List of top Questions asked in JEE Advanced- 1993

Let [.] denote the greatest integer function and $f (x) = [\tan^2 x]$, then:

The value of $ \int^{ \pi / 2}_0 \frac{ dx }{ 1 + \tan^3 \, x } \, is \, $

A current I flows along the length of an infinitely long, straight, thin-walled pipe. Then

Read the following statements carefully Y : The resistivity of semiconductor decreases with increase of temperature. Z : In a conducting solid, the rate of collisions between free electrons and ions increases with increase of temperature Select the correct statement (s) from the following

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless spring of spring constant k. A mass m hangs freely from the free end of the spring. The area of cross-section and the Young's modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to

A star initially has $10^{40}$ deuterons. It produces energy via the processes $_1H^2+_1H^2 \rightarrow _1H^3+p$ and $_1H^2+_1H^3 \rightarrow _2{He}^3+n$. If the average power radiated by the star is $10^{16}$ W, the deuteron supply of the star is exhausted in a time o f the order of $M(H)^2=2.014 \, amu;$ $M(n)=1.008 \, amu;$ $M(p)=1.007 \, amu;$ $M(He)^2=4.001 \, amu;$

Which one of the following has the smallest heat of hydrogenation per mole ?

The material used in solar cells contains

Let E and F be two independent events. If the probability that both E and F happen is 1/12 and the probability that neither E nor F happen is 1/2. Then,

Equal weights of ethane and hydrogen are mixed in an empty container at $25^\circ$ C. The fraction of the total pressure exerted by hydrogen is

The locus of the centre of a circle, which touches externally the circle $x^2 + y^2 -6 x - 6y + 14 = 0$ and also touches the Y-axis, is given by the equation

An unbiased die with faces marked $1, 2, 3, 4, 5$ and $6$ is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is

An ideal gas is taken from the state A (pressure p, volume V) to the state B (pressure p /2, volume 2 V) along a straight line path in the p-V diagram. Select the correct statements from the following

Two blocks A and B each of mass m, are connected by a massless spring of natural length Land spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in figure. A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B, and collides elastically with A. Then