JEE Advanced 2015 Question Paper

One mole of a monoatomic real gas satisfied the equation p(V− b) = RT where b is a constant. Therelationship of interatomic potential V(r) and interatomic distance r for the gas is given by -

The correct statement(s) regarding, (i) HClO, (ii) HClO2, (iii) HClO3 and (iv) HClO4, is(are)

Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain termination, respectively, are

In the following reactions, the major product W is :

In the following reactions, the product S is -

Consider the hyperbola H : x2 − y2 = 1 and a circle S with center N(x2, 0). Suppose that H and S touch each other at a point P(x1, y1) with x1 > 1 and y1 > 0. The common tangent to H and S at P intersects the x-axis at point M. If (l, m) is the centroid of the triangle ᐃPMN, then the correct expression (s) is(are)

Let P and Q be distinct points on the parabola y2 = 2x such that a circle with PQ as diameter passesthrough the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle ᐃOPQis 3√2, then which of the following is(are) the coordinates of P ?

Consider the family of all circles whose centers lie on the straight line y = x. If this family of circles is represented by the differential equation Py″ + Qy′ + 1 = 0, where P,Q are functions of x,y and y′ (here y′ = ), then which of the following statements is (are) true ?

Let y(x) be a solution of the differential equation (1 + ex)y′ + yex = 1. If y(0) = 2, then which ofthe following statements is(are) true ?

The option(s) with the values of a and L that satisfy the following equation is(are) = L ?

Two identical glass rods S1 and S2 (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 S1 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 S2. The distance d is :

A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivity (ε1 = 2 and ε2 = 4) are introduced between the two plates as shown in the figure, the capacitance becomes C2. The ratio is :-

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

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shownin the figure). Initially the gas is at temperature T1, pressure P1 and volume V1 and the spring is inits relaxed state. The gas is then heated very slowly to temperature T2, pressure P2 and volume V2.During this process the piston moves out by a distance x. Ignoring the friction between the pistonand the cylinder, the correct statement(s) is(are) :-