number patterns 2

Factorisation of trinomials of the form x 2 +bx+c Trinomials are expressions with three terms. For example, x 2 + 14x + 49 is a trinomial. There is no single method by which all trinomials can be factorised. We need to study the pattern in trinomials and choose t..

>Here, a and b may be any numbers. Pascal's triangle The coefficients of various terms in (a+b) n for different values of n follows the pattern given below: General term For 0 < r < n, T r+1 in the expression of (a + b) n is given by T r+1 = n C r a n-r b r . (r + 1) t h t..

Let us consider the marks obtained by four students in Physics, Chemistry and Biology for the first unit test. We have represented the data in rows and columns. (i) Rows show the marks obtained by each student. (ii) The columns show the marks in Physics, Chemistry, Biology obtained by each student...

Which two numbers completes the pattern? => 23, 27 or 24, 26 or 23, 26 or 24, 25..

If Z 1 = a + ib and Z 2 = x + iy, then we define their sum as Z 1 + Z 2 = (a + ib) + (x + iy) = (a + x) + i(b + y) which is a complex number..

If A and B are two sets, we define their symmetric difference as the set of all elements that belong to A or to B, but not both A and B, and we denote it by A D B. Thu..

If Z 1 = a + ib and Z 2 = c + id are two complex numbers, then quotient is defined as ..

To insert n Harmonic Means between two given quantities. Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. ..

Question: Define an odd number. Answer: A number when divided by 2 gives remainder 1 is called an odd number..

Assume the validity of the result for n equal to some arbitrary but fixed natural number, say, ..