List of top Mathematics Questions asked in AIEEE

Let $A=\begin{vmatrix} 5& 5\alpha & \alpha \\[0.3em] 0 &\alpha &5\alpha \\[0.3em] 0 &0& 5 \end{vmatrix}$ , If $\left|\,A^2\,\right|=25$,then $\left|\,\alpha\,\right|$ equals

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB (= a)$ subtends an angle of $60^\circ$ at the foot of the tower, and the angle of elevation of the top of the tower from $A$ or $B$ is $30^??. The height of the tower is

Consider a family of circles which are passing through the point (-1, 1) and are tangent to xaxis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

The set $S=\left\{1, 2, 3, \dots, 12\right\}$ is to be partitioned into three sets $A, B, C$ of equal size. Thus, $A\cup B\cup C=S, A\cap B = B\cap C = A \cap C=\phi.$ The number of ways to partition $S$ is

The largest interval lying in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ for which the function $f \left(x\right)=4^{-x^2}+cos^{-1}\left(\frac{x}{2}-1\right)+log\left(cos\,x\right)$ is defined, is

If $sin^{-1}\left(\frac{x}{5}\right)+cos\,ec^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2} $ then a value of $x$ is

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

In the binomial expansion of $(a - b)^n, n \geq 5,$ a the sum of $5^{th}$ and $6^{th}$ terms is zero, then $\frac{a}{b}$ equals

The sum of the series ${^{20}C_0} - {^{20}C_1} + {^{20}C_2} - {^{20}C_3} + ..... - .... + {^{20}C_{10}}$ is

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is

If one of the lines of $my^2 + (1 - m^2)xy - mx^2 = 0$ is a bisector of the angle between the lines $xy = 0$, then $m$ is

Let W denote the words in the English dictionary. Define the relation $R $ by : $R =\{ (x,y), \in\, W \times \,W$ : the words $x$ and $y$ have at least one letter in commona$\}$ Then R is

LetC be the circle with centre (0, 0)and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of $\frac{2 \pi}{3}$ at its centre, is :

If the expansion in powers of $x$ of the function $\frac{1}{\left(1-ax\right)\left(1-bx\right)}$ is $a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+ ..... ,$ then $a_n$ is :

Suppose a population $A$ has 100 observations $101, 102,..., 200 $ and another population $B$ has $ 100$ observations $151, 152, ..., 250.$ If $V_A$ and $V_B$ represent the variances of the two population respectively, then $\frac{V_{A}}{V_{B}}$ is :

$\int\limits^{-\pi/2}_{{-3\pi/2}}$$\left[\left(x+\pi\right)^{3}+cos^{2} \left(x+3\pi\right)\right]dx$ is equal to :

All the values of m for which both roots of the equation $x^{2}-2mx+m^{2}-1=0$ are greater than -2but less than 4 lie in the interval :

any three vectors such that $\vec{a}\cdot\vec{b} \ne 0, \vec{b}\cdot\vec{c} \ne 0,$ then $\vec{a}$ and $\vec{c}$ are :

The value of the integral $I=\int\limits^{6}_{{3}}$$\frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}}dx$ is :

The value of $\displaystyle \sum_{k=1}^{10}$$\left(sin\, \frac{2k\pi}{11}+i\,cos\, \frac{2k\pi}{11}\right)$ is :

If $A$ and fl are square matrices of size $n \times n$ such that $A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$, then which of the following will be always true ?

If x is real, the maximum value of $\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}$ is

$A B C$ is a triangle, right angled at $A .$ The resultant of the forces acting along $\overline{A B}, \overline{B C}$ with magnitudes $\frac{1}{A B}$ and $\frac{1}{A C}$ respectively is the force along $\overline{A D},$ where $D$ is the foot of the perpendicular from $A$ onto $B C$. The magnitude of the resultant is

If the coefficient of $x^7$ in $\left[ ax^2 + (\frac{1}{bx} ) \right]^{11}$ equals the coefficient of $x^{-7}$ in $\left[ax - \left(\frac{1}{bx^{2}}\right)\right]^{11}$ , then a and b satisfy the relation