List of top Mathematics Questions asked in AIEEE

Solution of the differential equation $cos\, x\, dy = y(sin\, x - y) dx,\, 0 < x < \frac{\pi}{2}$ is

A person is to count $4500$ currency notes. Let an denote the number of notes he counts in the nth minute. If $a_1 = a_2 = ...... = a_{10} = 150$ and $a_{10}, a_{11}, ......$ are in $A.P.$ with common difference $-2,$ then the time taken by him to count all notes is

Let $f : R \to R$ be a positive increasing function with $\displaystyle \lim_{x \to \infty} \frac{f\left(3x\right)}{f\left(x\right)} =1$ Then $\displaystyle \lim_{x \to\infty} \frac{f\left(2x\right)}{f\left(x\right)} = $

If the vectors $\vec{a} = \hat{i}- \hat{j}+2 \hat{k}, \vec{b} = 2\hat{i}+4 \hat{j}+ \hat{k}$ and $\vec{c} = \lambda\hat{i}+ \hat{j}+\mu \hat{k}$ are mutually orthogonal, then $\left(\lambda, \mu\right) = $

For real $x,$ let $f (x) = x^3 + 5x + 1,$ then

Let $A$ be a $2 \times 2$ matrix Statement-1 : adj (adj A) $= A$ Statement-2 : $|adj \,A| = |A|$

The shortest distance between the line $y-x=1$ and the curve $x = y^2$ is

The set representing the correct order of ionic radius is :

The ellipse $x^2 + 4y^2 = 4$ is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point $(4, 0)$. Then the equation of the ellipse is

The sum to the infinity of the series $1+\frac{2}{3}+\frac{6}{3^{2}}+\frac{10}{3^{3}}+\frac{10}{3^{3}}+\frac{14}{3^{4}}+......$ is

The number of $3 \times 3$ non-singular matrices with four entries as $1$ and all other entries as $0$ is

The area of the region bounded by the parabola $(y-2)^2=x-1$ , the tangent to the parabola at the point $(2, 3)$ and the $x$-axis is

: The variance of first $n$ even natural numbers is $\frac{n^{2}-1}{4}$ : The sum of first $n$ natural numbers is $\frac{n\left(n+1\right)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n\left(n+1\right)\left(2n+1\right)}{6}$

One ticket is selected at random from $50$ tickets numbered $00, 01, 02, ??, 49$. Then the probability that the sum of the digits on the selected ticket is $8$, given that the product of these digits is zero, equals

Let $A$ and $B$ denote the statements $A: cos\,\alpha + cos\,\beta + cos \,\gamma = 0$ $B: sin \alpha + sin\, \beta + sin\,\gamma = 0$ If $cos\left(\beta-\gamma\right)+cos\left(\gamma-\alpha\right)+cos\left(\alpha-\beta\right)=-\frac{3}{2}$, then

Given $P(x) = x^4 + ax^3 + bx^2 + cx + d$ such that $x = 0$ is the only real root of $P'(x) = 0$ . If $P(-1) < P(1)$ , then in the interval $[-1, 1]$

If $\left|Z-\frac{4}{z}\right|=2$, then the maximum value of $\left|Z\right|$ is equal to

Three distinct points $A, B$ and $C$ are given in the $2$ - dimensional coordinate plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $( - 1, 0)$ is equal to $\frac{1}{3}$. Then the circumcentre of the triangle $ABC$ is at the point

If P and Q are the points of intersection of the circles $x^2 + y^2 + 3x + 7y + 2p - 5 = 0$ and $x^2 + y^2 + 2x + 2y - p^2 = 0$ , then there is a circle passing through $P, Q$ and $(1, 1)$ for

The projections of a vector on the three coordinate axis are $6, - 3, 2$ respectively. The direction cosines of the vector are

In a binomial distribution $B\left(n. p=\frac{1}{4}\right)$, if the probability of at least one success is greater than or equal to $\frac{9}{10}$, then n is greater than

If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ , then

If $\vec{u}, \vec{v}, \vec{w}$ are non-coplanar vectors and $p, q$ are real numbers, then the equality $\left[3\vec{u}\, p\vec{v}\,p\vec{w}\right]-\left[p\vec{v}\,\vec{w}\,q\vec{u}\right]-\left[2\vec{w}\,q\vec{v}\,q\vec{u}\right]=0$ holds for

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

The differential equation which represents the family of curves $y=c_1e^{c_2x}$, where $c_1$ and $c_2$ are arbitrary constants is