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|`

State, whether the following statements are true of false. If a lt b , then a - c lt b - c

If a lt 0 and b lt 0 , then (a +b)^(2) gt 0 .

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 and b are negative real numbers and c is a positive real number, then which of the following is/are correct? 1. a-b lt a-c 2. If a lt b , then (a)/(c ) lt (b)/(c ) . 3. (1)/(b) lt (1)/(c ) Select the correct answer using the code given below.

If a and b are two negative integers such that a lt b " then " (1)/(a) gt (1)/(b) .

If (x-a) (x-b) lt 0 , then x lt a, and x gt b .

In which of the following cases, there exists a triangle ABC? (a) b sin A = a, A lt pi//2 (b) b sin A gt a, A gt pi//2 (c) b sin A gt a, A lt pi//2 (d) b sin A lt a, A lt pi//2, b gt a (e) b sin A lt a, A gt pi//2, b = a

In which of the following cases, there exists a triangle ABC? (a) b sin A = a, A lt pi//2 (b) b sin A gt a, A gt pi//2 (c) b sin A gt a, A lt pi//2 (d) b sin A lt a, A lt pi//2, b gt a (e) b sin A lt a, A gt pi//2, b = a

If f(x) = x (1 - log x), " where " x gt 0 , show that (a -b) log c = b (1 - logb) - a(1 - log a), " where " 0 lt a lt c lt b

Write increasing order of basic strength of following: (i). (a) F^(ɵ) , (b). Cl^(ɵ) , (c). Br^(ɵ) , (d). I^(ɵ) (A). a gt b gt c gt d (B). d lt a lt c lt b (C). d gt a gt b gt c (D). a gt d gt c gt b (ii). (a). CH_(3)^(ɵ) , (b). Cl^(ɵ) , (c) OH^(ɵ) , (d). F^(ɵ) (A). a gt b gt c gt d (B). d lt a lt c lt b (C). d gt a gt b gt c (D). a gt d gt c gt b (iii). (a). R-NH_(2) , (b). Ph-NH_(2) , (c). R-underset(O)underset(||)(C)-NH_(2) (A). a gt b gt c (B). a lt c lt b (C). a lt b lt c (D). a gt c gt b (iv). (a). NH_(3) , (b). MeNH_(2) , (c). Me_(2)NH , (d). Me_(2)N (A). a lt b lt c lt d (B). d lt a lt c lt b (C). d gt a gt b gt c (D). a gt d gt c gt b