List of top Questions asked in JEE Advanced- 2013

A particle of mass $M$ and positive charge $Q$, moving with a constant velocity $u _{1}=4 \hat{i}ms ^{-1}$, enters a region of uniform static magnetic field normal to the $x$-y plane. The region of the magnetic field extends from $x =$ 0 to $x = L$ for all values of $y$. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity $\vec{ u }_{2}=2(\sqrt{3} i +\hat{ j }) m / s ^{-1}$. The correct statement(s) is (are)

Let $\omega$ be a complex cube root of unity with $\omega \ne 0$ and $P = [P_{ii}] $ be an $n \times \, n$ matrix with $p_{ij} = \omega^{i+j}$ Then, $P^2 \ne 0$ when $n$ =

Two lines $L_1:x = 5\, \frac{y}{3-\alpha} = \frac{z}{-2}$ and $L_1:x = \alpha \, \frac{y}{-1} =\frac{z}{2-\alpha}$ are coplaner. Then, $\alpha$ can take value(s)

A line $l$ passing through the origin is perpendicular to the lines $ L_1 : (3+t) \widehat {i} +(1-2t) \widehat {j}+(4+2t)\widehat {k}, - \infty < t < \infty$ $ L_2 : (3+2s) \widehat {i} +(3+2s) \widehat {j}+(2+s)\widehat {k}, - \infty < s < \infty$ Then, the coordinate(s) of the point(s) on $l_2$ at a distance of $\sqrt 17$ from the point of intersection of l and $l_1$ is (are)

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}$ Then,the probability that the problem is solved correctly by at least one of them, is

A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is

The image of an object, formed by a plano-convex lens at a distance of $8\,m$ behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $\frac{2}{3}$ times the wavelength in free space. The radius of the curved surface of the lens is

A ray of light travelling in the direction $\frac{1}{2}(\hat{i}+\sqrt{3})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2}(\hat{i}-\sqrt{3} j)$. The angle of incidence is

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2 : 3$. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is $4 : 3$. The ratio of their densities is

In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$ the path difference (in terms of an integer $n$) corresponding to any point having half the peak intensity is

Using the expression 2d sin $\theta =\lambda,$ one calculates the values of d by measuring the corresponding angles $\theta$ in the range 0 to 90$^{\circ}$. The wavelength X is exactly known and the error in $\theta$ is constant for all values of $\theta$. As $\theta$ increases from 0$^{\circ}$

Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity $\kappa$ and the other $2 \,\kappa .$ The temperature difference between the ends along the $x$-axis is the same in both the configurations. It takes $9\, s$ to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is

Circle(s) touching X-axis at a distance 3 from the origin and having an intercept of length $2 \sqrt7$ on Y-axis is/are