List of top Questions asked in AIEEE

Percentage of free space in cubic close packed structure and in body centred packed structure are respectively

Let $z_1$ and $z_2$ be two distinct complex numbers and let $z = (1 - t) z_1 + tz_2$ for some real number t with $0 < t < 1$. If $arg (w) $ denotes the principal argument of a non-zero complex num ber w, then

If $\alpha$ and $\beta$ are the roots of the equation $x^{2} - x + 1 = 0$, then $\alpha^{2009} + \beta^{2009} =$

Gravitational acceleration on the surface of a planet is $\frac{ \sqrt{6}}{11}$ where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 1/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms$^{-1}$, the escape speed on the surface of the planet in kms$^{1}$ will be.

For two data sets, each of size $5$, the variances are given to be $4$ and $5$ and the corresponding means are given to be $2$ and $4$, respectively. The variance of the combined data set is

For a particular reversible reaction at temperature $T, \,\Delta H$ and $\Delta S$ were found to be both $+ve$. If $T_{e}$ is the temperature at equilibrium, the reaction would be spontaneous when

For a particle in uniform circular motion the acceleration $\vec{a}$ at a point $P\left(R,\,\theta\right)$ on the circle of radius $R$ is (here $\theta$ is measured from the x-axis)

Biuret test is not given by

A nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of light is $c$ The speed of daughter nuclei is

In the circuit shown below, the key $K$ is closed at $t = 0$. The current through the battery is

Two long parallel wires are at a distance $2d$ apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $'P'$ is such that it sweeps out a length $s = t^3 + 5$, where $s$ is in metres and $t$ is in seconds. The radius of the path is $20\, m$. The acceleration of $?P?$ when $t\, =\, 2\, s$ is nearly

Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}. The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}.$ If the four chosen numbers from an AP, then the set of all possible values of common difference is ${?1, ?2, ?3, ?4, ?5}.$

Let $S_{1} = \sum\limits^{10}_{j = 1}j\left(j-1\right) ^{10}C_{j} , S_{2} = \sum\limits^{10}_{j = 1}j ^{10}C_{j}$ and $S_{3} =\sum\limits^{10}_{j = 1}j^{2} \,^{10}C_{j}.$ $S_3 = 55 \times $2^9$$ $S_1 = 90 \times 2^8$ and $S_2 = 10 \times 2^8$.

The point $A(3, 1, 6)$ is the mirror image of the point $B(1, 3, 4)$ in the plane $x - y + z = 5$. The plane $x - y + z = 5$ bisects the line segment joining $A(3, 1, 6)$ and $B(1, 3, 4)$.

If two tangents drawn from a point P to the parabola $y^2 = 4x$ are at right angles, then the locus of P is

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

The area bounded by the curves $y =$ cos $x$ and $y=$ sin $x$ between the ordinates $x = 0$ and $x = \frac{3\pi}{2}$ is

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

Let $\vec{a} = \hat{j} - \hat{k}$ and $\vec{c} = \hat{i} - \hat{j} - \hat{k}$. Then vector $\vec{b}$ satisfying $\vec{a} \times\vec{b}+\vec{c} = \vec{0}$ and $\vec{a} \cdot\vec{b} = 3$ is

The equation of the tangent to the curve $y = x +\frac{4}{x^{2}}, $ that is parallel to the $x-axis$, 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) = $

A particle is moving with velocity $\vec{v} = k\left(y\hat{i} + x\hat{j}\right),$ where $k$ is a constant. The general equation for its path is