List of top Mathematics Questions asked in AMUEEE

The only integral root of the equation $ \begin{vmatrix}2-y&2&3\\ 2&5-y&6\\ 3&4&10-y\end{vmatrix} =0 $ is

If $ y = sec(tan^{-1}x) $ , then $ \frac{dy}{dx} $ at $ x = 1 $ is

If $ f(x) = \frac{x}{2} -1 $ then on the interval $ [0,\pi] $

A polygon has $44$ diagonals. The number of its sides are

If origin is the centroid of a $ \Delta PQR $ with vertices $ P(2a,2,6),Q(-4,3b,- 10) $ and $ (8,14,2c) $ , then the value of $ a,b $ and $ c $ are respectively.

Given that the points $ P(3,2, - 4) $ , $ Q(5,4, - 6) $ and $ R(9,8,-10) $ are collinear, the ratio in which $ Q $ divides $ PR $ externally is

Consider the following propositions : p : I take medicine q : I can sleep Then, the compound statement $ \sim p \rightarrow \sim q $ means

If $ A $ and $ B $ are two square matrices such that $ AB $ = $ A $ and $ BA $ = $ B $ , then

The function $ f(x) = cos^2x $ is strictly decreasing on

If $ \begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix} $ is to be square root of the two rowed unit matrix, then $ \alpha $ , $ \beta $ and $ \gamma $ should statisfy the relation

The sum of two numbers is $10$. Their product will be maximum when they are

The maximum value of $ \frac{log x}{x} $ is

The value of the integral $ \int_{-2}^{0}\frac{dx}{\sqrt{12-x^{2}-4x}} $ is

The integral $ \int \sqrt{16-9x^2} $ $dx$ equals

The value of the integral $ \int_{0}^{1} $ $ \frac{e^{5log_{e}x}-e^{4log_{e}x}}{e^{log_{e}x^3}-e^{log_{e}x^2}}dx $ is

$ \int \frac{x^3dx}{1+x^4} $ equals

A line perpendicular to the line segment joining the points $ (1,0) $ and $ (2,3) $ divides it in the ratio $ 1 : n $ . The equation of the line is

Find the maximum value of $|z|$ when $\left|z-\frac{3}{2}\right|=2, z$ being a complex number.

Let  \(f(x) = \begin{cases} \frac{x^3+x^2-16x+20}{(x-2)^2} & if x \neq 2 \\ b & \text{if x = 2} \end{cases}\)  If \(f(x)\) is continuous for all \(x\) , then \(b\) is equal to

The number of equivalence relations on the set {1, 2, 3} containing (1, 2) and (2,1) is

Let $ A = \left\{x\in R; x\ge\frac{1}{2}\right\} $ and $ B = \left\{x\in R; x\ge\frac{3}{4}\right\} $ If $ f : A \rightarrow B $ is defined as $ f(x) = x^2 - x + 1 $ , then the solution set of the equation $ f(x) = f^{-1}(x) $ is

$ Let \,A = [a_{ij}]_{mxn} $ be a matrix such that $ a_{ij} = 1,\forall $ $ i,j. $ Then,

The set of values of $ x $ for which $ \frac{tan 3x - tan 2x}{1+ tan 3x\,tan2x} = 1 $ is

The complex number $ z = x + iy $ satisfy the equation $ |\frac {z-5i}{z+5i}| = 1 $ lies on

The equation of the curve satisfying the differential equation $ y(x+y^3)dx = x(y^3- x)dy $ and passing through the point $ (1, 1) $ is