List of top Questions asked in AMUEEE

If $ x, y $ and $ z $ are all different and $ \begin{vmatrix}x&x^{2}&1+x^{3}\\ y&y^{2}&1+y^{3}\\ z&z^{2}&1+z^{3}\end{vmatrix}=0 $ then

Let the straight line $ x = b $ divide the area enclosed by $ y = (1 - x)^2 $ , $ y = 0 $ and $ x = 0 $ into two parts $ R_1(0 \le x \le b) $ and $ R_2(b \le x \le 1) $ such that $ R_1-R_2 = \frac {1}{4}. $ Then, $b$ equals

If $ \alpha,\beta $ are the roots of the equation $ ax^2+bx+c = 0 $ and $ S_n = \alpha^n + \beta^n, $ then a $ S_{n+1} + bS_{n} + cS_{n-1} $ is equal to

Let, $\vec {a} = - \hat {i} - \hat {k}, \vec {b} = - \hat {i} +\hat {j} $ and $\vec {c} = \hat {i}+2\hat {j}+3\hat {k} $ be three given vectors. If $\vec {r} $ is a vector such that $ \vec {r} \times \vec {b} = \vec {c} \times \vec{b} $ and $\vec {r} \cdot \vec{a} = 0 $ , then the value of $\vec {r} \cdot \vec {b} $ is

If $ \int_{0}^{\frac{\pi}{3}}\frac{cos x}{3 + 4 sin x}dx = k\, log \left(\frac{3+2\sqrt{3}}{3}\right) $ then $k$ is

Arrange the following materials in the increasing order of their resistivity. Copper, Platinum, Silver, Aluminium

In a given circuit, each cell has an emf of $0.15\, V$ and internal resistance of $0.25 \, \Omega $ . Find the current in the circuit.

An exothermic chemical reaction proceeds by two stages. Reactants ${ ->[Stage\, 1] }$ Intermediate ${ ->[Stage\, 2] }$ Products The activation energy of state $I$ is $50 \,kJ$ $mol^{-1}$. The overall enthalpy change for the reaction is $-100 \,kJ$ $mol^{-1}$. Which diagram could represent the energy level diagram for the reaction?

Figure shows three particles with charges $q_{1}=2 Q, q_{2}=-2 Q$ and $q_{3}=-4 Q$, each a distance $d$ from the origin. Find the net electric field $\vec{E}$ at the origin.

In Millikans experiment, an oil drop of radius $1.64$ am and density $0.85\, g / cm ^{3}$ is suspended when a downward electric field of $1.9 \times 10^{5} \,N / C$ is applied. What is the charge on the drop in terms of $e$ ?

A uniformly charged conducting sphere of diameter $1.2 \,m$ has a surface charge density of $8.1 \,\mu C / m ^{2}$. Find the total electric flux leaving the surface of the sphere.

If three-digit numbers $ A28, 3B9 $ and $ 62C $ , where $ A, B $ and $ C $ are integers between $ 0 $ and $ 9 $ , are divisible by a fixed integer $ k $ , then the determinant $ \begin{vmatrix}A&3&6\\ 8&9&C\\ 2&B&2\end{vmatrix} $ is

If $ A = \begin{bmatrix}2&3\\ 5&-2\end{bmatrix} $ be such that $ A^{-1} = kA, $ then $ k $ is equal to

The existence of the unique solution of the system of equations $ x + y + z = \beta $ $ 5x - y + az = 10 $ $ 2x + 3y - z = 6 $ depends on

28 g of $ {{N}_{2}} $ and $6\,g$ of $ {{H}_{2}} $ were mixed. At equilibrium, $17\,g$ $ N{{H}_{3}} $ was produced. The weights of $ {{N}_{2}} $ and $ {{H}_{2}} $ at equilibrium are respectively

A gaseous mixture containing $He,\, CH _{4}$ and $SO _{2}$ was allowed to effuse through a fine hole then find what molar ratio of gases coming out initially? (Given mixture contains $He,\, CH _{4}$ and $SO _{2}$ in $1: 2: 3$ mole ratio $)$.

Which one is least reactive towards nucleophilic substitution reaction?

Set $ A $ and $ B $ have $ 3 $ and $ 6 $ elements respectively. What can be the minimum number of elements in $ A \cup B $ ?

Plants can be made disease resistant through

Which of the following types of $RNA$ act as adapter molecule

Which of the following values is the correct order of nuclear density?

Which of the following are not eukaryotes?

Which of the following are not ureotelic?

Which is the least stable carbocation? I. $ CH_{3}CH_{2} \overset{+}{C}H_{2} $ II. $ CH_{3}\overset{+}{C}HCH_{3} $ III. $(CH_{3})_{4} \overset{+}{C} $ VI. $ (CH_{3})_{3} C \overset{+}{C}H_{2} $

What will be the product/s if benzal chloride is heated with a concentrated aqueous $ KOH $ solution?