List of top Questions asked in JEE Advanced- 1998

Among the following compounds, the strongest acid is

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is

Susceptibility of a magnetic substance is found to depend on temperature and the strength of the magnetising field. The material is a

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2,5 and 7. The smallest value of n for which this is possible, is

Let $ [ \varepsilon_0 ] $ denote the dimensional formula of the permittivity of the vacuum and $ [ \mu_0 ] $ that of the permeability of the vacuum. If $M$ = mass, $L$ = length, $T$ = time and $I$ = electric current.

Let $f(x) = x - [x] $, for every real number x, where [x] is the integral part of x Then, $ \int^1_{-1} \, f ( x ) \, dx$ is

The value of $\displaystyle \sum_{k=1}^6 \bigg(\sin\frac{2\pi k}{7}-i \cos \frac{2\pi k}{7}\bigg)$ is

Highly pure dilute solution of sodium in liquid ammonia

A particle of mass m is executing oscillation about the origin on the x-axis. Its potential energy is $ U (x) = k [ x ]^ 3,$ where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

For the first order reaction,

If in a $\triangle$ PQR, sin P, sin Q, sin R are in AP, then

Two particles, each of mass m and charge q, are attached to the two ends of a light rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is

A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance r from its centre

A charge + q is fixed at each of the points $x = x_0,x=3x_0,x=5x_0...8$ on the x-axis and a charge - q is fixed at each of the points $x = 2x_0,x=4x_0,x=6x_0...,8$ Here, $x_0$ is a positive constant. Take the electric potential at a point due to a charge Q at a distance r from it to be $Q/4 p\varepsilon_0r.$ Then the potential at the origin due to the above system of charges is

A concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let O be the pole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water, the image will be

During the melting of a slab of ice at $273 \,K$ at atmospheric pressure

Let f (x) = min { x, $x^2$ } for every real number of x, then

11. A real image of a distant object is formed by a planoconvex lens on its principal axis. Spherical aberration

A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is

In a collage of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently, equals

A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence $45^\circ$. The ray undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible value (s) of n from the following

A new carbon-carbon bond formation is possible in

Which of the following statement (s) is (are) correct ?

Which of the following will undergo aldol condensation?