List of top Questions asked in JEE Advanced- 2015

Suppose the gravitational force varies inversely as the nth power of distance. Then, the time period of a planet in circular orbit of radius R around the sun will be proportional to

For a simple pendulum, a graph is plotted between its Kinetic Energy (KE) and Potential Energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)

Planck's constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is(are)

The sum of first 9 terms of the series $ \frac{1^3}{1} + \frac{1^3+2^3}{1+3} + \frac{1^3+2^3+3^3}{1+3+5} +...$ is

In an aluminum $(Al)$ bar of square cross section, a square hole is drilled and is filled with iron $(Fe)$ as shown in the figure. The electrical resistivities of $Al$ and Fe are $2.7 ? 10^{-8 }\, \Omega m$ and $1.0 ? 10^{-7}\, \Omega m$, respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $?_1$ and $?_2$ and have total energies $E_1$ and $E_2$, respectively. The variations of their momenta p with positions x are shown in the figures. If $\frac{a}{b} = n^{2}$ and $\frac{a}{R} = n, $ then the correct equation(s) is(are)

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density $\lambda$ are kept parallel to each other. In their resulting electric field, point charges $q$ and $-q$ are kept in equilibrium between them. The point charges are confined to move in the $x$ direction only. If they are given a small displacement about their equilibrium positions, then the correct statements(s) is(are)

Let $f\left(x\right) = sin\left(\frac{\pi}{6}sin\left(\frac{\pi}{2}sin\,x\right)\right)$ for all $x \in R$ and $g\left(x\right) = \frac{\pi}{2}$ $sin\, x$ for all $x \in R$. Let $(fog) (x)$ denote $f(g(x))$ and $(gof) (x)$ denote $g(f(x))$. Then which of the following is (are) true ?

Which of the following values of $\alpha$ satisfy the equation. $\begin{vmatrix}\left(1+\alpha\right)^{2}&\left(1+2\alpha \right)^{2}&\left(1+3\alpha \right)^{2}\\ \left(2+\alpha \right)^{2}&\left(2+2\alpha \right)^{2}&\left(2+3\alpha \right)^{2}\\ \left(3+\alpha \right)^{2}&\left(3+2\alpha \right)^{2}&\left(3+3\alpha \right)^{2}\end{vmatrix} = -648\alpha ?$

The %yield of ammonia as a function of time in the reaction $N_{2}\left(g\right) + 3H_{2}\left(g\right) {\rightleftharpoons} 2NH_{3}\left(g\right), ?H < 0$ at $\left(P, T_{1}\right)$ is given below. If this reaction is conducted at $\left(P, T_{2}\right)$, with $T_{2} > T_{1}$, the %yield of ammonia as a function of time isrepresented by -

Copper is purified by electrolytic refining of blister copper. The correct statement(s) about this process is (are) :

Let P and Q be distinct points on the parabola $y^2 = 2x$ such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle $?OPQ$ is $3\sqrt{2},$ then which of the following is (are) the coordinates of P ?

Two identical glass rods $S_1$ and $S_2$ (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod $S_1$ on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside $S_2$. The distance d is

A ring of mass M and radius R is rotating with angular speed ? about a fixed vertical axis passing through its centre O with two point masses each of mass $\frac{M}{8}$ at rest at O. These masses can moveradially outwards along two massless rods fixed on the ring as shown in the figure. At some instant theangular speed of the system is $\frac{8}{9} ?$ and one of the masses is at a distance of $\frac{3}{5} R$ from O. At this instant the distance of the other mass from O is

Let $y(x)$ be a solution of the differential equation $(1 + e^x)y' + ye^x = 1$. If $y(0) = 2$, then which of the following statements is (are) true ?

In $R^3$, consider the planes $P_1 : y = 0$ and $P_2 : x + z = 1$. Let $P_3$ be a plane, different from $P_1$ and $P_2$, which passes through the intersection of $P_1$ and $P_2$. If the distance of the point $(0, 1, 0)$ from $P_3$ is $1$ and the distance of a point $(\alpha, \beta, \gamma)$ from $P_3$ is $2$, then which of the following relations is (are) true ?

In $R^3$, Let $L$ be a straight line passing through the origin. Suppose that all the points on $L$ are at a constant distance from the two planes $P_1 : x + 2y - z + 1 = 0$ and $P_2 : 2x - y + z - 1 = 0$. Let $M$ be the locus of the feet of the perpendiculars drawn from the points on $L$ to the plane $P_1$. Which of the following points lie(s) on $M$ ?

Let $PQR$ be a triangle Let $\vec{a} = \overrightarrow{QR}, \, \vec{ b} = \overrightarrow{RP} and \vec{c} = \overrightarrow{PQ}$. If $\left|\vec{a}\right| = 12, \left|\vec{b}\right| = 4\sqrt{3}$ and $\vec{b}. \vec{c} = 24$, then which of the following is (are) true ?

Let $X$ and $Y$ be two arbitrary, $3 \times 3$, non-zero, skew-symmetric matrices and $Z$ be an arbitrary $3 \times 3$, nonzero, symmetric matrix. Then which of the following matrices is (are) skew symmetric ?

The area (in sq units) of the quadrilateral formed by the tangents at the end points of the latusrectum recta to the ellipse $\frac{x^2}{9} +\frac{y^2}{ 5}=1 is $

From a solid sphere of mass $M$ and radius $R$, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

$Fe^{3+}$ is reduced to $Fe^{2+}$ by using -

The correct statement(s) about $Cr^{2+}$ and $Mn^{3+}$ is (are) - [Atomic numbers of $Cr = 24$ and $Mn = 25$]

A conductor (shown in the figure) carrying constant current $I$ is kept in the $x-y$ plane in a uniform magnetic field $\vec{B}$. If $F$ is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is(are)

A rectangular loop of sides $10\, cm$ and $5\, cm$ carrying a current $I$ of $12 \,A$ is placed in different orientations as shown in the figures below,

If there is a uniform magnetic field of $0.3\, T$ in the positive $z$-direction in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?