A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of \( 60^\circ \) by a force of 10 N parallel to the inclined surface. When the block is pushed up by 10 m along the inclined surface, the work done against frictional force is:
[Given: \( g = 10 \) m/s\( ^2 \), \( \mu_s = 0.1 \)]
A gas can be taken from A to B via two different processes ACB and ADB. When path ACB is used, \( 60 J \) of heat flows into the system and \( 30 J \) of work is done by the system. If path ADB is used, the work done by the system is \( 10 J \). The heat flow into the system in path ADB is:
Let \( A = \{-3, -2, -1, 0, 1, 2, 3\} \). A relation \( R \) is defined such that \( xRy \) if \( y = \max(x, 1) \). The number of elements required to make it reflexive is \( l \), the number of elements required to make it symmetric is \( m \), and the number of elements in the relation \( R \) is \( n \). Then the value of \( l + m + n \) is equal to:
For hydrogen-like species, which of the following graphs provides the most appropriate representation of \( E \) vs \( Z \) plot for a constant \( n \)?
[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]
The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is $ 4 \_\_\_\_\_$.
Minerals are the naturally occurring, homogeneous inorganic solid substances. They are having a definite chemical composition and crystalline structure, hardness and color. For example, copper pyrite, calamine, etc.
Impurities in an ore are called gauge. The removal of a gauge from the ore is called concentration ore.
Several steps are involved in the extraction of pure metal from ores. Major steps are as follows –