List of top Questions asked in AIEEE

At two points P and Q on a screen in Young's double slit experiment, waves from slits $S_1$ and $S_2$ have a path difference of 0 and $\frac{\lambda}{4}$ respectively. The ratio of intensities at P and Q will be :

After absorbring a slowly moving neutron of Mass mN (momentum $\approx$ 0) a nucleus of mass M breaks into two nuclei of masses $m_1$ and $5m_1$ ($6\, m_1 = M + mN$ ) respectively. If the de Broglic wavelength of the nucleus with mass $m_1$ is $\lambda$, the de Broglie wevelength of the nucleus will be:

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect the angular speed of the disc

A metal rod of Young's modulus Y and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by t$^{\circ}$C, the linear stress developed in its is :

A mass $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $m$ and radius $R$. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the pulley, is

Let $\vec{a},\,\vec{b},\,\vec{c}$ be three non-zero vectors which are pairwise non-collinear. If $\vec{a}+3\vec{b}$ is collinear with $\vec{c}$ and $\vec{b}+2\vec{c}$ is collinear with $\vec{a}+3\vec{b}+\vec{c}$ is :

The curve that passes through the point (2, 3), and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact is given by :

Define $f(x)$ as the product of two real functions $f_1(x) = x, x \in$ R, and $f_2(x) =$ $ \begin{cases} sin \frac{1}{x} , & \text{If x $\ne $ 0} \\ 0, & \text{If x = 0} \end{cases}$ as follows : $f(x) = \begin{cases} f_1(x).f_2(x) , & \text{If x $\ne $ 0} \\ \quad 0, & \text{If x = 0} \end{cases}$ $f(x)$ is continuous on R. $f_1(x)$ and $f_2(x)$ are continuous on R.

Let [.] denote the greatest integer function then the value of $\int\limits^{1.5}_{0}x \left[x^{2}\right]$ dx is : .

If $\omega \ne 1$ is the complex cube root of unity and matrix $ H =\begin{bmatrix}\omega&0\\ 0&\omega\end{bmatrix}$, then $H^{70}$ is equal to -

Let f be a function defined by $f\left(x\right) = \left(x-1\right)^{2 }+ 1, \left(x \ge 1\right)$. The set $\left\{x : f\left(x\right) = f^{-1}\left(x\right)\right\} =\left\{ 1, 2\right\}$ f is a bijection and $ f^{-1}\left(x\right) = 1+\sqrt{x-1}, x \ge 1.$

The lines $x + y = | a |$ and $ax - y = 1$ intersect each other in the first quadrant. Then the set of all possible values of $a$ is the interval :

The coefficient of $x^7$ in the expansion of $(1- x - x^2 + x^3 )^6$ is

A man saves Rs. $200$ in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. $40$ more than the saving of immediately previous month. His total saving from the start of service will be Rs. $11040$ after

A gas absorbs a photon of $355 nm$ and emits at two wavelengths. If one of the emissions is at $680 nm$, the other is at:

A car is fitted with a convex side-view mirror of focal length $20 \,cm$. A second car $2.5\, m$ behind the first car is overtaking the first car at a relative speed of $15 \,m / s$. The speed of the image of the second car as seen in the mirror of the first one is

In a Young's double slit experiment, the two slits act as coherent sources of waves of equal amplitude A and wavelength $\lambda$. In another experiment with the same arrangement the two slits are made to act as incoherent sources of waves of same amplitude and wavelength. If the intensity at the middle point of the screen in the first case is $I_1$ and in the second case is $I_2$, then the ratio $\frac{I_{1}}{I_{2}} $ is :

A beaker contains water up to a height $h_1$ and kerosene of height $h_2$ above water so that the total height of (water + kerosene) is $(h_1 + h_2)$. Refractive index of water is $\mu_{1}$ and that of kerosene is $\mu_{2}$. The apparent shift in the position of the bottom of the beaker when viewed from above is :

The value of enthalpy change ($\Delta$H) for the reaction $C_{2}H_{5}OH_{\left(I\right)} + 3O_{2\left(g\right)} \to 2CO_{2\left(g\right)} + 3H_{2}O_{\left(I\right)}$ at $27^{\circ}C$ is $-1366.5 \,kJ \,mol^{-1}.$ The value of internal energy change for the above reaction at this temperature will be :

The correct order of electron gain enthalpy with negative sign of F, Cl, Br and I, having atomic number 9, 17, 35 and 53 respectively, is:

The molecular velocity of any gas is:

When r, P and M represent rate of diffusion, pressure and molecular mass, respectively, then the ratio of the rates of diffusion $(r_A/r_B)$ of two gases A and B, is given as:

Consider thiol anion $(RS^?)$ and alkoxy anion $(RO^?)$. Which of the following statements is correct ?

A 5.2 molal aqueous solution of methyl alcohol, $CH _{3} OH$ is supplied. What is the mole fraction of methyl alcohol in the solution?

Two longitudinal waves given by equations : $y_1 (x, t) = 2a$ sin ($\omega t - kx$) and $y_2 (x, t)$ = a sin ($2\omega t - 2kx$) will have equal intensity. Intensity of waves of given frequency in same medium is proportional to square of amplitude only.