x + y + \alpha z = \alpha - 1$ has infinite solutions, if $\alpha$ is

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house, is:

The sum of the series $1+\frac{1}{4\cdot2!}+\frac{1}{16\cdot 4!}+\frac{1}{64\cdot 6!} + \ldots \infty$ is :

The normal to the curve $x=a\left(cos\,\theta+\theta\,sin\,\theta \right). y=a\left(sin\,\theta -\theta\,cos\,\theta \right)$ at any point $'\theta'$ is such that :

$\int\left\{\frac{\left(log \,x -1\right)}{1+\left(log \,x\right)^{2}}\right\}^{2}dx$ is equal to :

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number:

Area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ is :

Let $P$ be the point $(1, 0)$ and $Q$ a point on the locus $y^2 = 8x$. The locus of mid point of $PQ$ is:

If $C$ is the mid point of $AB$ and $P$ is any point outside $AB$, then :

Let $\alpha$ and $\beta$ be the distinct roots of $ax^2 + bx + c = 0$ , then $\displaystyle \lim_{x \to\alpha} \frac{1- \cos \left(ax^{2} + bx + c\right)}{\left(x-\alpha\right)^{2}} $ is equal to

The value of $a$ for which the sum of the squares of the roots of the equation $x^2 - (a - 2) x - a - 1 = 0$ assume the least value is

If in a frequency distribution, the mean and median are $21 $ and $22$ respectively, then its mode is approximately

$\displaystyle \lim_{n \to\infty} \left[\frac{1}{n^{2}} \sec^{2} \frac{1}{n^{2}} + \frac{2}{n^{2}} \sec^{2} \frac{4}{n^{2}}.......... + \frac{1}{n}\sec^{2} 1 \right] $ equals

If $x$ is so small that $x^3$ and higher powers of $x$ may be neglected, then $\frac{\left(1+x\right)^{\frac{3}{2}} - \left(1+ \frac{1}{2}x\right)^{3}}{\left(1-x\right)^{\frac{1}{2}}} $ may be approximated as

A real valued function $f (x) $.Satisfies the functional equation $f(x- y) =f (x) f(y)-f(a-x) f(a+y)$ where a is a given constant and $f(0) = 1$. Then $f(2a - x)$ is equal to

$A$ and$ B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is contained with them. The resultant of $A$ and $B$ after combining is displaced through a distance :

Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on the set $A = \{1, 2, 3, 4\}$. The relation R is

If $a_1, a_2, a_3,......, a_n $,.... are in G.P., then the value of the determinant $\begin{vmatrix}\log a_{n}& \log a_{n+1}&\log a_{n+2}\\ \log a_{n+3}& \log a_{n+4}&\log a_{n+5}\\ \log a_{n+6} &\log a_{n+7}& \log a_{n+8}\end{vmatrix} $, is

If $(1 - p)$ is a root of quadratic equation $x^2 + px + (1- p) = 0$, then its roots are

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is

If $\displaystyle\lim_{x \to\infty} \left(1+ \frac{a}{x} + \frac{b}{x^{2}}\right)^{2x} = e^{2} $ , then the values of a and b, are

The range of the function $f\left(x\right) = ^{7-x}P_{x-3}$ is

The coefficient of the middle term in the binomial expansion in powers of x of $(1+ \alpha x)^4$ and of $ (1 - \alpha x)^6$ is the same if $\alpha$ equals

The coefficient of $x^n$ in expansion of $(1+ x)(1- x)^n$ is

Let $A=\begin{pmatrix} 1&-1 &1 \\[0.3em] 2 &1 &-3 \\[0.3em] 1 &1&1 \end{pmatrix}$ and $\,10\,B=\begin{pmatrix} 4&2 &2 \\[0.3em] -5 &0 & \alpha \\[0.3em] 1 &-2&3 \end{pmatrix} $. If B is the inverse of A , then $\alpha$ is