If `|a x^2+b x+c|lt=1` for all `x` in [0, 1], then `|a|lt=8` b. `|b|>8` c. `|c|lt=2` d. `|a|+|b|+|c|lt=19`

If a gt b, " then " (a)/(c) lt (b)/(c) for all a, b and c in R , where c lt 0 . (True /False)

If A + B gt C + D and D + A lt B + C , then

If the point (a,a) lie between the lines |x+y|=2 , then which of the following is correct ? (A) |a| lt 2 (B) |a| lt sqrt(2) (C) |a| lt 1 (D) |a| lt 1/sqrt(2)

If alpha, beta be the roots of 4x^(2) - 16x + c = 0, c in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 , then the number of integral values of c is

Which is the following is always true ? (a) If a lt b, " then " a^2 lt b^2 (b ) If a lt b "then " 1/a gt 1/b ( c) If a lt b , " then " |a| lt |b|

If f'[x) exists for all points in [a,b] and (f(c ) -f(a))/(c-a) =(f(b)-f( c))/(b-c) where a lt c lt b , then there is a number l such that a lt l lt b and f''(l)=0

If x = sum_(n=0)^(oo) a^(n), y=sum_(n=0)^(oo) b^(n), z = sum_(n=0)^(oo) C^(n) where a,b,c are in A.P. and |a| lt 1, |b| lt 1, |c| lt 1 , then x,y,z are in