List of top Questions asked in AMUEEE

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

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

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

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

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

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

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

Starting from origin, a body moves along $ x $ -axis. Its velocity at any time is given by $ v = 4t^3 - 2t \,m/s $ Acceleration of the particle when it is $ 2 \,m $ away from the origin is

The expression of the trajectory of a projectile is given as $ y = px - qx^2 $ , where $ y $ and $ x $ are respectively the vertical and horizontal displacements and $ p $ and $ q $ are constants. The time of flight of the projectile is

The displacement $ x $ of a body varies with time as $ x = -\frac{1}{3} t^2 + 16 t +2 $ , where $ x $ is in metres and $t$ is in seconds. The time taken by the body to come to rest is

A drunkard walking in a narrow lane takes $ 5 $ steps forward and $ 3 $ steps backward followed again by $ 5 $ steps forward and $ 3 $ steps backward and so on. Each step is lm long and requires Is. Determine how long the drunkard takes to fall in a pit $ 13 \,m $ away from the starting point?

Mention the catalyst and reaction condition in the given reaction

The following reaction $ R - Cl + NaI {->[{\text{Acetone}}]} R - I + NaCl $ is known as

Which of the following is aromatic compounds?

Nylon $ 6 $ is obtained by the condensation of

$ p $ -Hydroxyazobenzene is

Which one of the following compounds can exists in Zwitter ionic form?

The carbocation formed in $ S_N1 $ reaction of alkyl halide in the slow step is:

The $pH$ of a solution obtained by mixing of $100\, mL$ of a $HCl$ solution of $pH = 2$ with $400\, mL$ of another $HCl$ solution of $pH = 3$ will be

The reduced volume and reduced temperature of a gas are $10.2$ and $0.7$ respectively. If its critical pressure is $4.25\, atm$ then its pressure will be