Question
Three statements are given, followed by three
conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All pages are diaries. Some diaries are books. All books are notebooks. Conclusions: I. No page is a notebook. II. All pages are notebooks. III. All diaries being notebooks is a possibility.Solution

If a + b + c = 12 and ab + bc + ca = 47, and a, b, c are real numbers, find the value of a³ + b³ + c³ − 3abc.
If a + `1/b` = 1 and b + `1/c` =1 , then the value of c + `1/a` is

A sum of Rs. 25,000 is invested in SIP 'G' which offers 7% p.a. simple interest for 7 years. The interest received from SIP 'G' is invested in SIP 'H' w...
If
= 2 then find In a best-of-two chess match between Player X and Player Y, the probability that Player X wins a game is (5/9), and the probability that Player Y loses ...
If 10x2 – 6xy+y² – 4x+4= 0, then find the value of (3x+2y).
If x 2  – 15x + 51 = 0, then determine the value of (x – 5) + {1/(x – 5)}.
For a =-4 and b = 5, value of a² – b² is: