List of practice Questions

The statement $(p \land (p \to q) \land (q \to r)) \to r$ is :
Let us consider a curve, $y = f(x)$ passing through the point $(-2, 2)$ and the slope of the tangent to the curve at any point $(x, f(x))$ is given by $f(x) + x f'(x) = x^2$. Then :
The distance of the point $(1, -2, 3)$ from the plane $x - y + z = 5$ measured parallel to a line, whose direction ratios are $2, 3, -6$ is :
A wire of length 20 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a regular hexagon. Then the length of the side (in meters) of the hexagon, so that the combined area of the square and the hexagon is minimum, is :
The number of \(f\) electrons in the ground state electronic configuration of Np (\(Z = 93\)) is _________. (Integer answer)
In Carius method for estimation of halogens, 0.2 g of an organic compound gave 0.188 g of $AgBr$. The percentage of bromine in the compound is _________. (Nearest integer)
[Atomic mass : $Ag = 108, Br = 80$]
The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to \(\frac{h^2}{x m a_0^2}\). The value of \(10x\) is _________. (\(a_0\) is radius of Bohr's orbit)
(Nearest integer)
[ Given : \(\pi = 3.14\) ]
The nature of oxides V\(_2\)O\(_3\) and CrO is indexed as 'X' and 'Y' type respectively. The correct set of X and Y is:
The gas 'A' is having very low reactivity reaches to stratosphere. It is non-toxic and non-flammable but dissociated by UV-radiations in stratosphere. The intermediates formed initially from the gas 'A' are:
Tyndall effect is more effectively shown by:
In which one of the following molecules strongest back donation of an electron pair from halide to boron is expected?
Which refining process is generally used in the purification of low melting metals ?
Deuterium resembles hydrogen in properties but :
The number of water molecules in gypsum, dead burnt plaster and plaster of Paris, respectively are :
In polythionic acid, H\(_2\)S\(_x\)O\(_6\) (x = 3 to 5) the oxidation state(s) of sulphur is/are :
A uniform conducting wire of length is 24a, and resistance R is wound up as a current carrying coil in the shape of an equilateral triangle of side 'a' and then in the form of a square of side 'a'. The coil is connected to a voltage source V\(_0\). The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is 1 : \(\sqrt{y}\) where y is _________.
A transmitting antenna has a height of 320 m and that of receiving antenna is 2000 m. The maximum distance between them for satisfactory communication in line of sight mode is 'd'. The value of 'd' is _________ km. (Radius of Earth = 6400 km)
The unit of the van der Waals gas equation parameter 'a' in \(\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT\) is:
If the velocity of a body related to displacement x is given by \(v = \sqrt{5000 + 24x}\) m/s, then the acceleration of the body is ________ m/s\(^2\).
In a photoelectric experiment, increasing the intensity of incident light :
A balloon carries a total load of 185 kg at normal pressure and temperature of 27°C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is -7°C. Assuming the volume constant ?
Two ions of masses 4 amu and 16 amu have charges +2e and +3e respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :
Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by :
Which of the following is not a dimensionless quantity ?
In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius \(2.0 \times 10^{-5}\) m and density \(1.2 \times 10^3\) kgm\(^{-3}\)? Take viscosity of liquid \(= 1.8 \times 10^{-5}\) Nsm\(^{-2}\). (Neglect buoyancy due to air).