Propostion & Theorem|| Deductive reasoning|| Axiom 1,2,3,4, Play fair axiom|| Incident axiom on line|| Equivalent Version OF fifth Postulate|| Some important term

Introduction To Euclid's Geometry - Axioms And Postulates|Euclid's Postulates|Theorem|Equivalent Versions Of Euclid's Fifth Postulate

Introduction|| Euclid's Definition|| Axioms & Postulate ||Elements axiom ||Examples -1,2,3,4,5.

Euclid's Fifth Postualte|Equivalent Versions Of Euclid's Fifth Postulate (1)|Equivalent Versions Of Euclid's Fifth Postulate (2)|NCERT Example |NCERT Exercise

Let R be the real line. Consider the following subsets of the plane RxxR . S""=""{(x ,""y)"":""y""=""x""+""1""a n d""0""<""x""<""2},""T""=""{(x ,""y)"":""x-y"" is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

Consider the binomial expansion of (sqrt(x)+(1/(2x^(1/4))))^n n in NN, where the terms of the expansion are written in decreasing powers of x. If the coefficients of the first three terms form an arithmetic progression then the statement(s) which hold good is(are) (A) total number of terms in the expansion of the binomial is 8 (B) number of terms in the expansion with integral power of x is 3 (C) there is no term in the expansion which is independent of x (D) fourth and fifth are the middle terms of the expansion