If \[a,\ b,\ c\]are the sides of a triangle ABC, then which of the fol – McqOptions

MCQOPTIONS

1.	If \[a,\ b,\ c\]are the sides of a triangle ABC, then which of the following inequalities is not true [Kurukshetra CEE 1996]
A.	\[8abc\le (a+b)(b+c)(c+a)\]
B.	\[3abc\le {{a}^{3}}+{{b}^{3}}+{{c}^{3}}\]
C.	\[6abc\le bc(b+c)+ca(c+a)+ab(a+b)\]
D.	\[abc\le (a+b-c)(b+c-a)(c+a-b)\]
Answer» E.

Discussion

No Comment Found

Related MCQs

In a \[\Delta ABC,\]if \[3a=b+c,\]then the value of \[\cot \frac{B}{2}\cot \frac{C}{2}\] is [Pb. CET 2003; Roorkee 1986; MP PET 1990, 97, 98, 2003; EAMCET 2003; Orissa JEE 2005]
If the two angle on the base of a triangle are \[{{\left( 22\frac{1}{2} \right)}^{o}}\] and \[{{\left( 112\frac{1}{2} \right)}^{o}}\], then the ratio of the height of the triangle to the length of the base is [MP PET 1993; Pb CET 2002]
In triangle \[ABC\]if \[\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}\], then the triangle is [Karnataka 1991; Pb. CET 1989]
If a,b are different values of \[x\] satisfying \[a\cos x+b\sin x=c,\] then \[\tan \text{ }\left( \frac{\alpha +\beta }{2} \right)=\] [EAMCET 1986; Orissa JEE 2003]
In a triangle \[ABC\], \[\tan \frac{A}{2}=\frac{5}{6}\] and \[\tan \frac{C}{2}=\frac{2}{5},\] then[EAMCET 1994]
\[\Delta ABC,\] if \[\cos \frac{A}{2}=\sqrt{\frac{b+c}{2c}}\], then [MP PET 1990]
\[\frac{a\cos A+b\cos B+c\cos C}{a+b+c}=\] [Orissa JEE 2004]
If \[\sin 2x+\sin 4x=2\sin 3x,\]then \[x\]= [EAMCET 1989]
If \[\sec 4\theta -\sec 2\theta =2\], then the general value of \[\theta \] is [IIT 1963]
The general solution of \[a\cos x+b\sin x=c,\] where\[a,\,\,b,\,\,c\] are constants