Duduli

A function given by f(x)=x³ is called the cube function. The domain and range of cube are both equal to R(i.e. f(x):R→R). Since, y=x³ is an odd function, so its graph is symmetrical about opposite quadrant, i.e., “origin”, shown as:

According to complementary principle the wave and particle aspects of matter and light are complementary rather than contradictory i.e both the aspects are necessary for complete picture of a system. It follows that the same experiment used for particle nature of matter also gives the wave nature of matter. Thus particle & wave nature of matter gives a complete description of the same system. Hence wave & particle nature of matter are complementary rather than contradictory.

A nuclear reaction is the process of strong interaction of a stable nucleus with suitable high energy elementary particle resulting in the formation of a new nucleus and one or more new particles.

Photoelectric cell is an arrangement which converts light energy into electrical energy. It is known as electric eye. Photo emissive cells are of two types (i) Vacuum type and (ii) Gas filled type.

Radiation consists of quantum of energy. Quantum of energy (packet of energy or quanta) is known as photon. photon is a particle. It possesses wave nature also. Rest mass of a Photon is zero.

Minimum energy in electron volts required to excite an electron from ground state to a higher state is called critical potential.

A relation f:A→B is said to be a function from A to B if (i) dom f = A (ii) No object of A has two or more different images in B.

Let A,B and C be three non-empty set. Let f:A→B and g:B→C be two functions. The composition of of f and g is a function from A to C such that gof(x) = g(f(x)) for every x € A.

It is the process in which a positron and an electron combine and their mass is transformed into the energy of gamma rays ( y- rays) is usually known as annihilation or pair annihilation. This is represented by (e^+) + (e^- ) → 2 y Where, e^+ = positron e^- = electron 

A relation R from a set A to a set B (R:A→B) is a subset of A×B . A relation R on a set A is defined to be any subset of A×A.

If S be a finite set consisting of n elements (say) then a composition(usually binary composition) * in S can be described by means of a table consisting of n rows & n columns in which the entry at the intersection of new headed by an element a € S is a*b . such tables are called composition tables. In order to verify group properties of a finite set under some binary operation, conveniently one can do this by the help of composition table.

The power set of a set A is denoted by p(A) and is defined by the set of all subsets of A. e.g if A = {1,2,3}, then   P(A)={∅,{1},{2},{3},{1,2},{2,3},{1,3},{1,2,3}}

A compound statement, which is always true for all possible assignment of truth values to its prime components, is called a Tautology.

A compound statement, which is always false for all possible assignment of truth values to its prime components, is called contradiction.

Let A be a matrix of order m×n .The kernel of a matrix A is the set of all vectors x € Vn such that Ax=O m×1.

When light of suitable wavelength falls on metal surface, then electrons are emitted from metal surface. These electrons are called photoelectrons.

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“Shift register is the logic circuit that can be used for the storage or transfer of data in the form of binary numbers. It is a sequential device which loads the data at the inputs & shift the data to the output once every clock cycle. Hence this device is named as shift register.” Figure 

The wavelength corresponding to maximum (λm) shifts towards shorter wavelengths as the temperature increases. The product of λm and absolute temperature (T) is constant.   I.e.   λmT=constant This  constant is called wien's constant.

According to this principle, quantum theory(i.e Bohr's theory) must give the same result as classical theory in the appropriate classical limit.

The Taylor's series method of solving differential equations numerically is restricted by the labour involved in finding the higher order derivatives. However there is a class of methods known as Runge-kutta methods which do not require the calculations of higher order derivatives and give greater accuracy. The Runge kutta formulae possess the advantage of requiring only the function values at some selected points. These methods agree with Taylor's series solution upto the term hⁿ when n differs from method and is called the order of that method.

These operations are called elementary row operations (i) Interchanging two rows. (ii) Multiplying a row by a non zero scalar. (iii) Adding to a row a scalar times another row.

The binary number system consists of only two digits. These 2 digits are 0 & 1 . The binary number system is known as base 2 system because it has 2 digits. The binary system is a place value system in which each binary digit has its own value expressed as a power or 2. The place to the left of binary point are positive powers of 2 and places to the right are negative power of 2. The term binary digit is known as bit. The left most binary digit is called the most significant bit(MSB) and the right most binary digit is called the least significant bit (LSB).

Packing fraction of a nucleus is defined as mass defect per nucleon of the nucleus. Thus,       Packing fraction = mass defect/A                                   = ∆m/A

Let V be a vector space over a field F, then, a non-empty subset W of V is called a vector subspace of V, if W is a vector space in its own right with respect to the addition and scalar multiplication compositions on V, restricted only on points of W. In an arbitrary vector space V, the sets {0} and V are clearly subspaces of V and are known as trivial sub-spaces.

The output of x-nor gate is in state 1 only when it's two inputs are at the same states with respect to each other. X-NOR gate is also known as exclusive nor gate or E-NOR gate. It is a digital logic gate which is the reverse or complementary or inverse form of xor gate. X-NOR gate is the combination of xor and not gate. The logic symbol for x-nor gate is shown in the figure

Let A be a square matrix of order n, then the values of λ for which the equation       Ax=λx   has non-trival solutions are called the eigen values of A. If  λ  is an eigen value, then the non-zero vectors x for which the equation Ax= λ x holds, are called the eigen vectors of A. ★ Eigen values are also called characteristics values or proper values. Eigen vectors are also called characteristics vectors or proper vectors.

It is also known as “external or auxiliary memory ”. It stores data & programms permanently. Hence it is non-volatile in nature i.e it retains its contents even when computer is switched off. It has much large capacity (usually in Gigabytes) & much cheaper than primary memory e.g pendrives, floppy disc, hard disc , magnetic tapes, magnetic drams etc.

The stack is a group of memory locations in the Read/Write memory which is used for the temporary storage of binary information (bytes) during the execution of a program. The starting memory location of the stack is defined in the main program and space is reserved usually at the high end of the memory map.

A decoder is a combinational logic circuit which converts N-bit binary input code into M output lines in such a way that one output is active for each input. The symbolic diagram of a decoder with N inputs and M outputs is shown in the figure

A function f:X→Y is said to be a one-one or injective function if for every x1,x2 belongs to X , f(x1)=f(x2) that implies x1=x2. e.g    f(x)=2x  is a one one function